FLuID DYNAMICS IN MAGMA CHAMBERS WITH

APPLICATION TO SULPHIDE SETTLïNG

A thesis submitted in conformity with the requuements for the degree of

MASTER OF SCIENCE

Graduate Department of Geology

University of Toronto

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muid Dynamia in Magma Chambers with Application to Sulphide Settling

Master of Science 2000

Dorota El-Rassi Graduate Department of Geology

University of Toronto

ABSTRACT

Expetiments involving mica particles and a glycerol-water mixture were designed to

study the mechanisms of sulphide settling and to determine the location of the settled

sulphides with respect to the chamber geometry. In addition, the influence of the

injection of different masses of fluid into an existing charnber on the dready established

pattern of settling has been investigated.

The results suggest that convective flow in a high viscosity environment enhances

settling of the sulphides. The largest accumulation of particles occurs directly above the

heat source caused by a shear force exerted dong the floor, increase in the vertical

boundary thickness or downflow of the injecteci denser fluid that transports the particles

away fiom the walls. The experiment confinneci thet the sedimentation pattern is

influenced by viscosity.

Since a portion of the particles concentrateci et the interface between convection cells,

accumulations of the dissemuiated sulphides might be found throughout an intrusion.

ACKNO WLEDGMENTS

1 wish to thank profcsson A.J. Naldrett and DeBaines for their guidance and helpful

revisions during the course of the writing of this thesis.

During the two years of my study, 1 have received a helping hand fkom many of my

fiiends and colleagues in the Mechanical and Industrial Department, University of

Toronto. 1 am particularly gratefùl for the assistance given by N. 2. Mehdizadeh, who

kindly helped me with tPking the images for the research and A. Collins for reviewing

parts of the manuscript.

Finally, 1 would like to express gratitude to my husband B. El-Rassi for constant support

and understanding.

iii

3.2. FLUID INJECTiON .............................................................................................................. 1 0 0 .................................................................................................... 3.2.1. Experimenta f Method 100

3.2.2. Res11Its .......................................................................................................................... 102 3.2.21. injection of lcss h fl uid. .................................................................................................... 102 3.223. Injection of slightly dumz fluid ............................................................................................... 1 2 3.2.2.3. injection of significautiy daiacr fiuid containhg mica particles .......................................... 1 5

TABLE OF SYMBOLS

a - diameter of crystal in magma

C - concentration of particles

C, - specific heat capacity

d - diameter of entrance into magma chamber, or dyke thickmss

D - chemical diffisivity of the light component in binary magma

g - gravity

h - height of fluid

ho - height of fountains hi - height of rise

hm - depth of magma chamber

H - length of the chamber-country rock contact

k - thermal conductivity

Ke - fiacture toughness

1 - length

L - latent heat of crystallization

Le - Lewis number

Nw - cumpositiod Nusselt number

NuT - thermai Nusselt number

PE - elastic stress

Pf - hcture extension

Ph - hydrostatic pressure

Pr - Prandtl number

P,, - viscous pressure drop

q - heat flux Q - ffow rate of the magma

R - Rayleigh number based on the imposed heat flux at the chamber wail

Ra - Rayleigh number

Re - Reynold's number

t - time T - temperature

Ti - initial temperature of experimental fluid T, - initial temperature of the surroundings

ATi - initial difference b e m n the temperatures of aperimental fluid and sumwndings,

CITq - averaged temperature difference between experimental fluid and surroundings,

v, - settling velocity

w - thickness (fkacture, dyke)

W - maximum convection velocity

W, - averaged convection velocity

WC - cdculated convection velocity

Vr - Volume of the experimental fluid

a - thennsl expansion coefficient

- compositional expansion coefficient

& - compositional boundary layer tbickness

& - thermai boundary layer thiciutess

q - vîscosity of magma

KT - thermal diffbsivity in magma

A - viscosity controst (ratio of a maximum to minimum magma chamber viscosities)

p - shear modulus Api - density difference between the

v - kinematic viscosity magma and host rock.

pc - density of crystal in magma vo - Poisson ratio

Apo - density dwerence between hon pp - density of particies

magma and the new magma entering the - density of experimental fluid chamber

TABLE OF FIGURES

Irigure 1. ï k buoyancyfirces acting in afieder cjlke: a) the variation of &nsity with cdepth; 6) the vcviation of total hyhstailic head with depth- 5 Figite 2. Double rdiJùw\ne convectiw l y r s in mcrgnu chambers cawed by the fm rlyfising component, i.e. heat. 16 Bgirre 3. Schematic of a convectjvefinger/low. 17 Figure 4. Relative thickness of velocity, temperaftire and compositional boun&uy layers ut the chamber wall. Sis the thicknem of the velocity b0und.y layer. 20 Figure 5. Eflects of the heat transfer through the roof of a magma chamber (Baines, 1999). 26 Figure 6. Intrusion of new pulse of mgma into an established magma chamber (Buines, 1999). 27 figure 7. Schematic of the erperimntal tank All dimensions in cm 32 Figure 8. Distribution of the surfme ana of mica p b s 33 Figure 9. Skilemutic of convection ce11 &veloped in the expriment with 0% glycemf. The b1ack rvrows indicate the streamlinesfir the obserwd convection wll. 36 F"gure 1 O. Front view of the tank showing the disîribution of the p t ic fes (0% glycerol). The fines drawn on the photograph illusaaile eddies in the turbuknt convection. Tffe area represented by the photo is 18~13.5 cm 37 Figure I I . Trend in convection wlocity (0% glycerol) with experiment duration. n e points represent convection velocity of selected parricles. The poriod behueen 5 to 18 hrs in which &ta are absent occurred ditring the night hours. 39 Figure 12. Cotwection veloci4 dsfribution as a firncfion of expriment &ration indcating waf1 velocity (0% glycerol)+ Nok thd the wall wlociw is systematicdEy higher than in o t k r parts of the system. - 39 Figure 13. Convection velocify as a/irnction of qeriment diirafion showing dsribution ofaverage values /or each Curectim (0% g lpro l )+ 40 R p r e 14. ObliqueJdl of a plore. JO FTgure 15. Weight percentage of concentration ofparticles in convection as a finction of time showing removal of particles us per equation 36 (0% giyceml). 42 Figure 16. Number ofprticles us ajïinction of time showing remwal oJparIicIes; best-jtting (0% glycerol). 44 figure 17. Number of particles us aJtcnction of tlme showing removal of particles without convection (0% gljcerol). 44 Rgwe 18. Plot of terminai velocity ofmica flakes versus the size of the particles induding increasing percentage of glycerol in water. 45 Figure 19. Skhematic of the co~tyection &, a) pont view, 6) top view. 47 F1pm 20. Front view ofthe tank Convection pattern, the linos mpresent only the appximate p t h of particles (20% glyeml). The horizontal lines are spoced at 1 cm intewul and the pliotogruph repremts wea of 9.5~9.5 cm 48 W e 21. Front view ofthe tank Conveciion wirh the insertion of I5 Oslopes (20% glyceml). The lines show appoximate movement of parhparhc1ez TIie area represented by the pholo is I W O cm. 49 Figirm 22. Front vî iw of the tmk Cfose-up to the 15 *slopc (20% glyeroî). Tho fines show the overu11 movement of the partides with indication oJe&es. ï k tueu reprclaented &y the Moto is 9.67~10.33 cm.50 Rgirre 23. Front view ofthe tank Corn-vction ~ e n r with the inwtion of 30 *dopes (XJ96 glprol) . Tlie lines sliow the owrall mmnrcnt ofporHclcn Thc m u r cpen ted by the plioto is IQ &XIO. 1 cm. 51 FC@m 24. Trtnd iiz thc cowectlon vefocittes (20% glyceroo aqünclion of îhe expcn'ment hration. The îong interva& without &ta inàicute t k nighttime prrfod O f the expriment 52 Figtcrc 25, C m c t i m velocitjt captribufion as afinction of expriment &alion sho wing particles moving in ail rhme dimctions (2095glycemI). 53 Fîgure 26. Comntctim veI0ciîy dsmmbuffon as a fittction oferpcriment diwation shwing mem values/or each rlirrtcttm (20% gIyccroI). 53

viii

Figure 27. Nmber O fp t i c les as a finction of eqwriment duration sho wing mmovaf o fparticles caIcu1ated manually (20% glycerol). 55 Fïgure 28. Sedimentation pattern ut the bottom of the tank. The dark regions mpresent areas wilh no parficles indimting siidng of the pmtîcles away Brn the wulls. The photo shows the top view ofthe tank with the id& dimension 2 M O cm (20% glycemr). 56 frigwe 29. Sedinientution pattem on the bononi of the tmk with inwtion off5 aslopes. Tlie darker regions repsent the arew with no particles indicating sliding B m the wuIIs (20% glycerol). The photo shows the top view of the tank with dimensions 20x1 O cm. 57 Rpre 30. Skdimentation pattern on the bonom of the tank with insertion of 30 Oslop. Thp darker regions repremnt areas with no particles. Top view of the tank with insicde dimension 2 W O cm (20% glyceruf). 58 Figure 31. Front view of the tank showing convection pattern. The fighter areas repsent high concentrrdion ofpticIes (30% gl'rol). The /aint horizontal lines indicate k m interval wi!h the total

.. .

area shown 7.5~7.6 cm. 60 Figure 32. Vectors and stremlines of the cunvection (30% gIycerol). 61 Figure 33. Comction pattern. Mew of îhe fiont wu11 with the insertion of 15 Oslops. -7'he lighrrr regions indicate higher concentration of ptartic les. The area repsented &y the photo is 9.W.7 cm (30% glperol). 62 figure 34. Convection velociîy bistribution asjimction of expriment &ration showing average valuesjbr each drection (30% glycerol) 63 Figure 35. Convection velocity as ajûnction ofexpriment &ration showing &end in convection velociîy (30% glycerol). The mnd curve is quasi-horizontal suggesting that AT did not vary &ring the course of the experiment. 64 Figure 36. Convection velociîy distribution as afinction of experiment &ration s h i n g the thtee difirent directions of theflow (30% glprol) . 64 Figure 37. Number of particles as a finction of tirne showing removal ofparticlex Best P t t d (30% g l ~ e m l ) 6.5 Figure 38. Top view of the container with inside dmensions of 20x1 O cm. Sedimentation pattern on the bottom of the tank (30% glycerol). The dark regions mpresent areas with not particle accumulation indicating slirftngjFom the walls. 66 Figure 39. Top view of the container with inside dmensions of 2Chrl0 cm. Sèdiimentation pattem on the bottom of the tank with 15 Oslopes (30% gl'rol). The danker regions represent amas with no particies indicating sliaïng@nt the walk. 67 figure 40. Front view of the tank showing convection with no slopes inseried (50% gfyceml). The iighrer areas indicate higher concenhation of particles. The area repsented &y the photo is 9.3x9.J cm. 69 Rgure 41. Parilines of the convecting particles (50% glycerol) 70 Fîgure 42. Convection velocities as a finction of expriment duration. Trend in comction velociîy indicating th& the AT d d nof vary swbstantial&j with linte (50% glycerol) 70 Figire 43. Convection velociîy dsiribution as afinction of expriment &ration indcating pnrticle

- -

movemnt in al1 three directions (50% gl'l) 71 Figure 44, Conwctitm veloc~~typn'file as afinction of expleriment duration showing mean valuesfir each direction (50% glywrol). The downward movingp~uticIes show higher values@ most of the readings 71 Figire 45. M'aiiy calculuted mmovai ofpcutic&s (50% glyceml) as afinction of tim. Since the particles are ~trongîy infienced &y îhefrow, a p r i d c i t y of ihe datapinîs is obamed 72 Figure 46. Top view of the container with imllSIde dmensiow of 2hiO cm. Sedimenfation pattern on the bottom of rht tank (50% giweroo. Tiis &ker r e g i o n s ~ p w t t mas with no particles. 74 I;?gtrm 47. Top view of the conkzhv W h the inside dimnsiotns of 2WO cm &dimentdi011 partena on the botiom of the tank with f5"slopcs (50% gIyceroQ- Tlie cknk w o n s n p s T n t mtar with no parlicim.

7 F I d

Figurt 48. Top view of the funk with the insikie dimellsloms of 2&10 cm Skdimentution pattern on the bottom of îhe tank with 30 ' s i o p (50% g ipml ) . The d t d mgions nprrsnt mas with no partides, 76 Fi' 49. F m view of the tank shUwing disîribuîion O fpmncks in rlie containers (9û% glyamo. Tlre lighter onas indcate higher conœn~ration of pîvîicles. Tnr m a mpsented by tk Moto is 8.3~9 0 a

78

Figure 50. Front view of the tank Convection pattern afler 5 days of cimdation (90% glycerol). The area mpesented by the photo is 1 1. 5x1 1.3 cm 79 Figure 51. Vectors andputh lines of p t i c l e movemmt (9û% gl'rol). Some of the vectors were ignored; therefore, the lines mpresent on& the appromprommaâed s h i l i n e s 80 Figure 52. Convection velocity as afinction of experiment &ration showing hend in wnvection (90% S I F Q ~ ~ 81 Figure 53, Co~wcction velocity dsiribution as afunction of expriment &rution shwing valuesfor each - -

di&tion ofirkc/low (90% glGero~. 81 Figure 54. ~unvecHon velociry dshibution as a Ifrnction of expriment &ration showing averaged value jôi each direciion (90% glyccroI). 82 Figure 56. Nuder ofparticles as ojhction of time showing remmd ofprticfes cdculating using ProPhs (9û% glycerol). 84 figure 57. Top view of the tank with the inside dlnrnsions oJ20x10 cm. Sdimentatim om the container Jlow showing a " butterfrv" panern (90% glycerol). Darker regions repsent arcas with no pwticles. - 85 Figure 58. Front view of the tank showing disafbuiion ofparticles in convecting Juid (iûû% glycerol). Only the main m a orne container is shm (iuithotrt the fime/). The lighter mgions indicate higher coneentmtion of mici Thr orro mpreanted bY the photo is 1 QxI O cm. -

-

87 Figure 59. Vectors and streamlines of convection (1 00% glyceroQ. 88 Figure 60. Front view of the tank showing coltvection 24 hrsjhm the storr of expriment. The light areas indicate high concentration ofiica mggesHng accumulan'on o/prticles in the boundary layers between and mund convection cells (1 ûû% glyceroi). The m a repre~nted by the photo is 9.7x9.7 cm. 89 Figure 61. Convection velaci& as afinction of experiment ditration showing wnd in convection velocities (1 00% gljeeml) 90 Rgure 62. Convection velociiy dsbibution asfiction of expriment duration showing valuesfor each - .

d i a i o n of thejlow (1 00% g&erol) 90 Figure 63. Convection velociiy &skibution as afinction of expriment duration showing averaged vdue & cach dsrection (100% g lp ro l ) 91 figure 64. Number ofparticles as a)hction of time showing remml of particles (I WH giycerol). - 92 Figure 65. Top view of the container with the inside dimensions of 2ûxf O cm Sedimentution pattern on the bonont ofthe tank and insi& the dits (1 00% glycerol). The lighter regions indcate uriem with higher concenIration of mica 93 Figure 66. Decreuse of Ra with increase o/viscosily. 95 Figure 67, Change in the convection ve ld@ wilji addition ofglyerol. 95 Rgure 68. Decrrease in heat bcuts/er q. 96 Figure 69. Change in thermal NusseIf naimber NuF 96

- --

FIS((~~ 70. ~ h m & in the boundory l a ~ and criticai concentration with the v i s ~ ~ ~ . 97 Figure 71. Skhernatic ofthe cxperimental tank 2. 100 Flgure 72. fipwimental setiing&r/Iuid injection expriment 101 Rgure 73. Intrusion phase. The turbulent fiuntain carries the injectedfiid through spreading it on the top of the ambient jtuid 1 03 Figure 74. Entrainment in the inlet. 104 Figure 75. FW view of t k tank showing entrainment of the ambient fluid by the fountain. The light regions reprcmtî higher concentration of mica in the inicr1a)rr andfillowing the ouifine of the enhainment, ï k thin haritonhl lines inaïcaîe 1 -cm intewaifar scaling. The horizontal extent ofriie photo is 2 1 cm. 1 05 Rpm 76- TIiennosyphonpirase. 106 Figum 77. Particles in the inlet, a) afler injection, b) befw injectioorr, The thin horizontai lines repesent i& intewai fir scafing. 107 Epre 78. Top view of tk tank showing sedimentath pattern afler injecria The lighter mguns indicated mas with h igkr cornenharion of mim. sptcifical& mund the in& anci in the scrtaiches. - I O9 Figure 79. Front view of the tank showing disttibution O fpwitcles 2 hous a* intwion, The ligfrt mas indicate conceilraaîion of mica V i partic&s p s n t in the nppr p r t of tk&uv showing he top lger of the injcctedJIirid TIie m a mpresented by llte M t o is 12x12 rn 110 Figure 80. D Y ~ b u t i o y ~ ofparncIes in= a) lighter top lwr, b) interhyv. c) dindiy &r intedmr. The distanm beîween tk horizontal lines in eachJ"m is I cm. II1 Fi@= 81. hiitulphme of inbwron. I I 2

Figure 82 hwnwrud movement of ilie injectedjltcid 113 Figure 83. Top view of the tank showing seàimentatioon pattern afected by the intrusion. m e Iight regions indicate areas with higher concenhation of mica ?nr puncles wem transported about 1 cm closer the inlet. Inside dimenstons of the tank are 20x10 cm. 114 Figure 84. Fmnt view ofthe tank showing injection phase. The phme was redked by the oppsite buoylrncy and stopped - 2 cm ubove the inlet. The photo repmsent the whole m a of the tank with dimension giwn in Figure 71. 116 Figure 85. Front view of the funks showing change of color in tk upper layer indicaüng SOM m-xing beîween theh i& The photo r e p m n t the main container with the inside dimensions of 2ûx 17 cm. - 1 17 Figure 86. Intnision Mase. Buoyancy of the hybnd laye^: 118 Figure 87. Interlayer behveen the dense injectedhid and the uppr ambient Juid me oreo repriesented

. .

by the phoro is 5x35 cm.. 119 Figure 88. Close-up on the fiont vicw of le tank showing dishr'htion oJparîicles in the injectedfluid Tire area mpsented by the piroto is 14x9, 5 cm 119 Figure 89. Top view of the tank showing sedimentution palternt m e inside dmensions of the container are 2&l O cm. 120 Fîgure 90. Parmeter S versus kinemotic viscosity, excludng the msultsfi.orn 100% water expriment. Thejlgure shows the observed values of W. Tiie thick line repsents îhe trend with the equaîion giwn in the jîgwe. 122 Figure 91. Pruameter S in magma chumbers versus kinematic viscosity of mcrgnta. The thick line indicates trend with the equation giwn in theJpm. 123 figure 92. Parameter S using calculded W (Eipaîion 25) versus klnematic viscosity of gl'erol /luid The thick line indicates fmnd with the equdion given in the figure. 123 figure 93. Settiing wlucity versus parride sizeJbr the expinientai fluidsr 124 Bgure 94. Settiing velocity wrsics site of the s u l ' i & h p l e t . 124 Figure 95. Increase in settling by increasing thickness of the boundmy layr in the center of the tank; a)

no dopes, 6) with 30 Oslopes. 125 Figure 96. Geological cross-section of the Jinchuan & p i f (ufler Tank. 1993) 128 Figure 97. Formation of the Sudbury Sn?rcture (a#er Ndrltett, 1999). 130 Figure 98. Possible convection in îhe Strdbury magma lrr)lers (Baines, 2000, personal comrntmication). 13 1 Figure 99, Concepaial mo&l jor Voisey 's Bay d e p i f showing IeveIs of emsion in d~Brent parts of the deposit (Ajîer Nalakett et al, 1996). 133 W r e 100. West -/rtcinggeoiogical section dmugh the ûvoid Deposit, Voisey 's Bay (Line 1300E). - 134

INTRODUCTION

Fluid mechanics in magma chambers has been the abject of many investigations in recent

years. Laboratory experiments involving cooling and crydlizing of aqueous solutions

have been used as analogues to magma chunbers and several important geological

processes have been studied. Recent quantitative studies have investigated crystd settling

and the nsidence times of crystals in convecting magma chambers.

Fluid mechanics hss many applications in economic geology, particularly with respect to

mafic (basaltic) magma chambers. The elliptically zoned Sudbus, Structure in Ontario is

host to world-class nickel-CO pper-PGE deposits, which are generall y regardeci as the

products of a single magmatic event. One of the scenarios for its interpretation is that the

Sudbury Igneous Complex is an impact melt (Naldrett, 1999). This lads to questions as

to why the sulphides occur in embayments that are filled by Sublayer nonte (Momson et

al. 1994). Convection and settiing mechanisms investigated here might explain some of

these occurrences.

Another major magmatic deposit that shows evidence of the effect of dynamic magmatic

processes includes the Jinchuan nickel-copper deposit in China. The genetic mode1 involves ascent and injection of mafic magma followed by intrusion of sulphide bearing

magma (Tank, 1993). The system was probably convecthg due to the subsequent pulses

of magma The settiing of the sulphide droplets resulted in their accumulation at the

bottom of the magma chamber.

Another application of fluid dynamics is found in u l t r d c flows similar to the

Kambdda komatiites. Turbulent movement of hot, low viscosity magma carrying

sulphide droplets would not rllow sulphider to settle eady in the principai channels

(Lesher, 1989). However, naturai traps rad slowing of the flow would enbance the

gravitationai settling of suiphides throu$h the Iow viricosity magma.

Multiple injection of magma into an existing chamber Mght be responsible for the

transport of sulphides fiom a lower to an upper chamber at the Voisey's Bay deposit in

Labrador (Naldrett et al. 1996). The same mechanism could account for massive sulphide

concentration within the feeder to the main intrusion.

The main purpose of this thesis is to study fluid dynamics in analogue chambers and its

impact on the movement of sulfide droplets (or crystals of sulfide minerals) in convecting

magma. The work focuses on the mechanism of sulfide settling, and determination of the

location of the settled sulphides with respect to chamber geometry. Additionally, the fluid

dynamical consequences of themal boundary layers on the movement of particle in

convecting chambers will also be considered.

It will be shown how the viscosity and density of the convecting fluid affects the settling

and movement of particles in the container, and the implications that this has to mafk

magma chambers. The role of the convection in sulphide deposition and its influence on

the sedimentation pattern will be determined. The experiments aiso investigate the

injection of different masses of fluid into the existing environment and its influence on the

already established pattern of settling.

It is important to detemine likely locations for the principal concentration of sulphides

within a chamber, which would assist in the exploration for magmatic wlphide deposits.

This research has many applications to the formation of the magmatic sulphides deposits,

both those already exploited end those ready to be explored. The Ni-Cu deposits

mentioned above originated as a buoyancy driven magmas that ascendeâ and stopped at a

certain depth to create a magma chamber or emded at surface. Fluid mechanics explains

the major processes that induce convection and mifit influence the subsequent d i n g of

sulphides and other crystals within the chamber.

LITERATURE REVIEW

2.1. BUOYANCY-DRIVEN FLUID FRACTURE - MAGMA

TRANSPORT IN DYKES

The objective of this thesis is to study the magmatic sulphide deposits that are hosted by

mafic intrusions, thenfore, only the theory that is relevant to the low viscosity matic

magma will be coasidered. The fïrst part of the review includes a description of processes

that lead to creation of mafic magma chambers. Since this type of magmatic aaivity is

widespread, magma chamben could open anytime during the earth's history.

Unfiortunately, not many chambers lead to formation of economic deposits.

Molten rock, or magma, generated in the upper regions of the Earth's mantie ascends tens

to hundreds of kilometres through the overlying, cold and brittle lithosphere, driven by the

buoyancy of the melt relative to the country rock. The buoyancy exerts enough pressure to

initiate magma-driven fracture, which it is considered as a dominant mechanism for the

transport of magma through the lithosphere.

The propagation ofa swemi of dykes through the lithosphere produces a considerable flux

of heat and mess fiom the mantle into the cmst. With repeated injection, this flux causes

large-de physicai and chernical changes in the crust. In continental settings, an

increased heat flux fiom igneous intrusion may be responsible for the generation of

granitic melts, metamorphic activity and cnistal reworbng (Huppert and Spark, 1988,

Campbell and Hill, 1988, Lister and Kerr, 1991). From an economic standpoint, an

understanding of the dynamics of magma would elucidate the mechanisms of formation of

many of the world's valuable magmatic ore deposits. The dynamics of magma include

fiachire and igneous intrusion as well as the fluid motion in the magma chambers.

Melts produced in the upper regions of the made are less dense thm the surrounding rock

and are thought to rise to collect at the base of the cnist. Transport of magma through the

lithosphere fiom depth takes place in dykes, which propagate upwards at velocities of a

few metres per second (Lister and Kerr, 1991). The velocity values may be inferred fiom

the zonation, composition and the size distribution of phenocrysts, which nuclated during

ascent (Pasteris, 1984, Carmicheal et el., 1977, Maaioe, 1987). Basaltic volcanism is

widespread, showing that mfic magmas are capable of reaching the Earth's surface.

However mafic magmas often corne to rest at shallow levels in the cmst where it cm be

stored in near-surface magma chambers (Ryan 1987). From the chamber, magma could

then be extruded laterally (either in fonn of dykes or sills) for tens of kilometres parallel

to, but beneath, the surface (Rubin and Pollard, 1987).

Most dykes that inter- the surface of the Earth have their intermediate ongin in crustal

magma chambers a few kilometres below the surface. In systems of magma transport,

such as in Kilauea Volcano, Hawaii, magma rises steadily €tom the made to wllect in a

summit storage region some 3 to 6 km below the surface. Episodically, pressure in the

sumrnit reservoir is relieved as dykes are initiated in the walls of the chamber, leading to

magma excursions. Many of these excursions take the fonn of dykes, which propagate,

laterally away from the summit reservoir (Rubin and Pollard, 1987).

The correct analysis of the dynamics of magma hctwe incorporates three important

factors: elasticity, fluid flow and bu0 yancy .

2.1.1. HYDROSTATIC PRESSURE (Pd

A body of magma is only in gravitational equilibrium if it has the same density as that of

the sumunding rocks. The density of the Earth generally increases with depth. Thus,

magma may be positively buoyant (moving upward) at the base of the lithosphere and

negatively buoyant (moving downward) near the surfiace. The horizon between the

regions in which the magma is positively and negatively buoyant is known as the levei of

neutrai buoyancy (LNB). At the LNB magma accumulates to fonn cnistal magma

chamben (Ryan, 1987). The position of the LNB is detedned by the dependence of the

density of the lithosphere and the magma with depth and will vary with the composition

and temperature of the magma and with the regional crustal structure (Figure 1).

The horizon of neutral buoyancy is coincident with the peak in the available magma

driving pressure Ph, indicating the preference of the magma to spread at this level. Total

hydrostatic (or "magmastatic") pressure is given by:

where: A P h - total hydrostatic pressure, Apl - density difference between crustal rocks and

magma, typical value of Ap is 300 kg/m3, g - gravity and hi - height of nse.

Figure 1. The buoyucy fonts acting in a f d e r dyke: a) t k variation of density with depth; b) the variation of total hydrostatic &rd with depth.

In Hawaii, magmas of density about 2600 kg/m3 have an LNB a féw kilometres tiom the

surface between upper and iower cnistal layers the density of which is between 2300 and

2900 kg/m3 (Ryan, 1987). Where mafic magma is intruding unconsolidated seâiments the

magma may be as much as 1000 kg/m3 denser than the sediments (Lister and Kerr, 1991).

2.1.2. ELASTIC STRES$ PE

The tirne scde of the deformation of crustal rocks is of the order of. at most, a few days,

based on the propagation velocities ofdyke and sills. The amount of &ah away fiom the

crack tip is usuaily small, approximately 1p (Maaloe, 1987). The strain dong the dyke is

proportionai to the ratio of thickness to length of an intmsion. Near the tip of the

intrusion, the strain rates are greater and plastic deformation or micro cracking may ocair

(Pollard, 1987). However, these effects are confinecl to a small process zone near the tip

and have little influence on the shape and dynamics of the propagating fracture (Lister and

Kerr, 199 1). The typical magnitude of elastic stresse is given by:

mw AP, =-

1

where m = ; V (1-vol

fiacture and 1 - length.

199 1).

- shear modulus, vo - Poisson ratio, w - typical thickness of

A typical value of m for cmstal rocks is 20 GPa (Lister and Kerr,

2.1.3. FRACTURE EXTENSION. (Pù

The hcture occurs due to extension of pre-existing micro-cracks. A critical stress

intensity factor, or hcture toughness Kc gives the criterion for crack propagation. in a

case when the stress intensity factor K < Kc the crack can extend only very slowly by

chernical corrosion at the ccick tip. However, if K >> K, then crack extension occurs at

about 40% of the speed of sound in the solid (Atkinson, 1984, Lister and Kerr, 1991).

Meewind values of& range fiom 0.6 to 2.2 ~ ~ e l r n ~ for granite, and 0.8 to 3.3 MPdmUJ

for basaits (Tucotte, 1987). According to Lister and Kerr (1991) the K, values have a

range of 0.5 - 1.6 ~ d m " for granite and 1.4 - 1.9 MPalrn'" for b d t s . Sinœ magma

fkactures cannot propagate fsster than the Row of magma into the f iaare tip, the pressure

distribution in the magma must adjust so that the vaiue of K exceeâs K, by an

infinitesimai amount (Lister, 1990). A variety of studies indicate that b d t i c magma

migrates upward at velocities in the range of 0.5 to 5 mls. A fluid-tilled crack propagates

with K s &, therefore, the internai pressure required for the propagation of a magma

fiactun is given by (Lister and Kerr, 199 1):

2.1.4. VISCOUS PRESSURE DROP Pd

The flow of magma in a dyke or siIl is driven by a spatial gradient in fluid pressure. The

vertical extent of most intrusions is much greater than their thickness (Lister and Kerr,

1991). Therefore, the walls of the intrusion are approximately paraIlel. The fluid pressure

is nearly constant across the flow and the pressure gradient and the mean flow direction

are parallel to the walls. The pressure drop in laminar flow dong the length of the fiacture

is given by:

where: q- dynamic viscosity of the magma, 1 - length of the M u r e , t - tirne since

initiation of fiacture and w - fiacture thickness (or dyke width).

The viscosity of magmas varies by several orders of magnitude. Modem basalts are

erupted with viscosity greater than 50 Pas (Huppert et al., 1984). However, the observed

viscosity of Mauna Loa volcano, Hawaii varied fiom 100 to 2000 Pas. A decrease in

temperature of 200°C causes a deuease in the viscosity of basaitic magmas of a factor of

about 10, while an increase in pressun of I GPa causes a demase in the viscosity of

about 35% (Kushiro, 1980). For purposes of this thesis, we assume an average viscosity

of 100 Pa S.

2.1 S. PRESSURE BALANCE IN DYKES AND S U S

In a stationary dyke, when it does not pmpagate at its upper tip, the fkacture extension (Pr)

is grrater and the sum of the intemal (Po) and hydrostatic pressure (Ph). Aiso, the elastic

pressure (P.) bdances the intenial and hydrostatic pressures. Thenfore, from equation 1,2

and 3 the maximum vertical extent and width of stationary dykes cm be calculated using

(Lister and Ken, 199 1):

Taking &=1 ~ p a l r n ' ~ for granites, m=lS GPa as typical for the granitic cru$ Ap=100

the hm, is in order of 100 m and w,, is in the order of 1 mm. Under the above conditions

the dykes are very nanow and h e quickly. The vertical extent h, may be exceeded if

suficient magma is injecteci into a dyke. Then the dyke will propagate upwards driven by

the buoyancy of its contents. From the equations above it can be deduced that as h

increases, Ph increases and Pfdecreases. Therefore, if h is significantly greater then 100 m

then Pfi<Ph, demonstrating that the resistance of the rock to fracture is considerably less

than the available driving hydrostatic pressures. Since the Pr is comparably sma11, the dyke

will continue to propagate until it reaches its LNB or until it fieezes.

The resistance of the host rock to fiaare plays a role only durlng the nucleation of a new

dyke. Once a dyke has grown to a critical length, the resistance Pr to firrther propagation

of the fiacnire is negligible in cornparison with the other pressure scales (Lister and Kerr,

1991). Hence, the viscous pressure drop in the melt provides the dominant resistance to

further fracture as it flows towards the dyke tip.

2.1 -6, FEEDER DYKES

Magma d l rise through denser regions of the lithosphere in vertical dykes, dnven by

buoyancy. Near the tip of the dyke, there is a balance between viscous and elastic

pressures. Away from the tip, a balance between buoyancy forces and viscous drag

dominates verticai transport in fader dykes (Lister and Kerr, 199 1). The motion of feeder

dykes is chen by elastic stresses only if the dyke is of smill vertical extent The

hydrostatic pressures, if not balanced locaily by viscous pressure dmps, are sow tens of

MPa and are sufficieat to deform the dyke margins by several rnetres and cause large

changes in the flow rate. However, if there is a variation in the local density difEerenceq

the elastic forces will smooth the necessary deformation of the dyke walls over a vertical

d e . Comparing APh - a, where APh-bpi& and AP.-mwn the ratio of the dyke's

vertical extent to its width is given by Lister and Kerr (1991):

Since the vertical extent is in the order of at least a few kilometres and the thickness of

dykes are in the order of a few metres then A P h a. Therefore, the transport of magma

is dependent upon the balance between the hydrostatic and viscous pressure. The flow

adjusts so that the local hydrostatic pressure gradient, dPh/dz is approximately qua1 to the

local viscous pressure gradient (IPJdz, and the dyke is of the appropriate width to carry

the volume flux d v i n g fkom depth.

If the elastic stresses and resistance of the host rock can be completely ignored then the

thichess of the dyke near the source is proportional to the flow rate and viscosity of the

magma, provided that flow rate varies with time (Lister and Kerr, 1991).

Since hydrostatic pressure is greatest at the LNB, the feeder dyke will widen at the LNB

and the magma will be emplaced laterally through dykes or sills initiated at the fiactured

mugins of the feeder dyke (Lister and Kerr, 199 1). Solidification at the edges of the dyke

is likely to limit the lated extent ofthe flow and concentrate it in a wider dyke that would

be capable of transporthg the melt without M e r solidification.

As the magma accumulates at the LNB it causes build up of elastic messes. Due to the

increase in the elrstic stress, the magma overshoots beyond the LNB through a s d l

verticai distance. This overshoot provides the hydrostatic head requind ta drive the

magma Iateraiiy dong the LNB or poduce a fountain in a magma chunber. If sufticiently

large, it will lead to a surface eruption (Ryan, 1987). The height of the overshoot is

related to the width (equation 7) of the feeder dyke at the LNB and both are, in mm,

related to the supply rate fiom below.

2.1.7. LATERAL EMPLACEMENT AT THE LNB IN DYKES AND S U S

The cising magma innates the uppennost parts of the dyke near the LNB. Therefore, the

thickness and penetration height above the LNB will increase slowly while maintaining

the balance dPh-dPC. As rnentioned above, the elastic stresses increase at the LNB and

offen e x a d the fiactwe toughness of a dyke initiating new fractures at LNB (Lister and

Kerr, 199 1). These fractures propagate along the LM3 as dykes or sills and relieve the

pressure by carrying magma away from the inflated region. Cycles of inflation con create

interconnectecf dykes and sills (Ryan et. al, 198 1)

A dyke will continue to propagate laterally along the LNB dnven by buoyancy forces,

restrain movernent of the magma both upward and downward. The lateral dyke remains in

vertical equilibrium as long as there is a balance between buoyancy and elastic forces. It

also depends on the density of the magma and the local stratification of the host rock. In

other wordq if the average level of the dyke is tw low relative to the LNB then the

hydrostatic pressure and stress intensity will be greater at the upper edge of the dyke thon

at the lower and the dyke will gradually rise until it fkzes or reaches the surface (Decker,

1987). The initiation of sills is encouraged by the fact that the LNB is likely to be a zone

of weakness between overlying sediments or altered cmst and underlying igneous rocks

(Walker, 1989).

The proximity of a lateral dyke to the Earth's d a c e tends to increase the stress intensity

at the upper edge of the dyke and thus encourages upward propagation anci eniption nther

than continued lated propagation. Dyke widths will be controiied by the elastic strain

energy stocd in the host rock at the moment of intrusion. Injection will continue until

over pressures within the magma chamber are reduced (Ryan, 1987). The vertical extend

of iateral dykes similarly to the vertical dykes typically exceeds LOO m @ecker, 1987).

Therefore, the resistance of rock to nPcturr couid be neglected. For a given volume of

magma nfeased fiom the reservoir, dyke height is approxhately constant, b u s e both

the top and the bottom of the intrusion attanpt to reach the horizon of neutral buoyancy

(Ryan, 1987). The tesuit is the attainment of remarkable dyke kngths over short periods

of time.

Ryan, (1987) recognises three modes of neutral buoyancy-controlled dyke formation. (1)

Slow initial leaksge with a gradually enlarging magma ûacture fiont, where the dyke top

ptogressively rises towards the surface, while the keel descends simultaneousiy. (2)

Abrupt initial leakage with a rapidly enlarging magma bcture fiont. The top of the dyke

grows rapidly towards the sufice, while the keel descends rapidly. As the pressure is

reduced the advancing fiacture front gradually narrows. (3) Harmonic oscillations of the

top and keel of the growing dyke, where the top and bottom of the extending dyke rises

and falls together as time progresses.

The mechanism of buoyancy-driven propagation along the LM3 is capable of explaining

the formation of individual blade-like dykes (Ryan, 1987, Rubin and Pollard, 1987). In

Iceland and Hawaii, such dykes are observed to propagate for tens of kilometres laterally

though these are typically only a few kilometres high and a few kilometres below the

surface (Rubin and Pollard 1987).

The cessation of the propagation of a dyke is ükely to be nlated to the fieezing of magma

at the dyke tip (Lister and Kerr, 1991). This is caused by fdling pressure in the source

r e m o u andor subsequent solidification of the slower flow.

When two or more magma fiactuns ascend in close proximity to each other the stress

fields induced by the individual parcels will mechanically perturb each other depending on

their crack-tip offsets, ovetlaps, and mutual distances (Ryan, 1990; Takada, 1994)

Heat exchange between flowing magma and the wdlrock is another important process in

magma transport. Whether magma tends to solidify in a magma conduit or whether the

waîlrock melts depends on the relative contributions of conductive heat transfer by the

wallrock and advective heat d e r by the flowing magma, respectively.

2.2. FLUID DYNAMICS IN MAGMA CHAMBERS

The purpose of this part of literature review is to familiarize the reader with fluid

mechanic processes that are thought to take place in magma chambers. These processes

include convection, heat transfer, boundary layers formation and particle (crystal and

liquid drops) senling mechanism.

2.2.1. EXISTENCE. SIZE AND SHAPE OF MAGMA CHAMBERS

The strongest evidence for the existence of magma chambers that undergo active

convection and crystal sorting cornes fiom plutons, which are the most fundamental type

of igneous body. They Vary considerably in shape and size. Some are very small (1 km3),

whereas others, such as those found in batholithic terraines, exceed 1000 km3 (Marsh,

1989). The shape of the chamben varies greatly. For example the active chamber that

feeds the Kilauea volcano, Hawaii is rectangular with dimension of 10x l x 10 km (Ryan,

1988). The Mid Proterozoic Jinchuan intrusion, China is 6.5 km long and up to 0.5 km

wide and has shape of an irregular dyke with a fume1 openhg towards the surtace (Tang,

1993). The Mid Proterozoic Sudbury Igneous Complex in Ontario resembles a basin with

dimensions of 60 km long and 27 km wide and about 3 km thick (McGrath and Broome,

1992). The diameter of the Early Proterozoic Bushveld cornplex is approximately 100 km

with thickness ranging ftom 5 to 10 km (Naldrett, personal communication). The

proposed mode1 for Voisey's Bay deposit resembles a shallow basin with steep sides and a

gently inclineci floor.

2.2.2. FLUID CONVECTION

Fluid dynamical processes, iike convection, may explain the crystaîlization product of

magmas in the chamber, which may be chemically zoned. Heat is transferred to solid

surfhces at rnuch higher rates by a flowing fluid t h by conduction. The fluid transports

hot zones npidly to colder zones and so moves hot fluid close to walls where conduction

curies the heat into the wall. The effect is larger h nubulent flow than in laminar because

the turbulent eddies have a velocity componem directeci toward the wdl.

Convection in magmas is driven by the density diffennces due to temperature or chemicai

compositional change. The tempera- and chernical composition daerences usually

onginate st the chamber (or dyke) walls andlor due to an injection of new magma into the

chamber. There are two basic foms of convective processes: convection from an

extended source and convection from a point or line source.

Convection, from point or line sources, ocaus when a new pulse of magma is injected in

the chamber as a jet, plume or fountain through a pipe (point source) or dyke (line source).

Magma injection by jet is characterized by a forced flow of magma of the same

temperature and composition as the ambient magma, emitted from an isolated source,

which can be either a small, nearly circular hole or a narrow dit (Campbell, 1996). The

properties of the flow are determined by the momentum flux at the source or by the

Reynolds number [Re] deflned by :

where: u - mean fluid velocity, d - diameter of source or dyke width, v - kinematic

viscosity. The flow is laminar when the Re is small. However, as Re rises above - 30 the

flow becomes increasingly turbulent and mixing is progressively more efficient. At

Re-400, the flow becomes fully turbulent and fùrther increases in Re have Iittle influence

on the eflïciency of mixing. The mixed fluid spreads out as a cone or wedge way from the

source.

A plume is a flow produced by an isolated source of buoyancy, Le. injecting magma of

different properties, due to heat or cornpositional differences. Plumes may be laminar or

airbulent based on similar flow criteria (Re) as for the jet flow.

A magma chamber which, is cooled nom above (or the side) or heated fiom below

prodwxs convection fkom extended sources. It is driven by small buoyancy diffennces in

a boundary layer at the margin of the chamber and it is cailed &ee convection. There are

two types: thamai boundary layers produced by diffusion of heat into the cool wails or

mot; and compositional boundary layers produced Dy diffision of mass at a boundary

where crystailization or melting is occurring.

At a vertical boundary, convective motion starts as soon as a buoyancy difference

dmlops (Campbell, 1996). The convection sets in once the thermal boundary layer

grows conductively to some critical thickness (Marsh, 1989). According to Marsh (1989).

fiiliy developed convection occurs when the magma has already crystallized to a mush.

However, this applies in the extreme case of fiilly saturateci, fùlly permeable wall rock.

As the depth at which the magma body is emplaced increases, these effects become less

important.

Convection is confined to a region in which the viscosity varies by no more than a factor

of about 10 (Stengel et. al, 1982, Richter et. al 1983; Morris and C a ~ g h t , 1984). In the

case of a cool thermal boundary layer in a basaltic magma chamber, heat diffises

relatively slowly into the wall but the buoyancy of the thin, cool boundary layer drags

much more fluid into motion through the action of viscosity. The Prandtl number Pr,

defined by:

where KT - thermal diffisivity in magma, is a messure of the relative thickness of the

viscous and thermal boundary layers during laminar flow. The Prandtl number provides a

measure of the relative effectiveness of momentum and energy transport by diffision in

the velocity and thermal boundary layers, respectively (Incropera and DeWitt, 1996). The

Lewis numbers defined by:

(where: D W the molecular diffisivity of the light component in binary magma) is relevant

to any situation involving simultaneous heaî and mass transfer by convection aad it is a

meosure ofthe relative thermai and concentration boundary layer thicknesses. Both Pr and

Le are ratios ofdifisivities and thetefore depend solely on magma properties.

Magma chambers lose most of the heat through the roof (Worster et. al, 1990, Turner and

Campbell, 1986, Koyagucbi et. ai, 1993). The heat uansfer (q) to the coder roof is (Hort,

1996, Cordoso et. al, 1996, Worster et. al, 1993):

where a is thermal expansion coefficient, g is gravity and C, is a heat trader. Using -7 2 p = = k@m3, a=5x 1 (Ys F', g= 10 m/s2, ~ ~ 8 x 10 rn /s, v=l O m2/s and CP= 1 1 O0 JASgfC

and AT40 K the heat flux would in order of 22 w/m2. According to Campbell, (1 996) a

deeply buried magma chamber, which has already cooled for tens of thousands of years

has a minimum heat flux of approximately 0.4 w/m2, while the heat flux in a shallow

charnber is about 4 w/m2. Therefore, the floor of the magma charnber is a major site for

crystallization during the early and middle stages of the evolution ofa chamber.

Most basaltic magmas melt the roof of the chamber, creating a ponded layer of felsic melt

with a liquidus temperature well below that of the remainder of the magma in the chamber

(Worster et. al, 1990). The pressure affects the liquidus temperature causing an increase

of the supersahiration in a homogenous magma. Consequently, a large degree of

supersaturation is formed at the bottom of the charnber and crystallization that is more

rapid occurs at the floor than the roof (Worster et. al, 1990). As olivine and pyroxene

minerais crystallize at the floor of a silicate magma chamber, the melt adjacent to the

crystal-liquid interfsce becomes depleted in dense components. Since the density of the

melt decreases, it moves upward away nom the growing crystals, starting

convection.

2,2.3. FORCm CONVECTION

During an intrusion of magma fkom a lower to an uppa chamkr the

through a àike by a pressure difference so the flow field and heat

a compositional

Iiquid is driven

msfe r are set

extemaily. This is one case of forced convection. The vigor of convection can be

measured by the rate at which heat is transferred. The NusseIt (Nu) number is the ntio of

totai heat flux to that wbich would be carrieci by condudon alone given the imposed AT

and is:

A Nusselt number of unity indicates pure conduction. In a very long dike with laminar

flow, the Nusselt numbers is a constant. It is unlikely that this condition is met in any

location because of the thin thermal boundary layer. For the dikes wider than 1 III, the

length wouiâ have to exceed 10 km for Nu to be constant. in typical locations, the flow of

magma enters the lower end with a uniforni velocity profile and velocity and themal

boundary layers grow dong the wall surfaces with distance fiom the entrance.

2.2.4. DOUBLE-DFFUSTVE CONVECTION

Double-diffisive convection occun when the flux of one property imposed on a gradient

of another property with a different molecular diffisivity, such as temperature and

composition, contributes to the buoyancy of the fluid in opposing directions (Clark et al.,

1987). In other words, double difbsion is considered as the superposition of two

competing buoyancy forces, thermal and concentration, since the temperature and the

components difising in the liquid influence the density. Hence, a series of horizontal,

convecting layers (Figure 2) are produced, each of them well mixed in temperatun and

composition and separateci by interfoces across which heat and composition are

transported by molecular diffusion, rather than a single, large-scale overtuming.

Figure 2. Dwble âiffisive convectivr layen in magma chrmbm cruseâ by #he f& diffusing corpontat, LC heat

Two distinct types of double-difisive convection may be identified (Clark et al., 1987).

The tirst occurs when the fast diffusing component has an unstable distribution (diffisive

regime, Figure 2). The second regime occurs when the slow diffiising component has an

unstable distribution (finger regime, Figure 3). Hear, wbich difises faster than mass, is

transfened across these diffisive intediaces and causes instability and convection in the

layers above, while the composition of the layer changes little and preserves the stable

density phases between the layers.

When hot compositionally dense magma overlies cooler compositionally lighter, magma a

finger interface will form (Campbell, 1996; Piasek and Toomre, 1980). The fingers act as

tubes that transport fluid fiom one convecting layer to the other. The flow in adjacent

fingers is in opposite directions (Figure 3).

Figure 3. Schematic of a coiinetive iïnger flow.

The downward moving fingers are losing heat and

upward moving fmgers release a tlux of light fluid

density difference between the convecting layers

interfaces becorne similar to dmsive interfaces.

2.2.5. FLUXES IN MAGMA CHAMBERS

their density is increasing, whereas,

at the base of the upper layer. The

increases with time and the finger

Al1 dynarnics and heat transfer in tiee convection are related to The Rayleigh number

(Ra). The Rayleigh number expresses the balance between the driving buoyancy forces

and two diffiisive processes, viscosity and the thermal diffisivity, which retard the motion

and tend to stabilize it.

where a is thermal expansion coefficient (OC-') and h is the total depth offluid. When the

Prandtl number is large, as is the case for a basaltic magma, the transition from laminar to

turbulent convection takes place at 1 06.

After a series of numericd calculation, Clark et al. (1987) concluded that the Nusselt

number for boundary loyers with viscosity variation could be simplifieci to:

Where A = eA is the dynamic viscosity contrast that is the ratio of maximum to minimum

magma chamber viscosities. This simplification irnplies that thermal Nu has little

dependence on Lewis number. Physically, this relationship indicates that in multi-

component convection the compositional buoyoncy of slow diffising chemical species

does not affect transport. Heat transport is affecteci only by the magnitude of the thermal

driving force and the viscous resistance. Numerical solutions of the goveming equations

by Clark et al (1987) were fitted by an equation 15 with the coefficient 0.42 and exponent

of 114 which is the value expected for laminar flow. The 113 power is the value expected

for turbulent flow and for Ra = 1014, therefore, the eqected values for Nu would be much

larger if the exponent of 1/3 was used.

In analogous manner compositional Nusselt number could be expressed as:

And compositionai Rayleigh number represented by:

The downward flux of light silicic materiai depends on both the thetmal driving force of

the convection and on the ratio of thermal and compositional ditttsivities. It does not

depend on the magnitude ofthe compositionai driving force (Clrrk et al. 1987).

Appropnate ranges of the goveming dimensionless numbers relevant to flow in cnistal

and upper mantle magma chambers are given in Table 1.

Tabk 1. Important dimensionlcrr n u a k n (Clark a al., 1987) DimensiorilWs n n m k Magma c h d e r mnge

Prandtl Number Pr 1 0 ~ - 10. Lewis Number Le lo4 - 1 0 ' ~

Rayleigh Number Ra 109 - 10"

Viscosity Contrast A 1 - los

Convection in magma chambers is driven by buoyancy anomalies that build up in

boundary layers at the roof wall or floor of the intrusion. Convection cells have narrow

thermal and cornpositional boundary layers of thickness & and &, respectively. The

region where the 95% of the variation in temperature or composition occurs defines the

boundary layer thickness.

The noor and roof boundary layers grow by diffusion and heat transfer until, at a critical

time, the local Rayleigh number, based on the boundary layer thickness, reaches a critical

vaiue of approximately ld (Campbell, 1996). At this time the boundary layer becomes

unstable and breaks away as a plume of buoyant material to join the convection in the

interior of the magma chamber.

Ifit is assumed h t no aystdlization or melting occurs at the top of the chamber, the heat

flux q through the roof must pass through the upper thermal boundary layer. Worster et

al. (1990) mggesteci that in a luge magma chamber most of the crystallization occun at

the floor even though most of the heat is lost though the mf Melting at the roof absorbs

latent heat and because heat is transfetred between the zone of melting and the underlying

basaitic mgma by convection, roof melting caa lead to a âramatic iacrease in the

effective heat flux (Brandeis and Jaupart, 1987; Worster et al. 1990). As a result, the

thickness of the boundary layer is given by (Martin et al. 1987):

If a dense phase such as olivine (@300 kg/m3) crystallizes at the floor of a magma

chamber a light magma is released giving rise to a buoyant compositionai boundary layer.

Martin et al (1987) have show that the width of the compositional boundary layer is

given by:

where L is latent heat of crystallization, is compositional expansion coefficient and C is

concentration. In addition, the release of latent heat of crystallization produces a thermal

boundary layer, which is also buoyant. Consequently two buoyant boundary layers

develop at the fioor of the chamber and, because heat diffises faster than mass, the

thermal boundary layer is thicker than the compositional boundary layer (Figure 4).

Figure 4. Wtm tbicknem of vûocity, temperature and compoaitionml boundry layen rt the chaakr wdi. 6 is tbe t h i c b s of tbe vdocity boundmy layer.

The thermal boundary layer thickness & and compositional boundary layer thickness &

vary inversely with Pr and Sc respectively . Clark et al. (1 987) simplified the equations to:

= 0.77b. P O 1

High viscosity contrast leads to a higher average velocity in the chamber. This conclusion

is a direct consequence of the lowered vimsity as temperature increases away from the

upper boundary. The velocity field also becornes asymmetric as A increases (Clark et al.

1987). Slower velocities are pnsent in the upper coder boundary layer. In the upper

boundary layer, diffisional transport is more important, relative to advection, than it is at

the lower boundary. For this reason the contrast in temperature and composition across

the upper boundary layer are greater than they sre âcrûss thc lower boudsry layer.

Therefore, both Nusselt numbers are proportionally dependent on A, and the boundary

layer thickness are inversely dependent on A.

Convection in ta11 bodies is dorninated by flow dong steeply inclined or vertical walls.

These flows may be important in forming double-difisive systerns (Huppert and Sparks,

1984; Turner, 1985) and in controlling heat and mass transfer (Spera et. al 1984). In

steady, well-developed flows the thermal boundary layers thicken with distance down the

wall. According to Spera et ai (1982) the time in which the boundary layer develops in

rnafic magma chambers is geologically rapid in order of 10 to 100 years. During this time

an initiaily purely conductive, cool border mne of constant thickness progressively

sloughs fiom the wdl and is replaced by a thickening downward thecmal boundary layer.

The thickness of the layer is obtained fiom (Marsh, 1989):

W is convection velocity defïned for middle chamber elevations by:

2.262 AppIicafion fa magma chamben

The dimensional heat flux through the roof of the c h b e r is given by (Clark et al., 1987):

3 2 If typical parameters are assumed: k 53.3 5 WlmK; r 10 m 1s. a=5x 1 u5 R*, AT = 5 K, g

= 10 m/s2, KT = 8 x 10.ï m21s, A = 102, with vertical extend of the chamber h, = 1 km, it is

found that: Ra = 3x 10' and q =1.69 w/m2.

Typical Rayleigh numbers range tiom 10" - 1016 for basaltic magmas. Taking the lowest

value of Ra = 10" the heat flux will increase to q = 6.4 w1m2. in many geothermal areas

heat fiow can be hundred times greater than the value obtained here. The equation above

applies to the laminar conditions but Ra in order of 1012 is typicd for the turbulent flow.

In this case, exponent 1B should be used instead of 114 resulting in increase of the value

of heat transfer to 102 w/m2. Using equations 14.1 5, 18 and 19, obtained values for

Nusselt number and boundary thickness are Nup100, Ne-1860, e 5 m and e 0 . 2 m.

The dimensional maximum convection velocity is given by (Martin and Nokes, 1989):

The above equation is applicable to magma chambers cooled fiom above and heated from -7 2 below. For Ra=3x109, K T = ~ X 10 m /s and depth of 1 km, maximum convection velocity

would correspond to 1.7 Wyr. (0.2 mk).

2.2.7. INJECTION OF A NEW PULSE OF MAGMA

Widesprd evidence now indicates that most magna chambas, at sometime dunng their

1Xe spui, are replenished by one or more new influxes of magma Most injected liquids

are denser than the resident liquid in the magma chamber i.e. basic magma intmding into

silicic magma chambers.

Chambers that are filled with magma of the same composition and temperature throughout

the chamber wiU remah well mixed during small new inflows only when the physical

properties of the new magma are close to those of the resident magma. However, a jet of

fluid at a high Reynolds number will mix rapidly with surroundings haviag the same

properties.

Huppert and Spark (1980) considered a case w h m a magma chamber is replenished fiom

below with hot, dense, more primitive magma. Thus, the hot picritic magma becomes

overlah by cooler fiactionated magma The two layers are sepanted by a thin, sharp

horizontal "double-diffisive" interface. Because the interâice is thin, heat is tramferreci

rapidly fiom the lower layer to the upper layer while compositional properties are

transported very slowly. In their calculations Huppert and Sparks (1980) suggest that rate

of cooling of the hotter lower layer is much faster than rate of cwling of a magma

chamber by conduction through its walls. The heat loss enables rapid crystallization of

olivine, which lowers the density of the lower layers and can lead to overtuming and

complete mixing between the layers (Campbell, 1996).

If the magma which is denser than the fluid in the chamber enters the chamber with

sufficient upward momentum a turbulent line fountain will result. The new fluid will

initially be carried upwards into the overlying magma. Due to the buoyancy forces acting

in opposite direction the fountain and the new pulse fdls back to the floor of the chamber

in a ring about the feeder oAen tilted to one side (Campbell and Turner, 1989). Since the

motion within the fountain is turbulent, it will draw the host magma into the fountain. The

resulting mixaire collects at floor of the chamber. nie height of the fountain can be

calailateci using following equation (BloomfieId and Kerr, 1997):

where: b-height reached by a line fountain, w-dyke width, Am-density dwerence

between the input magma and the host magma in the chamber, Api-mean density contrast

betumn the magma and the wall rocks and f-fiction factor with a value of 4-03. Taking

m as averaged thickness of the feeder to the Reid Brook Intrusion, Voisey's Bay

(Kiersnowski, 1997), Apo=30 kg/m3 (Campbell, 1 9%) as the maximum likely density

difference between the input magma and host magma, and Api=300 kg/m3, the height of

rise of a fountain is 2.5 km (at w=10 m, ho425 rn).

If the input magma is hotter than the ûactionated magma in the chamber, the hybrid layer

becomes thennally stratified with cooler, compositionally lighter magma overlying hotter,

denser magma. Because the destabilizing property, heat, diffises faster than the

stabilizing property, composition, the hybrid layer breaks up into a number of well-mixed

double-diniisive convecting layers (Campbell, 19%). Campbell and Turner (1989)

suggested that the lowermost layer in a magma chamber can be expected to rernain

stagnant, following the injection of a new pulse of magma, until the temperature of the

lower layer fils below the temperature of the temporary floor of the chamber. Baines et.

el. (1990) showed that the density gradient in the layer of the hybtid magma below the top

of the fountain contimially demeases, and will become very mal1 at large times. It was be

predicted theoretically, that the fountain top rises at close to haif the speed corresponding

to the rate of addition of magma in the fountain.

Campbell and Turner (1985) found that if the injected magma is less viscous than the host

magma, very little mixing occurs at moderate flow rates, even if flow within the fountain

is fully turbulent. As the incoming ûuid distorts the outer suiface of the fountain, the

fluids will mix eficiently if the outer surface is rough. This implies that the magma

entering the chamber has to have sufficient momentum to entrain the outer fluid.

Campbell (19%) suggest thot this is possible when uw>kv2 (u-mean fluid velocity, w-

dyke width, kanstant and vt-viscosity of the outer fluid). Quoting Cimpbell(1996): If WU/v2>70, the i@mng mgma mixas with t h kwt ntanurgino a9 ifthere w m ))O vkmOSIty

riii'ffere~e between !km but, ifWfl;/v2c7, linle w m mwng a r u r s even if motion within

the fmntdn isjklly turbulent. The above can be expressed in tenns of Reynolds number

of the inf'iow:

v2 Re, =->k- VI

where VI is viscosity of the idowing magma.

A turbuient plume will fiorm when light fluid is injected at the bottom of a homogeneous

layer and the Reynolds number is high (Spark a al., 1980). Jets and plumes are often

obserwd in nature discharging into an enviconment with temperature and composition

stratifications. Baines and Chu (1 9%) explaineci the complexity of the interaction of the

jets and plumes with the stratification in the environment. The fluid at the source is

initial1 y lighter than the fluid of it s sunounding environment. The entrainment of denser

fluid tiom its environment causes buoyant fluid density to inmease continuously with

elevation until the difference between the plume and mounding reduces to zero. At this

level, it spreads out laterally at a level that is dependent on the buoyancy flux at the source

and the density gradient of the environment. Continuous inflow of lighter fluid will build

up a stratified layer at the top, bounded below by a sharp front that moves downwasds

(Baines and Turner, 1969). The fluid that has already spread out dong the boundary and

become part of the environment will lower the density of the subsequent plume fluid

mixing with it, so the iightest fluid will always be deposited at the top. If the input fluid is

hotter than the host fluid the intrusion will dso be hotter than that fluid above or below

the intrusion. A diffisive interfàce will fonn at the top of the intrusion and a finger

intefiace at the bottom (Campbell, 1996).

2.2.8. MELTING AND SOLIDIFICATION IN MAGMA CHAMBERS

During the early stages of cooling the magma in the chamber can assimilate the wdls

(roof. floor) of the chamber if the melting point of the country rock is less than the

temperatun of the magma. The proass will continue until the start of crystallization at

the contact. Fresh input of magma into the chamber might melt the layer of aystailine

rock and furtûer assimilation of country rock un OCCUT~

Since most of the country rock is compositionally lighter than the magma in the chamber,

the magma produced by melting of the walls will cise away fiom the contact and be

assimilated imo the upper lighter layer. Light melts generated at the mof will rise and

collect at the high points of the chamber. The chamber will stratify with the bulk of the

chamber being filled with basaltic magma and the upper part with felsic magma

(Campbell, 1996). Campbell and Tunier (1987) argue that thm is little mass transferred

across the interface between the felsic magma at the roof and the basaltic magma below.

Cardoso and Woods (1996) suggested, however, that lighter molten rocks overlying

basaltic magma would drive a vigorous convection. The convection will drive mixing of

basaltic magma with more silicic magma resulted fonn melting of the country rock. This

may produce crusta1 contamination necessary for producing sulfide liquid.

Gronitic Country Rock Oriqinal Roof

ii = - ' y / / / / / / / / / / I l / Levei

Melted Roof

L Mofic Moqrno

T

Filun 5. Effiits of the &n transfet through the roof of a magma charnôet (Baina, 1999).

The hot rnafic magma solidifies at a higher temperature than that at wbich the solid felsic

rock melts (Huppert and Spwks, 1988). This means that the tiquid mafic magma cannot

be in contact with the granitic host rock (Baines, 1999). The most likely possibility is a

layer of melted host rock between the granite and mafic magma (Figure 5). The

convecting mafic magma thus transftrs heat to the solid layer, which transfers it to the

melting intedace. At the mof, the liquid layer of molten granite is lighter than the d c

magma so the layer becomes stable. The anaiysis of heat ttansfet tiuough the roof

(Huppert and Sparks, 1988) showed that the wldest magma is adjacent to the interface

with the melt layer. Thus crystals would form here because the colder the liquid the

higher the concentration. These would be convected to the mass of magma by the descent

of the cold, heavier liquid.

Large density dürerences between the mafic magma and molten layer of the host rock

(-300 kg/m3) cause about 5% contamination of the granite layer with basalt; however as

high as 20% may be expected for density diffennces of 100 kg/m3 (Cardoso and Woods,

1996).

G r m i t i c Country Rock

I Convect ing ~ u g m o I

1 7 1 New Maf Magma

r o m (Ir-ystal Laysr

Figure 6. Intrusion of ncw pulse of m y m r into rn atabüshed magma chrmkr (Bainu, 1999).

When the new pulse of magma is injeaed into the chamber, it causes erosion of the

cumulate pile (Figure 6). if the produa of erosion increases the density of the melt, the

contaminateci magma accumulates in a pond et the base of the chamber, and erosion is

npidly arrestd. If, however, the products are light, these are swept away by compositionai convection and replaced by uncontanrinateci magma aiiowing erosion to

continue (Campbell. 1996). Caiculations done by Snyder and Tait (1995) indicate tht a

basic replenishment may flow for tens of kilometers before substantial cooiing of the

interior of the flow.

2.2.9. CRYSTAL SETTLING

Mid-depth convective velocities in magma chambers often greatly exceed settling

velocities of typical crystals. However, particles may still settle out of such vigorously

convecting fluid, because the convective velocities diminish as the boundaries are

approached.

Stokes' Law gives the terminal settling velocity ofa sphencal particle:

where: ApC - is the density difference between crystal and the magma, pc - is the density of

the crystal and a - is the diarneter of the crystal. The above equation applies to the solid

particles. To simplify the calculation surface tension of a liquid droplet was ignored. The

convective velocities might be suficiently large, when compared with the crystal-settling

velocities which implies that al1 crystals are in suspension so no crystaf setthg at the floor

of chamber occurs. A magma density of 2500 kg/m3, sulphide density of 4000 kg/m3

(Naldrett, 1999 - personal communication), a - 1 x lu3 m and kinematic viscosity of 100

m21s will correspond to settling velocity of 3 x lu9 m/s. However, whereas a parameter S,

defined as:

is generaily very small(10" < S < 1 for basaltic magmas), the convective velocities must

tend toward zero as the boundaries of the flow are approached (Martin and Nokes, 1989).

If v.=3x1u9 m/s and ~ = 4 x l 0 ' * m then S becornes 1 .5xWS. This suggests that aystal

settiing wiU be effective at the bottom boundary of the fluid. Martin and Nokes (1989)

noted the static loyer at the floor bat am as a trap fbr particles. Any particle, wbich

entas this layet, fdls to the bottom ("crystai capture").

Martin and Nokes (1989) performed a set of experiments simulating magma chambers

with convection driven by cooling nom &ove and heating fiom below and magma

chambers undergoing heat loss fiom both the roof and the floor. In the case when the

magma chamber is cooled tSom above and heated fiom below, the plumes rising off the

floor are able to re-entrain particles which had previously settied out. If the re

entrainment rate is constant then the decay in the number of particles in suspension will be

given by:

where: N - number of particles in suspension in the fluid. NO - initiai number of particles

in suspension in the fluid, R - rate of re-entrainment of particles nom floor (s*'), and h,,, - depth of the chamber. Martin and Nokes' (1989) work was based only on low

concentrations of particles in the convecting magma and they did not consider the effect of

boundary layers on the vertical walls.

Above a certain critical concentration (Sparks et al, 1993), convection is unable to keep

the particles suspended, so the particles d e , leaving behind a layer of convecting fluid

vimially free of particles. Discrete sedimentation events are predicted each time the

concentration exceeds the critical value:

where: Tl - temperature of lower fluid layer and Tu - temperature of upper fluid layer.

Asswning p, = 4000 ke/m3 and AT = 1 I the CO of sulfides will be 1.538xl0~. As the

temperatun ditFerence rises the criticai content of sulfide mua be higher and the thickness

of the sediment layer fonned will increase. Using the concentration given above, the

thichess of the layer f o n d by the particles is approxhately 10 cm. if the viscosity of

the liqyid is low enougb, the particles forrned in the upper ôoundary layer are able to

escape fiom the layer and contribute to the o v d concentration of particles in the

convecting magma

Since the thermal and compositiod boundary layers play critical roles in keeping the

particles tiom the circulating fluid, it is important to detennine the thickness of these

layers. Acwrding to Martin and Campbell (1988), and Martin et al. (1987). the critical

thickness of the horizontal boundary layer, before the particles become re-entrained in the

liquid, is obtained by equating the Rayleigh number to 10' and repnsented in equatiod~l8.

At v=100 m2/s, K F ~ X 10.' m2/s, a = ~ x loos F', Cp=l 1 0 0 J ~ C . q=4 w/m2 the cnticd

thiclcness is 3.1 m.

EXPERIMENTAL DATA

3.1. CONVECTION VELOCITIES AND PARTICLE

SETTLING

The main purpose of the experiments was the examination of panicle circulation in a

convecting fluid and the pattern of the resulting sedimentation on the container floor.

The first set of experiments, involving convection with several fluids of differing

viswsities, was conducted using a container with intemal dimensions of 20x 1Ox 15 cm as

shown in Figure 7. Although natural magma chambers have various complicated shapes,

the rectangular shape of the tank was chosen to simplify the simulation. The dimensions

of the tank were large enough to produce the turbulent and laminar unstable convection

necessary for obsetvation of the particle movement. The walls of the container were made

of Xi' thick transparent, acrylic sheets. Scaling lines were drawn on the fiont wall of the

tank at 1-centimetre intervols to provide reference lines on the cornputer screen. Since

most of the floors in magma chambers are inclined to a certain extent, for each liquid

mixture, the experiment was repeated to enable observation of the influence of a sloping

bottom d a c e on the flow pattern. Therefore, a pair of 15' and 30' wedge shape slopes,

made of transparent aaylic sheets, were inserted into the container to simulate the inclined

d a c e forming the base of a chamber.

The experimental fluids were water and water-glycerol mixtures of various proportions.

Glycerol 99+% was used to increase the viscosity ud density of the fluid, without

iduencing the tnnsparency. The density was meamed using a Caiailating Digital

Density Meter PAAR, DM.45 with an accuracy to the five significant figures. The

viscosity of the glycaol-water mixture w u measured using both the Cannon-Fenske

visameter and tabulated values with lin- interpolation taken fiom the Handbook of

Chemistry a d Physics, 56* edition (1975-76) (the probable accuracy of interpolation is

about 1%)). The density increase of the experimental fluid was enough to simulate

sulphide settling in convecting mafic magmas (Ap1300 k@m3). Since glycerol is highly

hygroscopic, sealing the top of the container using laboratory film "Parafilm 'My ensured

a constant viscosity over the course ofthe experiment.

Figure 7. Sckmrtic of the upuimentd tank. ALI dimensions in cm.

The particles used were mica plates covereâ by titanium dioxide, which both increase

density of the particles and reflects light from the fIat surfaces. The density of the particles

was 2860 k@m3. In the experiments, plates were used rather than sphencal particles.

because small spheres cannot be seen as easily as plates. Additionally, smdl spheres have

tendency to cocrgulate, which would affect the results. However, the static charge on the

surface of particles might r d t in attraction benmen the particles thus affecting thek

satling. A series of microphotographs were taken to determine the various sues of the

plates (Appendix). The d a c e ana of one side of a particle ranged from -10 pm2 to less

than -500 & and theu distribution is presented in Figure 8.

To simplify the calculation, it is assumed that the shape of the particles resembles a

square, with a typical edge length mging fiom 3 prn to 70 pm and an wnimed thickness

of 1% of the length. The light sources, which provided illumination of the particles, were

placed 10 cm away from the lefi wall and 20 cm fiom the bottom of the tank. To sirnulate

a modal of a magma chamber which is heated from below and cooled fiom above, the heat

source, provided by a 60W tight bulb, was placed 20 cm from the bottom of the tank. The

initial concentration of the particles ranged from 0.001 1 to 0.00 18 wt % depending on the

volume of the fluid in the container. The low concentration was used for clMty of the

observation.

Figure 8. Distribution of the surface arca of mica plates

The temperatun of the fluid and the surrounding environment was measured continuously

using a K-type thermocouple and digital meter to O.l°C. Since the daily temperature in

the mom fluctuated -5°C in the summer and -2°C in the winter, the position of the heat

source was adjusted to accommodete the fluctuation. The average temperature difference

between the environment and the fluid in the tank (AT) ranged fiom 8-10°C.

The experiments involved the introduction of particles into Plready convecting Buids.

Convection started as soon as the fluids were htroduced into the tank The particles were

mixed manuaily tbroughout the fluid to e n m on initial, uniforni distribution in the tank.

The developing convection and its subsequent progress was observeci using a charged

wupled device (CCD) camera aad was ncorded on a video cassate recorder (VCR). The

experimeat was recorded fior several days to examine the disappearance of the particles by

sedimentation, as well as any other changes in the system.

Tabk 2. Thermophysicd Propertm of glycerin and wrter (Incroperr and DeWitt, 19%)

Glyce rol

290

300

3 10

320

Water

290

300

3 10

320

.49==p[28(293iT- l)]

The initial 20 minutes of the taped experiment was used to calculate the removal rate of

the particles. This time interval was usually initiated as the particles were stabilised in the

fluid. Digital image exposures were taken at 30-second intervals using a Frarne Grabber

SDK and device driver DT3 152. The number of particles in suspension was detennined

both manually counting the number of dots in a representative area of each photograph,

and using the available program ProPlus for image analysis. The manual procedure was

repeated three times to ensure precise particle counts. A representative photograph h m

each -riment is show in the Appendix. The data culled fiom individual exposures

were compiled, plotted and an expoaentid curw was fitted. The fitted curve with the

associated equation was graphically represented in each experiment. The data tiom

manud counting was chosen over that from image anaiysis due to the under-counting of

the particles in the darker areas and variable range of the g r a y d e useâ by the software

affi ing the latter methoâ.

Convection velocities were calculateci fiom successive W e s of the video take. The

distance of the 2-dimensional particle path was measured directiy fiom the cornputer

saeen and scaled using ceference Iines on the froM waIl of the container. For accuracy,

each time and distance reading was taken three times. The directions of velocities were

divided into thm groups: up, dom and sideways. The velocity vector that did not e x c d

45" from the horizontai was assigneci a sideways direction. At any given time, several

values were computed in each direction. The resultant disparate configurations of data

were plotted separately. Furthemore, the pattem of the velocity values in relation to

temporal changes was outlined to enable the practicai application of the experiments to

real-life magma chambers.

3mf.l.lm E m unaI)nis of the convecllon velocily

The objective of the thesis was to p d o n an exploratory investigation which focused on

defining the important ph ysical processes and obtaining measurement s, w hic h

demonstrated the resuits that can be obtained fkom small sale models of magma chamber

processes. Although the experiments were repeated to observe the sedimentation pattern

and particle distribution, the convection velocity analyses were performed oniy once.

Thus, the repeatability of the test cannot be evaluated and it is not possible to make a

statistical maiysis of such a data set. However, the accuracy of measurement of the

various panuneters can be used as a gauge of the magnitude of error in individual

measurements:

Length - measurements made on the monitor were to the nearest 0.5-mm, which should

be compareci with the total height of the saeen of 3 1 cm. Measurements using the Image-

Pro software were to the nearest pixel with the total width of 640 pixels.

a Time - particle velocity w u determined by dividing the measured distance by the time

between the images. The t h e was memured using a chronometer with a precision of 0.01

S. The rding of time wcis perfonncd three times to ensure the rrcuracy of the final value

to O* 1 S.

3.1.2. RESULTS

The purpose of the experiments was to determine the effect of increasing viscosity on the

sedimentation pattern and the distribution of particles in the tank. Six different water-

glycerol mixtures (O, 20,30,50,90 and 100%) were tested.

Since the fiame supporting the container had not yet been fully constructed, the heat

source for this initial experiment was placed on the left side of the tank, approximately 3-

cm fiom the bottom. tn al1 subsequent experiments, the heat source was placed undemeath

the container. Rapid convection developed as soon as the particles were stabilised in the

fluid. The calculateci Rayleigh Number was 8 . 3 2 ~ IO', raiggesting turbulent flow. The heat

transfer obtained using Equation 24 was of the order of 3.6 kw/mz. Although the overall

flow pattern indicates a single cell, the movement of particles was random, as show in

Figure 9 and 10. Due the position of the heat source, a single ceIl developed.

Convection ceil 7

\

HEAT NO convection zone

Figure 9. Scbemrtic of convection cd1 devdopcd in tbe aperiment with 0% 3yœmI. Tbt blrek rrrows indicrtt t k stmumlinm for tbe observed convedon d l .

Figure 10. Front vkw of tôe tank showing the distribution ofthe puticla (Wh dyccrol). Thc lines dnwn on the pbotolnph iUiatrate ddWl in the turbuknt convection. Tbl a m

mpmentcd by t k photo ir 18d3.S cm

The experiments were repeated to observe the influence of the oblique bottom surface on

the flow pattern. Again, due to problerns with the supporting fiame, the heat source was

placed as defuied above. Pain of 15" and 30" slopes, made of transparent acrylic sheet,

were inserteâ into the container to simulate the inclined walls of a magma chamber. The

sloping sheets did not have any impact on the upper seaion of the convection. in

addition, there was no convective movement in the triangular a r a between the slopes

(Figure 9). in the ana of no convection, the particles settM at their terminal velocity.

Figures 1 1 through 13 present dflerent configurations of convection velocities. The trend

curve in Figure 11 indicates the overall tendency of the convection velocity to decrease

with time. This decrease is caused by a reduction in temperature difference between the

experimental fluid and the surroundings. The same is observeci in natural systems, in

which the magma cools down with time und it solidifies. Therefore, fiom this aspect, the

experiment had a practical application to a magma chamber.

The average convection velocity 1 . 7 2 ~ mls was cafculated by applying the equation:

where zWr represents al1 of the convection velocities measund as mentioned above.

Figures 12 and 13 show a plot of convection velocities indicating the wall velocities and

the mean values, respectively, measured at a given time. The velocity rate dong the walls

is slightly higher than that in other directions due to the higher rate of heat transfer. The

slowest movement is detected in the sideways direction.

For most of the convection velocity readings, excluding the wd velocity, mid-convection

iveas were chosen. A pointer was inserted in the middle of the t e and a narrow depth

focus camera was focused on the puticles circulating midway between the pointer and the

fiont waii of the container. Aithough the camera focuses on a very iwow deph range,

the readings could have ban taken nom a volume about 2 cm thick, rmulting in soma

error in the obtriibed data. This problem couM be resolved by taking a large number of

readig (-1000). However, due to the restriction of time oniy a reiativeIy s d l number

of convection velocities coukl be measured, which is only a representative sarnple. in the

fiiture, if the appropriate programs were &en to speed up the process, more readings

should be taken.

Figure 11. Trend in conmtion velority (030 glycerd) with uperimnt durition. The points rrprercnt convection velocity o f rdccted particles. The period between 5 to 18 brs in which

data are absent occurred during the night hourr.

A rida

x

B

Figwe 12* Convection vdocity diribution as r frnction of updment duntioa indicatiag rd veiucity (@% &cemi). Note thit tâe w.P vclocity ir systemrticdy ûighet t h u in ot&r

of the qca.

Figure 13. Convection velocity as a fundion of upcriment duratioa showing distribution of average values for e r h direction (Wh glyctrol).

The shape of particles resembles flakes rather than spheres, and this affect4 their settiing

velocities. The velocity varied as particles changed orientation (Figure 14).

Figure 14. Oblique f d of i plate.

Using r vertical component of the terminal velocity of a thin cimilar disk derived by

Happe1 and Brenner (1%5) the following equation for dculating terminai velocities was

obtaineti

Since the thichess of the plates is significantly smaller than the other two dimension, the

thickness t used in computations was assumed to be 1% of the particle's typical length a.

If one assumes t = O. la then the velocity would increase substantiall y. If the maximum

values of the tenninal velocities are taken into consideration, the angle at which the disk

would be settling is 4k90 and c o s m . However, the plates are settling at al1 angles,

hence to approximate their tenninal velocities an average value was considered by using a

45' angle, and the equation becornes:

In the experiment, the terminal velocities ranged from 3 . 2 9 ~ lu7 to 2.64% 104 mis. The

averaged convection velocity was 1.72~ 10'~. The Parameter S, defined earlier as:

is generally very small for basaltic magmas (lu5 < S < 1). The values obtained in this

experiment ranged from s=l.gl x 10" to S=I. ISX 10''. According to Martin and Nokes

(1989) such low values of S suggest that settling of the smallest pprticles will be effective

only at the bottom boundary of the fluid. The observeci convection velocity was smaller

than the one obtained from W = 0.09rT~a~/h = 5 .76~ 10" by a power of 1 ~ ' . Following

th assumed process (Martin and Nokes, 1989): for particle concentration in magma

chambers the equation for the conservation of the particles is:

with the solution:

The above is valid for turbulent convection which distributes particles throughout the

chamber. Furthemore, the particle loss is due to particles falling to the tank floor with the

terminal velocity. Applying equation 36 to the conditions of the experiment, the largest

mica plates are removed in 2.5 hours, yet the smallest must r e d n in convection for over

80 days (Figure 15). In the calculations, the maximum settling velocity (@=go0) was used

in order to emphasise the particle disappearance. From the obssrvations, however, no

particles were visible aAer 4 days of circulation. Moreover if the thickness of the particles

had b a n 1% of the typical length, the particles would be predicted to stay in circulation

for over 13 days. If the calculateci sedimentation of particles by terminal settling is more

than 83 days, then in order for them to be removed within 4 days the convection must

have provided an additional means of settling.

1 .OE42

Figure 15. Weigbt pemntagt of concentrition of particles in convection as i function of tint rhowing removd of particles as per quition 36 (0% gîycerol).

The experimental obmtion does not agne with the predicted satling of particles using

Equation 36. lWth and Nokes anaiyseâ a case for walls that are perf i ly insulateci JO

there is no heat tramfer. It is the sune for a container of innnite or vecy large lateral

ment. The fIow in this case is a large turbulent zone with a thin, static boundary layer on

the floor. W n g is so effdve that the concentration of puticles is uniform throughout

the turbulent region. Any particle, which fdls into the boundary layer is removed ûom

the system and so represents a loss to the turbulent region. This gives a simple two-

dimensiod conservation equation (with solution shown in Equation 36) for the particles

in that region.

In the case of a finite size chamber heat is lost to the walls by fne convection. That is, a

downward flowing boundary layer carries fluid Born the wdls to the floor boundary layer.

The thickness and volume flux in the wall layer increases in the downward direction by

entrainment from the central zone, which is being mixed by convection. This entrainment

c h e s with it the concentration C of particles. Al1 of these particles are transporteci to the

floor layer where, to the first approximation, al1 settie to the floor. Thus the conservation

equation is:

which has the solution:

where vt is the terminal velocity, v. is the velocity of entrainment, Ar is ara of the

container floor, AT is the total area of the wails and V is the volume of the fluid. Equation

38 shows that the concentration will decrease faster than the value from Equation 36 since

the numerator of the apomnt is much larger. There are two effects, the larger surface

ana and the velocity of entrainment is larger than the fa11 velocity, particularly for mal1

particles.

The entrainment velocity can be estimated fkom the theoretical solution of the velocity

profile quoted by Inwrpera and DeWitt (19%). The velocity profile is integrated to give

the discharge per unit width. An approximate value for the average over the height h is:

The entrainment is independent of the particle size so the entrainment &kt is stronger for

the srnaller particles. Another reamn why the particles settle fâster than predicteâ by the

Equation 36 is that there might be a static charge on the particle surfaces causing attraction

between the particles, increasing theu size and thus af'Eecting the settling velocity.

Figure 16, Number of puticles as a function of time showing removal of particles, krt- fitting (O.! glycerol).

F i ~ n 17. Nuaber of pattiekr u a function o f time sbwing rcaovd of partich without connetigon (0% IEycrrd).

The convection was steady and provided a re-cuculating pattern, which diaiised the

particles and pnvented quiescent satling. An approximation of the removal of the

particles is plotted on semi-log paper in Figure 16. The vahies in the figure are

independent of particle size.

The periodicity of the results in both Figures 16 and 17 could be explaineci by the method

of data gathering, which was perfonmd manually and therefon was subjected to the

human error.

Comparing results from figure 16 with the results in Figure 17, it cm be concluded that

the removal of particles is slightly enhanced by convection. The dope of trend lines in the

experiment with the convecting fluid is steeper (4.1) than in the experiment in which no

convection was involved (-0.07). The precision of the dopes of the curve are within of

5% error. This observation is applicable to natural magma chambers containing viscous

magma, which inhibits sulphide settiing. Convection, therefore, could provide an

additional means by which the particles accumulate at the bottom of the magma charnber.

F i p m 18. Plot of taminil nkcîty of mica fiilpr vvru t k size of the particles including incuaaing perceam of giyceml ln water.

Figure 18 shows the settiing velocity of the particles without their king influenced by the

convection. In this experiment, the height of the fluid was 0.13 m. Therefore, the time

requid for the settling of the smallest particle dong the liquid column was 110 hours

(4.6 days), slightly -ter than it was obsefved in the experiment (less than 4 days)

The boundary layers act like traps that extract the particles fiom the chlating fluid. The

criticai thickness of the boundary layer required to prevent the panicles fiom becoming re-

entrained was calculated to be 0.26 m (Equation 18). This layer thickness was large

enough to allow for an entire mica particle to sale without re-entrainment. If the flow is

not affected by the concentration of particles, then the flow field detennines the

concentration at any given point. Thus, at any point, the ratio of the concentration to the

mean varies only in space. From the observation of the convecting fluid the mica particles

were not distributed evenly in the container but moved in layers of higher concentration.

in other words, they were influenced by the flow

Above a certain critical concentration, convection is unable to keep the particles

suspended. Each time the concentration exceeds the critical value, discrete sedimentation

occun. Applying equation 3 1, the critical concentration for sulfides circulating in the

basaltic magma is 0.015%. Magma chambers with possible economic deposits would

probably have sulphide concentrations higher than the critical concentration. in the

experiment the Ce is 4.055%, which is below the initial concentration of particles.

Therefore, the CO nducted tests analyzed conditions that are applicable after discrete

sedimentation had occurred in natural magma chambers.

Sb t2b 1. Mltttum of -ter rnd NICI

This experiment was design to observe the influence of increased density without a change

in viscosity. Therefore, 1 1% NaCl solution was used.

P, - 2860 kg/d ATi 10°C, ATa- 7.2"C b- 1154 k&m3 Co - 0.0013%or 3.8~10" gll Ap - 1706 k g / d -7 2

KT - 1-41x10 m /s NaCl (0.93 kg): NaCl solution 1 1% a - 3.60~ 104 1 PC

-7 2 v = 7.0~10 m /S Wi - unluiowtl. WC - 4.17E-02 d s -3 3 Vp- 2 . 6 ~ 10 m , h = 13 an R. -5.14~ 10"

T,- 3 1°C, T, -21°C

A heat source was placed on each side of the container bottom. Four convection cells

developed as shown in Figure 19. The uneven placement of the heat sources resulted in

the left ce11 becoming larger than the right one. The -riment was repeated twice to

observe the influence of sloping surfaces on the convection pattern. In the area between

the slopes, no activity was deteded, just as had ban seen in the former tests.

Figure 19. Schematic of the convection celb, a) fiont vkw, b) top view.

The calculated Rayleigh Number was 5.14x10', slightly lower than in the previous

experiment (Ra = 8.32~ 1 os), due to lower value of ATn=7.2"C. The heat transfer q was

2.1 7 kw/m2. Because of a recording error, the averaged convection velocity could not be

detemineci in al1 of the experiments. However, the convection obtained fiom calailation

of WC = 4.17E-02 mis was similar to that in the former experiment (W,=5.76E-02 d s ) .

The critical boundary layer thickness was 0.03 mm, sufficiently large to prevent re-

entrainment. The initial concentration was 0.0013% which was significantly lower than

the critical concentration for the experiment 0.06%, therefore discrete settling did not

ocair. The settling velocity showed a small decrease fiom the previous experiment,

ranging fiom 2.59~10~' m/s to 2 . 0 7 ~ 1 0 ~ d s (3.29~10~' ds to 2 . 6 4 ~ 1 0 ~ d s ) . The

decrewe in the settiing velocity was caused by the increase in the density of the fluid. The

particles therefore stayed in circulation slightly longer.

The purpose ofdiis experiment was to observe the influence of a small increase in density

and viscosity on the sedimentation pattern and distribution of puticles in the ftow.

Figure 20. Front vkw of tbe tank. Convection pattern, the unes -ment only tbe rpproximite path o f partickr (20% giyrud). Tbe hotizoatr~ liaa are sprced i t 1 cm

i n t d and the photogrph rcprcscnb .rra of 9.Sk9.S cm

Figure 21. Front view of the tank Convection with tbc insertion of lSO dopa (20% Ilyœrol). The a n a show approximatt moveaciit of pdda. Tbe uu repmcnted by the

photo u LM0 cm.

Pigure 22. Front v i m o f tbe tank Cîoseup to the lSO skpe (2OH giycerol). The lines show the ovecd niovement of the p ~ * c I m with indication of eûôies. The uea represented by t k

photo ir 9.67d0.33 cm.

Figure P. Front vim o f the tank. Convection pattern with t k insertion o f 3W dopa (2Wh glyarol). The liaa show the o v m l movcwat of partides. Tbe uei npnruitcd by the

photo ir 1O.î.sl0.1 cm.

A single heat source was p l a d under the tank as shown in Figure 7. The calculateci

Rayleigh Number was 7.52x10', indicating unstable laminor flow, and the heat ir~nsfer

was of the orda of 2.2 kw/m2. The overall flow pattern, with and without inserting the

sloping surfaces, developed as indicated in Figure 20. The flow is turbulent with many

eddies; therefore lines were drawn to emphasise the main course of particle movement.

There were four distinctive cells. However, the convection close to the sidewalls was

airbulent and the direction of the flow movement changed erratically. Both Figures 21

and 22 illustrate the convection direction in the container with the insertion of 15" slopes.

The flow is very turbulent but the overall pattern can be discemed. Similady, Figure 23

shows the convection pattern with the 30' slopes inserted.

Figure 24. Trend in the convection veiocitia (2- gîyarol) ir function of the apenment duration. The long intewib without data indicite the nighttime ptriod of the experiment.

Figum 24 through 26 represent different conAgurations of convaion velocities. The

velocity values decreased with time as indicateâ by the trend line in Figun 24.

Convection is proportionai to the change in temperature of the qstem. The dope of the

trend m e is -0.0223 which is smailer than the trend nom first experiment (-0.0382),

wbich indicates bat the temperature differences towards the end ofan expairnent did not

Vary extensively fiom the initial AT. The lower dope in this experiment was cwsed by a

Figure 25. Convection vdodty distribution u r functioli of uperiment durition showing pir t icb nioving in dl three directions (2096 Jycerol).

Both Figures 25 and 26 illustrate values of the coavecting velocities measured at a given

time. The averaged convection was 4 . 0 8 ~ 1 0 ~ d a , lower thaa thet calculated value of

1 . 7 5 ~ 1 ~ ~ d s by a fiictor of 100. The mean values shown in Figure 26 were deterrnined

using Equation 32. The particles rnoving in the downward direction were moving slightly

faster than the particles moving in the other directions, probably due to the additionai

eff- of the settling velocity.

In this experiment, the settling velocity ranged Born 1.1 sx IO*' to 9.24% IO-' m/s. assuming

@=4S0. The values ofthe parameter S varied ûom 2 . 8 2 ~ 10" to 2 . 2 6 ~ WL, suggesting that

the largest particles were easily removed from the fluid. According to the settling velocity

calculated from Equation 34. the smallest particles require 241 hours to senle completely

(-10 days). From observation, however, no particles were visible after 5 days of

circulation. Again, the accelerated settling of the smallest particles could have been due to

an increased dze resulting ftom the static chPrge on the particle sudixes (attraction

between the particles).

An approximation of the removai of the particles is plotted on semi-log paper in Figure

27. The addition of 200/0 of glycerol increased the viscosity by 137% and caused a

decrease in the convection velocity of 76%. However, the slope of the trend curve

remainad similar to the slope obtained in the 1000!% water experiment with a value of

approxirnately -0.1 as measureâ. The slight increase in viscosity did not have a major

impact on particle remowl.

The critical thickness of the bottom boundary layer was 0.34 mm, which was suffcient to

keep the particles from bccoming mentraineci bythe cuculating fluid. The wall boundary

was approximately 0.6 mm thick The vertical Iayer, unlike the horizontal boundary layer,

did not wntain as many particles. Particles trapped in the ôoundary Iayers settled with

theu hl1 terminal velocities. However, ifthey am close to the margin of the layer they

could be re-entraiiiHi in the convection as soon as the cntical thicbiess of the layer is

aceeded. Yet, extra trapping by the wali layen is not an adequate explanation for the

observeci fut me of settiing. As the vertjcal bodary incread towards the bottom of

the tank, the circuIating fiuid moved away h m the walls, affecting scdimeatation on the

floor (Figures 28-30). Thus, the particles settled, sliding away Rom the sidewalls by 0.93,

1.15 and 1.63 cm for exphment with 0°, 1 S0 and 30° slopes respectively. The maximum

sedimentation occurs in the middle of the bottom d a c e where the convection flow

direction was upward.

0.0 20 4.0 6.0 8.0 10.0 12.0

tim [min]

Figure 27. Numkr of parti& as a functioa of uperinwnt durrtion ihowing removil of particla cdculated miaurlly ( 2 W glycerol).

Wit h increasing visw sity, the wnvecting velocity decrused, reducing turbulent rnixing in

the tank. As a result, Iayers with a heavier concentration of particles became more

apparent. The critical coucentration increased to 0.061 percent. Again, there was no

discrete sedimentation. t

Figure 28. ~ m e ~ ~ t a t i o n pattern it the bottom o f the tank The d u k regions reprrrent ucu with no pUtibdes indicatimg rüding of the pytickr rriy Imm the w d k The photo

SLOWS the top vkw of the tank with the inside dimension ZOIlO cm (2û% gîycerol).

F i i r e 29. Sedimentition pattern on tbe bottoi of the Wt with insertion of 1P slopes. The darket repment the ut- with no putKies indicatiog riiâing froa the willr (2-

giyœml). The photo sbows the top view of tbe rulr witb dimesriona 2Q10 cm.

Figure M. ScQcitation pattern on the bottom o f the tank 4th insertion of MO slopch The &rkr mgiona repment uur rvitb no puticles. Top view of the tank with inside dimension

zoitlo cm (20% gljmml).

As indicated in the previous experiment, the objective was to obsme the influence of

gradually increasing density and viscosity on the sedimentation pattern and distribution of the

particles in the flow.

pp - 2860 kg/m3

pW- 1077 kg/m3

Ap - 1783 kg/m3 -6 2 v - 2.45~ 10 m /s

3 3 Vf-2.2~10 m , h-ll cm

Te 35.3"C

Ti - 26.S°C

ATi - 8.8OC, AT.-1 1 O C

Co - 0.0013% KT - 1 . 2 6 ~ W7 m2/s

a - 3.997~ 104 1PC

W. - 7.1~10~ m/s. WC - 1.77~101~ m/s

Ra- 1.13~10~

The experiment was set up as shown in Figure 7. The Rayleigh number decreased by 13.6%

compared to the 10W water experiment. Nevertheless, with Ra = 1.13 x 10' rapid convection

developed as soon the particles were introduced into the tank. Although some of the

parameters changed, the difference between the temperature of fluid and the surroundings

was large enough to produce turbulent movement. The values of q were also reduced. Heat

transfer was 1.92 kw1m2, which was 45% less than in the first experiment.

A typical convection pattern is shown in Figure 3 1. The image was refined by removing the

shadows of the air bubbles fiom the container fiont w d . The flow is very turbulent and the

particle movement changed direction continuously. In order to present the overall motion,

the direction of particle movement was measuted at each reading of the convection velocity.

The nsults were plotted and a single velocity vector for each tirne interval was assigned. In

Figure 32 meamlines of convection were drawn following the direction of the vectors.

Although thae is some turbulence shown, four distinctive cels were visible throughout the

experiment. The le& ce11 is significantly smaller than the right one due to the position of the

h a t source. Figure 33 shows the effects of 15' slopes on the convection movement.

Figure 31. Front v*n of t h tank showing convection pattern. The lighter .MI mpresent bigh concentration of particks (3û% giycemI~. The fiiit horizontai lhrr iadicate lem intewd with

tbe totil ana rhown 7.517.6 cm.

Figure 32. Vecton and rtrrimlinta of the convection (103C gîyceral).

Figure 33. Convection pattern. V i t of the froat w d l witb the insertion of lSO SIO~S. The lightet indice higber concentration of partickr. Tlw uea repraentcd by the photo is

9.os9.7 cm (30% gIyCeml).

The values of convection velocities are presented in Figures 34 through 36. Figure 35

indicates decreasing velocity with time. However, as the temperatures of the surroundings

fluctuated substantidly (-7OC) during the daytime, it was dEicult to control AT.

Consequently the convection velocity did not decrease with time as much as in the pievious

experiments. The trend cuve is quasi horizontal with a slope of -O.OO2S.

The averaged velocity of cirailating particles was higher, 7.1 x 104 mls, than in the prior tests,

since the AT was larger by 2OC. As in the experiment with the 20.h glycerol fluid, the

calculated ~ = 1 . 7 7 ~ 1 0 ' ~ was 100 times higher thm the mean convection fiom the

observation.

Figure 34. Convection velocity distribution as function o f experimeat durition showing average values for erch direction (Wh glycerol)

Due to an UmuK in the viscosity by -5û%, settiing velocities slightly decreased cornpand

with the 20"h glycerol solution. They ran@ fiom 5 . 2 8 ~ 1 0 ~ to 2.64~ WS mls for the smailest

and largest particles respeaively. Similady, the parameter S was reduceâ to 7 . 44~10~ and

3 -72x1~' h m 2.82~ lo4 and 2.26~ 10" for 3ü!! and 2 W @y& rrspeaively.

Figure 35. Convection vdoety u i function of expriment duration showing trend in convection velocity (30% glycerol). The t m d c u m is quasi-horizontal suggiting thit AT did

not viry drring the course of the expriment.

Figure 36. Convection nlocity âistribution u a functbn of upaimcnt durition showiag the thme diffienat directions o f Ut flow (30% giyccrol).

Based upon the settiing velocity considering fa11 of the particle at -5' and the height of

the fluid 10 cm, the srnallest particles require 526 hotus (22 days) to settle. A distinctive

decrease in particle concentration was noticed in the experiment after 20 hours dconvection,

and the total particle removd ocaineci after 10 days fiom the beginning of the experiment.

Again, the surface static charge could affect the size of the particles causing accelerated

settling.

Figws 37 represent approximate particle disappearance within the first 12 minutes of the

experiment. The dope of the trend curve is in order of -0.062, which indicates slower

removal than in previous experiments. The removal may be affected by either stronger

convection preventing settiing or increase in the fluid viscosity that caused particles to

remain in the convection longer.

10000 :

Figure 37. Numkr of partich u r funbion of tirne showing nmovrl o f particles. Best fitted (Wh glycerol)

The criticai thickmss of the horizontai bounâacy layer gadually increases with the viscosity.

It was caiculated to be 0.38 mm, 0.12 mm larger dw the layer in the lWh water

experiment. Similarly, the wail boundary compand with lW! water inaeased by 0.096

mm. Howem. the vertical bouadary layer depends strongiy on convection velocity. In this

experiment convection is sienificuitiy hi* than in the 2û?h glycer01 experiment resulting

in a decrease in the thickness ofthe boundary laya.

Figure M. Top vkw of tbt contiinet with inside dimensiom of20.10 cm. Seâimentitiion pattern on tac bottom of the tank (3û% giycerol). 'Cbe duk regions npntcnt ireas with not

partiele accumulation indicrsing rliding fmm the wdls.

Figure M. Top vkw of the conbiwr wîth inaide diasions o f 2ûsîO cm. Scdiruntation pattern on tLr botton of the tank witb 19 rbpa (3û% glycetoi). The d w k mgions repnicnt

uerr ritL no putidcl Miciai( clîûiy fmm the wiUr.

Mer several hours of convection, a pattem ofsettling was observed at the bottom of the tank

(Figun 38). Note the triangular shape close to the container corners. As the rate of particle

dement slowed down, the pattern became more clearly defined. Air bubbles coverd the

bottom of the tank. The bubbles were carefully removed, using a needlepoint metal r d . in

orda to determine theu effect on mica sedimentation. No particles were visible in the bubble

area, which implies that the bubbles were obstnicting the settlement of the particles. The

sliding of mica âom the sidewafl was 1.36 cm for no slopes and 1.6 cm with lSO slopes

(Figure 39).

The objective of this experiment is to observe the sedimentation pattern and particle

distribution in 50-50 water-glycerol solution.

The experimental setting follows the schematic in Figure 7. The Rayleigh Number 6.14

xlo7, indicating that the convection was lamina but unstable. Heat transfer d e c r d to

1.63 kw/m2. A noticeable upwird moving plume developed in the container (Figure 40).

Due to the turbulence the plume ww not stable. Ahhough the overdl flow was more

stabilised than pnviously, eâdies were present throughout the tank. The general motion of

the fluid is indicated in Figure 41 where the direction of the particle rnovement is plotted as

path lines. The four of the convection a l 1 were symmctncai.

Figure 40. Fmnt vim of the tank showing convection witb no slopes iarcrtd (503C glycerol). Tbe iighter m u iadicrte bigher concentration of particles. The ire. represeoted by the photo

k 9.3s9.4 cm.

Figure 41. Plthlines of tbe convecting particles (50.k giycerol)

vùocity Udicatîng th& tûe AT did lot v u y subitana'rlîy with t i a t (Wh dyarol)

Figure 43. Convection vdocity distribution as i function of uperiment duration indicating partick movcacnt in al1 three directions (SOW glycerol)

Fiaure 44. Convection vùocity pmfik u i functioa of aperimcnt duration r k w i y mean vdum for a b direction ( S m glyœmi). Tbt dormird i d m g pmtkkr show highcr vdua

for most ofthe mdinp.

Figures 42 through 44 represent the convection velocity distribution. The trend cuve in

Figure 42 is aearly horizontal suggesting diat the temperature differences did not Vary

signifiuntly with tirne. Hence, the curve is quasi-horizontal with the dope of 4.002. The

averageâ velocity of the convecting fluid was 2 . 2 ~ 1 0 ~ d s , lower than velocity calculated

using equation 25, which was WC = 1 .09~10~ ds. If ATa is kept at the same level,

convection should decrease as the viscosity increases. Velocity of downward moving

particles was slightly larger thaa particles moving in other directions (Figure 44).

Mica flakes settled with velocities of 1 .97~10~ and 9 . 8 4 ~ 1 0 ~ for the smallest and largest

particles respectively. The panuneter S varied fiom 8.9% 100' and 4.48% 10". Convection

had the largest effect on settling rate of the smallest particles. Al1 large mica settled down

within the first 24 hours. Very few particles were present after 8 days of the expenment.

However, due to time constraints, the total nrnoval period was not determined.

Io00 -

Figure 45. S.udly crlcrlateâ rcmovd of puticles (Sû% giyœol) as a hinction of tinte. Since tbe p&ck% ue rtn,ngiy infiuenced by tht flow, 8 priodicity of t& data points is obsetved.

Disappearance of the particles is presented in Figure 45. The calculations were performed

for the data gathereâ within the first 20 minutes of the expriment. The slope of the trend

curve is mon horizontal than previously (-0.034); still sufficiently steep to indicate quick

settlement. However, the concentration of the particles was not evenly distributeci

throughout the tank. which may account for the several lows and highs on the graph. This

periodicity is caused by the convection, since the particle distribution is strongly influenced

by the flow. With time, the trend w e flatteru as the concentration of mica decreases.

The thickness of boundaries increased to 0.45 and 0.53 mm for horizontal and vertical layers

respectively. With the incream of the thickness of the layer, the particles have a greater

chance to settle with their full terminal velocity. Discme sedimentation will occur if the

concentration of particles exceeds 0.074%.

With increased viscosity, the pattern of settling is very prominent resembling a "butterfiy"

(Figures 46-48). The corners of the container influence the flow inducing viangular shape of

the sediments close to the edges. The angular area is more pronounced with steeper bottom

walls. The sliding of the particles deposition fkom the walls i n c r d to 1.6, 2.0 and 2.74 cm

for the experiment with O", 15" and 30' dopes respectively. Again, the majority of the

particles concentrate in the area where the flow was moving away fiom the bottom surfiace,

directly above the heat source.

Figure 46. Top view of tbe container with insi& dimenrions of 2O.LO cm. Sedimentition pattern on the bttom o f the tank (!Sû% dyramI). Tôe d u k r regions repnrcat uctl with no

puticka.

Figure 47. Top view of tbe contuwner with the insiâe dimensions of U h l O cm. Wimentrtion pattern on tbr bottom of the tank with 19 kpes (JOH *mi). Tht duk regioar - m o t

vcir with w pdckr .

Figure 4&. Top view of tbe tank with the incide dimenaions of 2OxlO cm. Sedimentition pattern on the bottom of the tank with JO0 a i o p (WB6 dyceroi). 'Che &tk rrpDoas repnvnt rrcu

with w particles.

3. f.2.5. Mi'um of fO% water and 80% gI 'emI

Higher concentration of glycerol was chosen for this experiment to observe its influence on

the particle distribution and the sedimentation pattern.

The heat source was placed beneath the tank, 2 cm fiom its center to determine the influence

of its position on the panicle settiing. The calailateci Rayleigh number 4 . 5 4 ~ 1 0 ~ is

sigaificantly smaller than in previous experiments yet the flow was still turbulent. Heat

transfer decreased to 565 w/m2, which represents oniy 2Vh of q l m ~ wm and 35% of

qs-. The reduction is caused by the change in the fluid properties since the AT. was

maintained at a level similar to that of other expehents.

The convection flow pattern was well defined with eight main cells visible. The cells are not

symmetncal; the four cells on le& side of tank are smaller due to position of the heat source.

Figure 49 illustrates that the particles were not unifonnly distributed tbroughout container,

but w e moving in layers of heavy concentration. Very few plates are visible in the center

of the rising plume (dark areas in the photo). Similarly, ûarker aines are present both close

to the w d boundary and at the bottom corners. One of the reasons there were fewer particles

in the center of the tank is that the mica flakes were deposited directly underneath the rising

piurne.

Figure 50 shows the cowection der 5 days. The particles are less evenly spread and the

layers of heavier concentration are mon distinct. The warm fluid aggregated in the center of

th tank creating a diamond-outlined ma, which wntained fewer particles. This ara is produced by the convection cells ~eparation occurring in the middle of the container height

and length. Strdines in Figure 51 are drawn accordingly to the dinaion of the velocity

vectors.

Figute 49. Front vkw of tbe tank showing distribmtion of particies in the containers (90% &&OI). Tk lighter uru indiate higber coaccntration of puticles. Tbe uu rcpmented by

tâe photo is 8.3s9.0 cm.

Fime 50. Front view o f t k tank C o d o n pattern rfter S days dcirculrtion (9- glyceroi). Tbc ami repnreated by the photo L 11.Sxî13 cm.

Figure 51. Vecton rad path üna of pirtick movement (9030 glycerol). Som of the vecton were ignored; theretoir, the lines represent only the rpproximated stmmlines.

Figures 52 through 54 show diierent configurations of convection velocities. The trend

curve in Figure 52 has a gentle negative slope denoting a decrease in the AT with time. Since

most of the readings were pafomed at the edge of the horizontal boundaries, the highest

values of the convecting velocity were reached by the particles moving sideways.

The average convection velocity was 1 . 7 ~ lo4 rnls. This was only slightiy lower than in the

experiment with 50% giyceroi, suggesting thst the funher addition of glycerol had only a srnail efféct on the convection velocity. However, the decrecw in the calculateci velocity

~ 4 . 3 3 ~ loo3, which is strongly influenced by Ra, indicates that the prdicted velocity should

have ban affécted by the viscosity change.

Figure 52. Convection vdocity as a function of experiment durrtion showing trend in convection (90°h glycerol)

Figure !ü. Conmgon vdocity dibributioi as a Laetion of amacnt duration showing vi lua for uch direction of the flow (w giyan,I).

Figure 54. Convection vdocity distribution as a function oluperiment duration showing i v e r y c d vdue for eich direction (9ûV0 glycerol).

Mer 14 days the heat source was removed in order to reduce AT to zero and stop the

convection. Figure 55 shows the distribution of the mica plates following three days of no

convection. The particles were stagnant and f o d long horizontal layers. Convection cells

were absent. The difference in panicle concentration, both throughout the tank and on the

floor, was not visible. By applying the heat source, convection restaneci resulting in a slight

decrease in mica concentration.

Settling velocities ranged fiom 8 .69~ 1 ~ " to 4.35~ 10'' d s (0.0001 to 0.1 pds ) had a

decreasing rmlt on values of parameter S, which varied fiom 5.1 1 x lo4 and 2 .56~ 1 oo3. According to W n md Nokes (1989), such low parameters indicate that the settling will be

effédive only at the horizontal bundary layer. From obsenntion, approximately 40-SM of

the mica settîed after 5 days. From the puticle size distribution in Fi- 8, 35% of mica

plates are larger than 1 p2. Thus, within the fint few days almost dl of the particle with an

a m -ter than 1 p d were probably trappeci at the h m ofthe tank.

The slope in Figure 56 indicates that the particles were removeci as fast as in the previous

experiment. Yet, the curve of particle concentration is oscillating due to movement of mica

in layers. The readings were taken within the first 10 minutes of the experiment, hence the

curve in Figure 56 most ükely represents removal of the largest particles. if the time of the

readings were extended the trend line pahaps would be more horizontal. Hence, it is

difficult to prdct if the slope was & a m correctly. The critical thickness of the horizontal

layer was 0.98 mm, double the vaiue of the SV!% glycerol fluid. It occupied 10% of the liquid

height denoting that moving particles were easily trapped inside the tayer before it became

unstable. The vertical boundary was 0.475 mm and critical concentration was 0.084%.

Figure 56, Nuiber of putickr as a fuaction of time showing removal of particles calculatiig uaing ProPlus (W.! ~lycad) .

The e f f i of 15' and 30' slopes could not be detennined since the density of the acrylic

sheets was smaller than the density of the fluid and they kept floating on the top of the fluid.

The shape of the mica sediments resernbled a "butterfly" anaiogous to lower viscosity fluids

(Figure 46). However, the overall pattern had smooth, circular contours; no angulu cornen

were visible (Figure 57). The heat source was purposely placeci away fiom the container

enter to con6nn bat the higbest deposition of particles occm directly under the upward

moving plume. The accumulation bsd a sienificant tbickness of 0.8 mm and it was divideâ

into k e e main elliptical ueas. The division was cwsed by the separation of the upward

flow into four diffient convection celis-

Figure 57. Top vkw of the tank with the inai& diaenrions of #hl0 cm. Scdimentation on the

In this expaiment, 10W of glycerol was used to observe the particles movement and

sedimentation in the highest viscosity (in this research) fluid.

pp O 2860 k@m3 ATi - 12.0°C, ATa- 9.5 O C

- 1260 kg/m3 Co - 0.0014%

Ap - 1600 kg/m3 -8 2 KT-9.8~10 iîî /S

-4 2 v - 2.76~10 m /s a - 4 . 9 ~ lo4 OC' -3 3 Vp2.2~10 m , h- 10 cm Wa - ~ 2 x 1 0 ~ m/s.

T, - 4O.O0C WC - 1 .77~10~ m/s

Ti - 28.0°C Ra - 1.8xlo6

The experimental setting was changed to accommodate a fluid injection test. The schematic

of the aperture used is outlined in Figure 72. The Rayleigh number of 1 . 8 ~ 1 0 ~ remained

similar to the 90% glycerol fluid. The flow continued to be unstable laminar but the

turbulence was not as visible as in lower viscosity fluids. The heat transfer was reduced to

420 w/m2, approximately 12% of the q IOOS W.

The convection pattern is illustrated in Figure 58. Note that the heat source is tilted to the

lefi causing the observai shift in the upward movement. in Figure 59, streamlines of

convection were drawn complying with the direction of the velocity veaors. The 15' dopes

were built into the tank together with the fiinne1 entq at its bottom. The heat source was

adjusted to increase the tempenture in the fbnnel in order to simulate a magma chamber.

Subsequentîy, the convection pattern changed as shown in Figure 60. Within a few hours,

mica particles starteci to accumulate in the layers separating the alls. Five main convection

ceils developed four in the main tank and one inside the fùnnel.

There was a visible diffierenœ in the number of particles cuculating in the main container

and the fuanel. Only a small amount of the mica was circulateci in the fime1 due to the

upward movement of the flow, which infiuenced the deposition at the bottom of the funnel.

Figure S. Front vim o f tbe tank showing diatributiw o f particies in conncting muid (1Wh gtyceroi). ûnîy tk main ucr of tk container is shown (without the funnel). Tbt liahter

rrpOas indice bighet conctitrrrtt*oa of mica. The u# repnwateâ by the photo ir lm cm.

Figure 59. Vecton and stmmlinm of convection (1007C giycerol).

Figure 60. h a view of tbe tank skwing c o d o n 24 Ln h m the start of expenmcnt. Tbe üght 8- hdicate Lfih concentration of mica s m n g .rcumuhlion o f p.Cttcks in tbe

bounduy layen k h a n and m u i d convtctioa cdb (1- giyccnl). The ami rtpmtnted by Ut photo U 9.7s9.7 a

Figure 61. Convection velocity rr 8 funetion of uperiment durrtion showing trend in convection velocities (1ûûS glyctrol)

Fiwe 62. Convectian vdocity distribution u fundon of upcrimtnt duration rhowing vdwr for eacb direction of tbe I b w (100K gîycerol)

The values of convection velocities in the experiment were plotted in Figures 6 1 through 63.

The data in Figure 61 iadicate a decreasing trend in the convection strength with the slope of

4.0075. The slope is slightly steeper than in previous experiments as the AT cbged âom

an initial 12O to S0 toward the end of the test. The average convection velocity was l.2xlo4

O down

Figure 63, Convection vdocity distribution u i function of uperiment duration showing iveraged value for eacb direction (100% glycerol)

With the addition of 1% of glycerol, the satling velocity decreased slightly compared to

that observed with the 900/. glycerol mixture ranging 3.59% 10'" to 1.87.1 x IO-' d s .

Similarly, the pafameter S varieci fiom 2 . 9 4 ~ 1 0 ~ to 1.47x10", which is about half of the

values of the -riment with Wh glycerol.

The experiment was wnducted for over 20 days and a signifiant amount of mica was

concentrateû at the bottom of the tank. After 9 days of observation, the heat source was

rernoved in order to determine whether the convection had an effect on sedimentation. As

predicted the particles did not senle faster, but were awpended in the fluid. One of the

possible explanations is that by lowering of the temperame the fluid viscosity increases, thus

Sffectillg the particle senling.

Figure 64 shows the removal of particles in the experiment. The values were nonnaliseci to

avoid high maximum and minimum in the function. The nsult indicates a smaller slope but

still large enough to provide settling of the particles.

Figrn 64. Numkr of particles u a function o f time showing removd of particles (IWh glycerol).

The criticai thickness of the boundary was found to be 1.37 and 0.75 mm for the horizontal

and verticai loyers respectively.

A very distinctive pattern of d i n g developod during the expriment (Figure 65). Most of

the particles were concemted mund the fumet and in the corners of the nimel's floor. A

aiangular depoait close to the &me1 entry had o thickness exceeding 1 mm. The sliding of

the purticles fiom the walls was -3.5 cm The floor of the container was scntched by

abrasion to provide MW tnps for the partictes to be caught within. As Figure 65 indicates

accumulation indeed o c d inside the -0.3 mm thick dits.

Top vWiv of the conbi*ner with the iiiide dimtndooa of M O cm. M n in the bottor of the tult and indde the Jib (1- giyarol). Tbe ligùtct

indicate uur with bigûer concentrition of m i u

rti ion

3-1.3. SUMMARY OF RESULTS

The results of the settling and convection experiments are summarized in Table 3 and Figures

81 through 85 are the gtaphical representations. The rwlts fiom the experiment with 30?4

glycerol mixture were affecteci by the higher AT and therefon caused an anomaly in the

observed results.

Tabk 3, Vlirirbks and resulb

Eiqmiment In% 11% 20% 30% 50% 90% 100%

/ACopcify water NaU glyewl glyerol glyfad glyeeml g & c d

Initiai 30 Temp. [COI

In order to include experiments conducted with NaCl solutions in the graphical

representation, a glycerol content of 3% glycerol was assigned to the results. Excluding the

value for 300/r, the exponential decrease in the Rayleigh nurnber is consistent with the

increase in viscosity (Figure 66).

O 20 4 0 80 80 1 O0

% o f glycerol

Figure 66. ûecreue of Ra with incnur of viscosity.

Likewise, the velocity W decreased as the concentration of the glycerol in the water

increased. The addition of 20% glycerol to the water resulted in a dramatic decrease in

convection velocity (87%). However, further increases in viscosity had relatively minor

effect (Figure 67). The change of viscosity between the Wh and 90% of glycerol was of

order lu2 but the decrease in velocity was ody 22%.

Figure 67. Cbaage in the convcctioa velocity with addition of giyctrol.

Furthemore, heat transfer was consistent with the change of the Ra number (Figure 68).

However, the AT was only 7' C in the experimeat with NaCl solution therefore, ~N.CI was

slightly lower than 9 2 ~ . The decreased was also observed in the results for Nusselt numbers

(Figure 69).

% of g lycerol

Figure 68. Decrease in heat tram fer p.

O 20 40 60 80 1 O0 W of glycerol

Figure 69. Change in thermal Nusselt numkr Nu=.

Excluding values for 3Ph glycerol, there was a steady increase in the thickness of the

verticai (dwd = "6") and horizontai boundacy layas (de = "6"), and critical concentration

(c) (Figure 70). Cntical concentration ocaus when thae is a large number of particles,

which cannot be supported by convection md most of these d e rapidly. The typid length

of mica plates was nom 3 p ta 70 pm and the lowest value of the boundary layer before it

becarne unstable was 0.26 mm (260 pm), indicating that there was sufficient space for a

particle to d e at its terminai velocity. The plates moving dong the upper part of the

bowidary were re-entraineci in the flow. The O. 1 g of mica ocaipies a volume of 0.035 cm3

(35 mm3), hence it is possible that al1 of the mica could be held within the boundary layer

without becomiag re-entraineci in the convection flow.

Figure 70. Change in the boundary Iiyen and critical concentration with the viscosity.

For basaltic magma chambers 1-km high with typical thermal parameters the cntical

thickness is 3.1 m. The thickness wouid diminish as the volume of the circulating magma

deaeases due to the crystallisation at the charnber floor. However, Worster a al. (1990)

puggested that by increasing the heat transfer to the roof, the height of the chamber would

increase due to partial melting. The increase in vertical dimension results in increase of

Rayleigh number causing vigorous convection Neverthelem, a boundary this thick would

provide suficient space for sulphide accumulation. This is most Iikely to occur diredy

above the heat source that in magma charnben is representeâ by the feeder opening as it was

observeù in the sedimentation pattern during the experirnent with 1Wh ofglycerol.

In the acperiments, the thickness of the horizontal boundrry layers increased substantidly

with fluid viscosity. The h c m e in the viscosity reduccd the rate of convection in the

chambas, however the larger boundary laya ptovided the means for the particles to escape

fiom the flow and settîe at the floor. If the viscosity is high enough it m y pnvent settling of

dphide droplets that are trapped inside the boundary Iayers at the roof and between

convection cella. As a result, upon the cooling of the magma, layers of more disseminated

sulphide could develop throughout the chamber.

Disme sedimentation occurs when the concentration of crystals e x d s the critical

concentration c'. For sulphides in the basaitic magma with the temperature differences of 1

K between the upper and lower fluid layer, the concentration is ~ 2 0 . 0 1538% (equation 3 1).

Usually, the concentration is higher then this critical and there are many other crystais (i.e.

olivine) that accelerate wilphide settiing.

In fluids containing a concentration of crystals below the critical value, Martin and Nokes

(1989) suggested that senling occur according to equation 36. However, particles in al1 of the

experiments were removed faster than predicted âom equation 36 implying this equation

does not apply to my experiments.

The thickness of the vertical boundary layer usuaily increases as the flowing fluid moves

towards the floor. The thickness a h increases with increasing viscosity. Flow close to the

boundary carries a large amount of the mica. From the observation, in the area at the bottom

corners of the tank there were only a few particles present. It appeared that the particles

followed the convection movement and settled when the flow approached the horizontal

boundary. As the vertical boundary grew with the viscosity, the sedimentation pattern was

aff ied. With increasing amount of glycerol the tendency for deposited particles to slide

dong the floor in the direction of movement of the fluid increased significantly. Table 4

summarises the offset.

Applying this observation to magma chombns where the viscosity is much higher, crystals

and sulphide droplets would more likely deposit close to the ana where the heat source is

placeû (tieder) than adjacent to the chamber walls.

It w u detected that viscosity bad a major effa on the o v e d pattern of settiing. Whenever,

the viscosity wu, low (Le. or 200? glycerol) the particles spread out over the entire

bottom of the container with no distinguîshable areas of concentration However, in

experiments with higher glycerol percentages the arrangement of mica plates resembled a

"bunerfly" with the area of maximum concentration lying directly above the heat source.

This could be explained by the increase in thiclcness of the boundary layer around the area

over the heat source, where most of the particles Canied the flow by were forced into the

layer. Additionally, the maximum deposition anss were divided into section by the

convection cells (Figure 57). There were et least four different cells present at bottom of the

container manging the particles in the ovd s b p e regions where the cells were separating.

Tabk 4. Sliding of the particies i n r y from the container's wdls.

From the experiment with 100% glycerol, it is clear that if there are cavities on the t'foor on

the magma chamber they will provide natural mps for the settling crynals. Unless caught in

those nanird cracks or embayments, the sulphide droplets will deposit close to the entry of a

feeder dyke, which is likely to be the major source of heat entering the chamber.

Figure 60 shows tbat the mica particles were following the boundaries of the convection

cells, concentrating in areas between cells (outer boundary layers). Additionally, the plates

were not domi ly distributed but tended to concentrate in specific layers in the flowing

fluid. Applying the phemmena to economic geology, sulphides might well not becorne

evenly distributed throughout the chamber but might nther fonn layas of more concentrateci

disseminated sulphide. -$ive sulphides are likely to be found around the fiinne1 or cracks

and cavities on the floor.

33. FLUID INJECTION

The second set of experiments was conducted using a tank with internai dimensions as show

in tigure 71 (Ail the dimensions are in cm.) With the exception of one wall, al1 of the

container wails wen made of 1" transparent, acrylic sheets. The remaining wall, the front

wd, was made using %" acrylic sheet to facilitate obsavation. The fiont wall of the

container had scaling lines dmwn at l-centimeter intervais to provide viewing reference point

on the cornputer screen. Slots were cut into the sidewaîls measwing either 1 mm x 1 cm or 2

mm x 1 cm. These were placed 3 cm apart to examine the potential movement of particles

towards the fissures. In order to simulate the irregular floor of a magma chamber, the bottom

surtace of the tank was abraded (- 0.3 mm thick lines) randomly.

2 mm crack

Figure 71. Se&mitit of tht apnmental tank 2.

The experhental fluids consisted of a water-glycerol mixture in various proportions. The

tirst phase of the experirnental procedure follows the method of the fust set of convection

experiments. A fluid comprising 9Wh glycerol wu used to increase both the viscosity and

density. A single heat source was placed approximately 20 cm bemath the container to

induce convedor Mica plates covered with titanium dioxide were introduced to the fluid

and manuaily mixed to provide as an even distribution as possible. The whole system was

maintainecl in a state of convection over a period of several days. This was done to allow as

many particies as possible to srnie, thus inducing the sedimentation pattern.

Figure 72. Eitpcrimentd for muid injection expriment

In the second phase of the experiment, the heat source was removed. The fluid temperature

decreaseâ causing inmase of the viscosity. Mer a few days of cooling, a hot, dense, low

viswsity fluid was injected upwards into cwler, less dense, more viscous üquid through a 4

cm by 4 cm slot in the tank. These experiments were intended to provide an analogue of a

basaltic magma being fed through a dyke into a more silicic magma chamber, which have

been convecting for sometime. The setting of the experiment is show in Figure 72.

The injected glycerol was approximately 10' warmer than the fluid in the container. The

entin procedure was observed using a CCD carnera and was recorded on a VCR. The

bottom surface of the container was photographed before and after the injection to examine

any changes in the particle-settling pattern.

Adjusting the vertical distance between the two containers regulated the velocity of the flow

in the I I T ' Tygon tubing. The diarneter of the tube was 2 times smaller than the entry inlet,

simulating narrow dyke that expands to the funnel shape before the magma enters the

chamber. Changes in convection pattern were recorded using the VCR The viscosity of the

glycerol mixture remained relatively constant because both the tank and the beaker were

sealed

3.2.2. RESULTS

3,2.2, (1. ln@ctbn of k# dense #uM.

Initial conditions of the experiment: pc(tank) = 1230 kg/m3, pi(injected) = 1 15 1 kg/m3, vi =

6 . 8 ~ W3 kghms wl S r 10-' kpjm-s AT=14.2°C.

in this experiment, a mass of fluid of lighter density and lower viswsity (due to the higher

temperature) than the mass of fluid in the tank was injected. The conditions of the

experiment were chosen to simulated influence of the injection of the lighter magma into the

cbamber occupied by denser magma. The liquid in the tank haâ been convecting for several

days before the injection to induce sedimentation pattem. Some of the mica particles hd

aiready settled to the floor of tank. The rernains of the particles were in suspension. The

fluid at the source is initidly üghter than the fluid of the swrounding environment. 'ïhe

entrainment of denser fluid nom the enviromnent caused the density of the buoyant tluid to

increase continuously with elevation until the difference between the plume and its

surroundings was reduced to zero. In the expeciment the buoyrnt jet of liquid traveled up

through the container to the roof of the tank. At this levez it spread out laterally over the top

of the mounding fluid (Figure 73). Coatinuous inflow of lighter fluid will result in the

build up of a stratifieci layer at the top of the original fluid with a sharp fiont between them.

However, the density of the top layer is dependent on the differentiation (buoyancy flux) at

the source and the density gradient of the environment. Haice, its density could be

detennined by deasity difVerence (Ar 79 kg/m3) between the original and injected fluid and

the density reduction produced by entrainment. The extent of entrainment of the

environmental fluid is shown in the Figure 73 as curves representing distributeci sink. Note

that the sinking of the fluid followed a gentle cwve rather than straight line.

Figure 73. tntruaion ph- Tbe turbulent fountain carries the injected luid through spreding it on the top o f the uibient fiuid.

Amrding to Campbell (19%). a less viscous fluid entering the chunber that contains a high

viscosity fiuid has to have a reasonable momentum in order to entrain the outer fluid.

Campbeii (19%) suggested that if the expression udlvhoaff>70 the (u-velocity of fluid, d-

diameter of the dyke and - viacosity of the host fluid) inflowhg 1iNd mixes with the

ho& liquid as ifthere was no viscosity différence between them. Foiiowllig equation 27, the

Reynolds numba of 6780 fkom the expriment was pater than the ratio of viscosity of the

host fluid end the viscosity of injected auid (-1000); therefore the two liquids mixed rapidly

as o b s e d . The thickness Ah of top layer will increase due to the mass flux nom injection

and the fluid entrained fiom the environment at the rate Q. per unit height. In this

experiment, the discharge Q into the tank was 2.46 l/s with an inlet velocity of 4 mis.

Since the tank inlet ( f b e l ) was larger in section than the tube through which the fluid was

injected, a cuculation and entrainment process developed within it. The plume velocity

decreaseâ with the height. As the entrainment velocity was proportional to the infiow

velocity, its rate was strongest in the inlet (Equation 41). However, the volume flux of the

environment fluid was distributed evenly throughout the height of the plume since the width

of the entrainment increased with the height .

Equation [40]

V, = 1.06V Equation [4 11

where: Vo is the inlet velocity, h is the height of the plume, d is the diameter of the plume

(Baines et. al 1990).

There was thus a strong downward flow dong the containers walls proceeding towards the

inb. Figure 74 shows the entrainment in the narrow plume in the inlet. The flow exerts a

shear stress on the slopping botîom of the tank. This nsults in the transportation of most of

the particles, which were previously deposited on the floor near the inlet, into the inlet

chamber. A portion of these particles was carried back out of the funne1 because of their

becoming entrained in the plume.

Figure 74. E~atrriaicit in tôt iakt.

Figure 75. Front vim of the tank rhowing entninment o f the rmbient luid by the fouitain. The ÿ b t mghr repmut higher coneentiatioo of mica in the intcrliyer riid following the outliv of the entninment. Tbe thin horizontal lines indkate l e m interval for scaling. Tle

horizontal extent o f tbe photo ir 21 cm.

The injection phase had two stages. The first stage was fpst anci turbulent intrusion, wbich

lasteci only 21 seconds. In the second stage, injection of 3 mm thick, bulging plume of the

lighter fluid continued for approximately 15 minutes. Dunng this relatively short phase, the

injected fluid produced a top layer, which containcd small number of the particles. which

were either entrained from the environment or swept off the floor by the plume. As the

intrusion progressed, about 80% of the onginai fluid mixed with the incoming nuid (Figure

79, and the particles followed the outlines of the mixed liquid. At the end of the injection a

mushroom type plume ascended at about 1 cm from the tank floor comprising mica in its top

layer.

A significantly longer phase of a thermosyphon foiîowed the intrusion. Thermosyphon is a

mechanism for the transport of fluid vertically in a narrow passage produced by buoyancy . It arises whenever there is an unstable density gradient. That i s when there is a steady supply

of light fluid at the bottom or heavy fluid at the top of the chamber. The duration of this

phase depended upon a temperature difference between the liquid in the supply line and tank.

Since there was no mass flow, the upward and downward motions were balanced. The rising

plume became laminar; therefore, the entrainment was less than that in a turbulent flow. It is

a simple shear motion of the liquid surrounding the plume, where the hot center of the plume

does not increase in diameter appreciably as it rises.

Areo of no mixing

/'-

No nixing be tween the l o y e r s

Figure 76. Tbmioryphon pbut,

In the thermosyphon phase, the density difference between the plume and the environment

WU less than in the injection since AT was smaller. Therefore, the density of the plume was

lower than the density of surrounded fluid but higher then the density of the top layer. As the

plume stopped at the inteflace of the top layer, it spread Iaterally forming interlayer of

different density (Figure 76). This intalayer would ultimately mage with the lower layer by

heat transfer but it would aot merge with the upper layer since diffision is much slower than

heat transfer is. From the obsmration, the two layen did not aiix even aAer a few days.

On the top of these motioas were the steady circulation in al1 thne layers driven by the heat

loss fiom the fiee surface. These distribute the particles throughout the individual layers.

Steady accumulation occurs at the tank's floor except in the vicinity of the inlet. Here, the

particles are carried toward the source by the entrainment-dnven circulation in the tiinnel

chamber. There was a significant increarre in the number of particles circulating in the inlet

compared with the convection before the intrusion (Figure 77).

Fiwre 77. PaltKkr in the inlet, a) ikt injection, b) before injection. The thin horiwitd l ina repmnt I-em i n t m l for wiliag.

This might be cause by stronger entrainment ocauhg during the first phase. Additionally,

as the entrainment rate increased the shear stress exerted by the flow increased also inducing

particles movement on the floor towards the inlet. As indicated in Figure 78 the injection

caused Iarger sedimentation of particles in the f i e r , dthough the overali contour of

deposition nmained similu to the particles sntling before the intrusion phase (Figure 65)

Figure 79 presents the distribution of the mica panicles 2 hours &er the intrusion phase.

The particles becsme concentrated in the layers, which outüned the plume movement. The

upper edge of the mushroom plume was also outlined by the mica plates, and as this

expanded it left behind a layer of mica close to its boundafy with the fluid within which it

was developing. The above confirmed that the heavier concentration of particles occurred in

the boundary layers between the convection cell.

Figure 80 compares the particles distribution in al1 t h layers. The upper, lighter layer,

which was a product of the intrusion phase, contained oniy small number of particles (Figure

80a). As the injection plume moved thmugh the denser fluid in the tank, it captured some of

the mica suspendeci in the host fluid or deposited in the inlet. The highest wncentration of

mica was visible in the interlayer (Figure $Ob). One of the reasons for larger number of

particles in this layer, is that the mica picked up by the injection, have settled out fast 6.om

the upper layer since the layer was lighter and less viscous. Hence, the particles accurnulated

at the interface where the density and the viscosity of the lower fluid were much greater.

Additional accumulation in the erra occurred during the themosyphon phase when the

interlayer indeed was formed. The rising plume transporteci particles to the upper edge of a

convection cel), where they were trappexi in the boundury layer. Figure 80c shows the

particle distribution in the area bdow the interlayer. The concentration here is significantly

higher than in the highest layer, however it chged paiodically as the particles were moving

with the convection flow.

Figure regions

7ûe Top view dthc Wr, s M a g urlinttntation pattern &et injection. The iigb i n d i c d areas with bigber concentntba o f m i c i spihcrlly uound the ialet in

the scratches.

Figure 79. Front vim of the tank sbowing diatribution of particâm 2 hourr a k t intrusioa T b Kght ucro indicate coacenttrtioon of mica. V e q (n* particles ptacnt in the u p p p u t of the figure showing tâe top Iayer of the injectai luid. The m a rrpmcntcd by the photo it 12x12

C E

Figure 110. Distribution o f partirka in: a) lighter top Iqrr, b) inkthyer, c) di- un&r interlryer. The diitrnce between the horizonhl lines in euh fmre is 1 cm.

Initial conditions of the experiment: @(tank) = 1234 kg/&, pi(injëcted) = 1254 kg/&, =

3% IV' kg/m-s b=7.0x lu1 kg/ms AT=8.OoC

In the experiment, a denser, less viscous fluid was injected into the tank containing lighter,

more viscous fluid. The parameters for this experiment were chosen to resemble an intrusion

of a primitive mafic magma ( ~ 2 7 0 0 kg/m3) into a magma chamber that has already went

tbrough sorne olivine crystaliization ( ~ 2 6 8 0 kg/d). Prior the intrusion, the fluid in the tank

was convecting for 12 days ailowing part of the mica particles to settle on the container's

floor. The experiment was set up following the schematic in Figure 72. The fluid at the

source was initially slightly heavier Ar20 kg/m3 thaa the surrounding fluid. The

entrainment of lighter fluid fiom the environment slowly decreased the density of the

intrusion. The srnall viscosity difference between the two liquids allowed for umstrained

mixing. The fluid entend the tank with sufficient momennim so it was initially carried

upwards into the overlying fhid, forming a fountain. The initial entry velocity of the inflow

was 3.5 mh. The injmed fluid spread lateraily on the top of surrounding fluid (Figure 81).

The mushroom shaped plume fonned a stratified layer at the top.

Erten t of in1 tial entrainment dur ing in jectian

Eventually the negative buoyancy forces overcame the initiai upward momentum of the

plume and the new pulse falls back to the floor h g the tank wails (Figure 82). While the

injected fluid was moving downwards, it created vertical layers approximately 1 cm thick

that endad up spreading on the container floor. Since the intruding iiquid did not comprise

any mica particles, no visible amount was observed in either the vertical or the horizontal

layers.

The motion within the piume was laminar with the entry Reynolds number only 108.

However, the host fluid was drawn into added fluid. The resulting mixture collected at the

base of the plume fonning a hybrid layer that spreaâ out on the bottom of the tank. As the

intrusion continued the hy b rid layer thickness increased and the plume entrained now bot h

the hybnd fluid and the host fluid.

Figure 8 2 Downwud movement o f the injected nuid

The mixing continued during the thennosyphon phase, whete the upper layer was transponed

down completely. However, the vertical layers and part of the floor layer of the den= tluid

were unaffecteci by the convection. At the end, the mica particles deposited earlier on the

tank bottom were moved closer toward the feedet (Figure 83). Compareci to the previous

experiment more puticles wece swiped into the fder, however the wmecting tube

containeci fmer particles. The rest ofthe particles were distributed throughout the container

concentrating around the bounduies of convection cells.

ure û3. Top v i m of tbe tuik rhowing aedimcatrtion pattern affcetcd by the intrusion. t mgions indicite a m with b i g b concatratioi~ of mie t Tbe p d c k r mre tnnspo

about 1 cm c h e r to the i n k Inai& dimensions of tbt tank i re 2ûd0 cm.

Initiai conditions of the experiment: @(tank) = 1187 kdm3, pi(inje~ted) = 1260 kg/m3, pi =

3 . 5 ~ lu ' k g h s ~ 8 . 7 6 ~ 1 ~ ~ k g h s AT=13.0°C

This expriment was the injection of a mass of fluid of higher density and lower viscosity

thoa the mass of fluid in the container. The liquid in the tank was mixture of 700/. glycerol

and 30% water at rwm temperature. The injected fiuid was 100% glycerol with 0.1 g mica

particles. The Uranine-Fluorescein Sodium Salt - C2&IiaNa20s was added to the intruding

fluid for contrast purpose. The parameters of the two fluids were chosen to nsemble an

intrusion of a mafic magma (p2700 kg/m3) canying sulphide droplets into the magma that

have alread y went through olivine cry stallizat ion ( ~ 2 6 2 0 kg/m3).

As the denser fluid entered the tank, it entrained some of the ambient fluid into the initial up-

flow, increasing the plume radius and decreasing the source fluid density. The momentum of

the rising auid was reduced by the opposing buoyancy force until the flow first came to rest

at an initial height above the source (2 cm) (Figure 84). The falling fluid remained denser

than the ambient, so the flow spread dong the base of the tank. The flow was laminar with

initiai Reynolds number of 122. Since the flow was very laminar, no signifiant entrainment

of the ambient fluid was observeci.

Initially, the upper surnice of the source layer was smooth, and there was no mixing with the

ambient fluid dong theù interface except the area over the inlet. The area was the site of the

most intense thermal plume. When the injected liquid was hotter than the ambient üquid, the

upward flux of heat into the ambient liquid induced themial convection in the latter. This

convection dragged injectai liquid upward aithough the injected liquid was aiways denser

than the overlyiag liquid The f'low w u not twbulent and the viscosity dürennce was high

enough to prevent strong entrainment. Thadore, lilimed amounts of dense material were

mixed in secludeci anrs with the ambient fluid transporthg the mudure to the roof of the

container. Figwe 85 shows the change of color of the environment fluid due to the mking.

Figure M Front vkw of Ur tank showiag injection ph- Tbe p l u w w u rcduceâ by the oppite buoywy and ctopped - 2 cm above the in# Tbe photo npment the whole uu of

the tank with dimension &en in Fivre 71.

Figure 116. Front vitn of tbe tanks siowing change of cokr in the upper Iryet iodicdng roae muing ktneen the IIuidr. Tk pboto tepment tbc main container with the inri& dimenrioas

of 17 cm.

The entrainment of the trapped ambient fluid on the tanks floor produced thin hybrid layer.

The hybrid layer was less dense than the source and moved locally through the dense fiuid.

The hybrid layer was denser than the ambient fiuid therefore it spread out laterally on the top

ofthe source liquid (Figure 86).

Figure û6* Intrusion ph- Buoyuicy of the hybrid Iryer.

L m

In1 t d ou time of the in j ~ c t e d

Immediately &er the intrusion phase a separate convection developed in both fluids.

Stronger convection flow was observed in the upper lighter layer than in the lower one. The

mica particles were introduced to the environment with the intrusion. Since there was no

extensive mixing between the fluids, the particles were not present in the ambient fluid at any

time. However, some mixing occurred producing an interlayet, which enclosed the hybrid

layer that was moved by buoyancy fiom the tank floor (Figure 87). As the themosyphone

continued in the source fluid, the particles were carried throughout it by the flow. Due to the

settling and convection redistribution, the particles were not visible in the upper part of the

dense fluid and in areas adjacent to the containers wail. Most of the particles were

concentratad in layer folowing the mushmm shape of the convection plume, which was

divided in îhree main areas (Figure 88).

c p-*

Injectecl dQnSof :Luici

A . . . 4 . m. r.

Foiiowing two days of themosyphone phase, deposition of mica was o b s e d on the tank

bottom. The convection did not influence the aedunentation pattern, as it was a case in

previous experhents (Figure 89). The partides were distributeci throughout the container

ftoot, concentrating in the cracks and in th iniet. No visible pattem w u observed.

denser Cluid

Tropped onbient

Figure 87. Inttriiyer b a n tht dense injected luid rad the upper imbitnt muid. The ar repnrcnted by tbt photo is 513.5 cm..

Figure 88. -up on the front v i m of t b tank rhowing distribution of pirtida in t k iajected (luid The iier rrpmentcd by tbc photo 5 14.9.5 cm.

Figure 89. Top vim of tbe tank showhg #diment.Lion pattem. The inside dimensions of the contrinet are 2ikî0 cm.

4. DISCUSSION

The experiments have ban d e d out in a simplified system. There are several limitations

when applying the results to geological situations such as crystal settling in magma

chamben. The most important difference between these experiments and crystallization in a

magma chamber is the driving force of convection. In the experiments, convection was

driven by heating the container fiom below, wbereas the driving force of convection in

magma chambers is mon complicated. The convection in a magma chamber can be dnven

by both thermal and compositional contributions at the roof and the floor. Additionally, in

the experiment, particles were initially distributed unifonnly and there was no change in the

number or sue of the particles as convection proceeded. In magma chambers however,

crystals can nucleate and individual crystals can grow during d i n g and, in addition,

sulphides drophs may form. The sulphides droplets would settle fsstet if there were other

large crystals (i.e olivine) present forcing the sulphides to settle. The sulphide droplets wet

the silicates (Ip and Toguri, 1993), therefore, by attaching to the olivine the sulphides should

settle faster.

Heat transfer in the experiments was significantly larger (420 wlm2) than would be the case

in magma chambers (1.7 w/m2), due to the small dimensions of the experimental containers.

The experiments were performeâ for purpose of demonstration. However, the more rapid

heat transfer would not a f k t the quality of the tests. If the parameten of the experimental

tank were increased to 1000 m. the heat transfer would decrease to 0.05 w/m2. Convection

flow was unstable Iminar for the experiments with the higher viswsity fluids. From the

literature, it would seem likely that the flow in magma chamben is turbulent. This is

probably due to the high Rayleigh numbers involved in the process, which result nom the

large dimensions of the chambers.

The sizes of the mica particles were sufficiently small that the dimensions of the container

did not obstnict their flow path. if the typical volume of the expecimentaî fluid was 2 . 2 ~ 1 ~ ~

m3 (20 cm x 10 cm x 10 cm) and the volume of the largest particle was 5x 10-'' m3 then the

ratio of the two volumes would be in order of 10". If the volume of Kilauea magma

chamber is of the order of 10" m3 and the volume of a sulphide droplet with a 1-mm radius -9 3 is of the order of 10 m , then the ratio of the two volumes would be around 10". Therefore,

the parameters of the particles and the container provide a reasoaable analogue to the magma

chambers for mperimentd purpose.

However, in order to sale the experiments to the natural system the ratios of settiing velocity

to the convection velocity (parameter S) should be compared. Figures 90 to 92 compare the

results obtained in the rewuch to the conditions of sulphides in magma chambers. Parmeter

S=V,/W was plotted agoinst the increasing viscosity of the fluid. The parameter is generally

very ~mall(10'~ < S < 1 for basaltic magmas) and the convective velocities must tend toward

zero as the boundaries of the flow are opproacheci (Martin and Nokes 1989). This suggests

that crystal settiing will be effective at the bottom boundary of the fluid. Convection

velocities in Figure 90 represent values acquited fiom observation. The slopes (4.992) are

thm times steeper than those in Figwe 91 (-0.3 1) which are values calculateci for magma

chambers. Senling and convection velocities in Figure 91 wen obtained using Equations 28

and 25 respectively applying typicd parameters for mafic magma charnben from the

Figure 90. Parameter S versus Irineartk vkoiity, exdudimg the m u k fmm 1oO.h wrtcr aperimmt The figure sbws the obrcrved dues of W. Tbe tbick liœ rcpraents t k trend

with the qui tka ghen in the figura

1 .OE-û2 1 .OE-01 1.0€+00 Kimmrtic viscosity [mas1

Figure 91. Parimeter S in magma chamkrs venus kiaemitic viscosity of magma. The thick lire indium trend witb the quition given in the figure.

Figure 92. Par- S usiag cdculilcd W (Equition 25) venus Linernatic viscoiity of gîycerol luid. The tbick line indicites trend witb the equitioi given in the figure.

Howevcr, Figure 92 has ken plotted using caiculated vaiues W (Equation 25), for the

conditions of the experiment. The dope obtained (-0.366) w u roughly the same as the dope

in Figure 9 1 (-0.306). Since the m e @on was used to d d d e convection velocity of

the magma and the glycerol fluid, and the stopes of the plotteâ fine ue similar, then the

conditions of the expairnent are comparable to the MW systems. Equation 25 detemines

convection velocity for pure mixing, where the turbulence dispersion distributes the particles

in a container. Hat transfi constaatly adds energy to the system However, it was not

included in the equation 25, whereas the obsenred values of convection in Figure 90 were

direct product of the heat transfer. Additiondy, the velocity of the conveaing particles

includes the values that were meastueci close to the walls where the heat transfer was the

highest causing steeper dope in Figure 90.

1.OE-04

1 Kinematic 1.OE-05 VI-ity

of the fluid [mus1

+ 7.OE-07 -C 1.7E-a 4 2 4 E 4 8 ++ 5.96-08 *?.19€-04 + 276E-M

1 .O€-06 1 .OE-05 1 .O€-04 Pwtlck a b (ml

Figure 93. Smüng vdocity versus prrtick s i n for the experimecitrl lui&.

mqmr mw

Figure !M. SciUing vdocity venus size o f tbe sdpbi& d t o p k

In order to correlate the experiment to the natumi qstems the approxhate scoüng of the

settiing between the partictes and the suiphide is needed. Figures 93 and 94 compare satling

velocities of mica flakes in the ertpeiimental fluid and the suiphides droplets in typical d c

magmas. Eqyation 25 (sphericai puticle) was useâ to caiculate the sealllig of sulphide

dropkts. Experience in senliag of most dmpIets shows that settiing of soli& sphaicai

particles is a reasonable approximation of the liquid droplet settiing. However, the above

equation does not include infîuence of the d a c e tension of a sulphide liquid, which mifit

result in wetting of silicate crystals, thus dancing the overall settling. A I mm sulphide

droplet d i n g io the lowest viscosity magma would fdl with the velocity less ( 4 . 6 ~ 104 m/s)

than the mica flakes with side dimension of 6 3 p in the 50% glycerol mixture ( 7 . 9 ~ 10~) .

Additiodly, the minimum settling velocity for the particles in experiment was 1 . 8 ~ 10*~ mls

which compares to the sulphide droplet with diameta of 0.1 mm settling in the magma with

viscosity of0.741 m21s. Therefore, in the experiments the particles settle slightly faster than

the sulphide would in the natural system.

1 1 t

Convection

Qutiine O F t h e boundory Mo ximum

sedimenta tion

lncreosed Thickness of boundùry

O ) 1 a y e r

Uutline of the boundory

1 I

thickness sedimen t o t ion o f boundary

Loyer

Figure 95. Increme in vstling by irmasiag thickncrr of tbe boundary lvyet in the center ol the tank a) no alopes, b) Uith 300 SIOPCI,

It was obsefved that the thickness of the bottom bounâary layer varied dong the tank bottom

d e . In addition, as convective flow moved aiong the container floor, it carrieci the mica

flakes toward the center, where the boundary wu thickest (Figure 95). Tmnsporting the

particles towards this area was one of the mechanisms responsible for increased

sedimentatîon that was observed at the center of the container floor.

in addition, the thickness of the boundary layer directly above heat source was increased by

inserting 1 S0 and 30" slopes dong the tank bottom. This resulted in a larger number of

particles settling in this area. Laminar re-circulation differed fkom turbulent convective flow

in that a nearly steady pattern of convection was produced. It was shown tbat under these

conditions, a sufficient period of time for the particles to be transported to the boundary is

provided.

As particles in a convecting fluid exceed a critical concentration, a discrae sedimentation

occurs. In magma chambers, the crystallization of olivine and the fomtion of sulphides

droplets would give rise to a sufficient number of particles to allow waves of the rapid

settling followed by periods of slow sedimentation in the boundary layer. The expeciments

did not oonfinn the latter hypothesis since the initiai concentration of particles was always

below the critical value for discrete sedimentation, and this was never detected.

The expenments contirmecl that the sedimentation pattern is strongly influenced by the

viswsity. The higher the viscosity of the convecting fluid, the more pronounced is the

tendency for particles to concentrate above the source of heat. With increased Mscosity, the

verticai boundary layer on the container wdls became larger. Consequently, the floor-

settiing pattern was affected by the sliding of particles away from the walls. Application of

this observation to a magma chamber containkg a viscous fluid is that sulphide

mineralization is not likely to be found close to the chamber walls but some distance from

them.

One of the examples in which the main sulphide deposit is locatcd close to the feeder is richuan Nickel-Coppet deposit in China. The sulphide-bearing ultiamafic pluton was

intnided h o metamorphic rocks of the Lower Proterozoic Formation. The intrusion is 6500

m long and a few tens of meters to over 500 m wide (Tang 1993). The magmatic ore deposit

c m be di* into three types, accordhg to the sequence ofemplacement: In srni liquation

ore, deep-seated liquation-injection ore, and late-stage injection ore. In situ orebodies ocair

as Ienses in dl parts of the intrusion. They range in s h s up to a fm hundreds of m e r s

long and fiom 1 m to a few dozens of meters thick. The larger orebodies occur in the mon

olivinarich lhenolite and are located in the lower-miLddle parts of the intrusion. The main

o n type is disseminated mlphide. The sulphides occur as irregular patches generally 1-3 mm

across, evenly filling the interstices between silicate minerals such as olivine and pyroxene.

Interestingly, the disseminated sulphides occur throughout the intrusion; this could be

mplained by the themosyphon phase, during which the convection distnbuted sulphides

around the cells. ui the experiments, particularly in the test with 1W/o glycerol fluid, the

themosyphon phase was allowed to develop for several hours and the convection pattern

became nearly stable. In Figure 60 five distinctive, convection cells are visible where the

particles are present throughout the container with the tendency to concentrate at the

boundary layers between the cells. The experiments confhned the preference for the

accumulation to occur in the outer boundary layers of cells. in magma chambers, crystals

and sulphides similarly would be more concentmted in the boundary layers than in the rest of

the charnber (except the floor). The larger orebodies of the inditu type in the Jinchuan

deposit occur in the lower-middle parts of the intrusion. in my experiments, this was the

location of the inteditce between convection cells, where large accumulations of particies

developed (Figure 60). The particles were moving in layers of heavier concentration

suggesting that the suiphide in magma chambers may occur in patches scattered throughout

an entire intrusion. A study of the distribution of sulphides as revealed by drilling might

provide an indication of the nature and size of convection cells.

Additionally, al1 of the experiments indicated that the main deposition occurs on the tank

floor, with the particles accumulating in significant thicknesses around the inlet. It has ban

shown that the particles aggngated primarily d i r d y above the heat source. Similady, in the

Jichuan deposit, the deepwaîed and the hre stage injection orebodies occur in the lower

part of the chamber, close to the feeder entry. The deepseuied o r M i e s are large, ranging

fiom a few dozens to hunâreds of meters in thickness and several hundred to a few thousand

meters long (Tang 1993). They mainly occur at the basal or deep-east part of the intrusion

although a few are located near the hanging wall. Sulphide aggregations, 1-6 mm in size, fil1

the interstices between silicate minerais, fonning net-texturd ore and making up 1245% of

the rock. In typid mahc mgma chambers, the bottom, t h d boundary layer wouid be

approximately 5 m thick if the vertical extent of the chamber wae 1 lun As the oiivhe

crystalIizes. the boundary would change its position but the thickness would not be greatly

afbcted. The sulphides deposit between the olivine crystals or in natural traps existing in the

chamber.

Figure 96. Ccologicil cross-section o f the Jincbuan dtposit (afttr Tank, 1993)

In the expenment show in Figure 72, the thermosyphon phase promoted significant

circulation of the particles. The larninar upflow during this phase was very slow, but still

produceci mng shear drag dong the container floor, which swept particles towards the inlet.

Both the shear drag and thermal convection fîow, llustrated in Figure 95, provideci the

necessary mechanism of transport of mica flakes back towards the boundaq layer and the

primary accumulation of the panides around the inlr This might explain why the ide stage

injection ore (massive sulphides) is located in deep-seated liquation-injection onbodies or in

the contact zone between such ores and counm rocks in the deepest part of the intrusion

(Tank 1993). The orebodies ocair as inegular lenses and groups of veins, a few meters to a

few hundnds of meters long, and tens of centimeters to over 20 m thick. Semi-massive and

brecciated ores are sometimes present at the ends and margins of the orebodies (Figure 96).

Figure 98 shows the distribution of padcles on the container tloor after injection and a

thennosyphon p h . The highest accumulation ocws around and in the Met analogous to

massive sulphides. At the edges area of concentrateci particies, the sedirnentation is less

substantial and occurs mostly within the slots cut in the floor. These could correspond to the

semi-massive and brecciated ore at the margins of the orebodies.

A different approach must be taken toward the elliptically zoned Sudbury Structure in

northem Ontario. The Sudbury Structure is host to wortd-class nickel-copper-PGE deposits,

which are generally regardeci as the products of a single magmatic event. The mineralization

et the Sudbury Structure occurs in three geological environrnents as contact-type deposits,

offset dikes and footwall-type deposits (Momson a al., 1994). The contact-lype deposits

occur et the base of the structure withh a contact phase, commonly known as Sublayer. The

sulphides mineralization within the Sublayer ranges fiom extensive zones of disseminated

sulphide to zones of massive sulphides. The most intense minerdiration is found within the

troughs. The offset dikes consist of zones of Sublayer and extend for many kilometers into

the waii rocks. Some of the offset dikes host large sulphide deposits (Le. Copper Cliff). The

f001wulZ-type mineralization occurs in the fonn of stringers, veins and massive sheets and

disseminated sulphides tbat migrated fiom the base of the Footwail Breccia and penetrated

deeply into the wall rocks.

The development scemio of the Sudbury Structure presented by Naldrett (1999) proposeci

t h t the impact of meteorite melted the sunounding rocks, inciuding a high proportion of a

pre-existing mafïdultramafic intrusion. Melting of this invusion gave rise to the 'hocite"

layer. Extensive re-melting of the overlying Basal Member, as r ed t of superheat within the

melt sheet withîn the mater, r d t e d in a mng chernid gradient developing within the

impact melt, from a more felsic top to more rnafic base. Upon staôiiization of the

compositional heterogeneity, two layes developed, an upper "Grrnophyric" layer and a

lower Wont ic" layer that convected inde pendent ly (Figure 97). During the development of

the sulphide immiscibility in the Norite, the resulting sulphides starteci to settie to the base of

the Crater in the low viscosity, superheated magma. Some of the magma h m the Noritic

layer was forced out by the overpressun in the chamber laterally and downward into

fractures in the country rocks creating "ofBetsn. The magma carrieci some of the sulphides,

depositing them in the pod-iike ore zone within the offsets.

/ -- --

levack Gneiss, Granulites O O 40 80 km

Figure 9'1. Formation of tbe Sudbury Structure (ifter Nddrett, 1999).

Figure 97 indicates the mode1 for sulphide settiing and migration within the Noritic Layer.

Part of the sulphides deposited at the base of the structure, in embaywnts that acted as

natutal traps. Since the temperature of the superheated magma was high, the viscosity of the

melt was quite low. Low viscosity together with a rapid heat transfer from the melt to the

m u n d i n g rocks is likely to have caused turbulent convection within the layer. Turbulent

convection would have inhibitexi the fkee settljng of the sulphides, increasing their resident

time in the suspension. Boundary iayers developed on the wails and in the basin. With high

Rayleigh number, the Nbulent flow dong the walls would move down rapidly. The steady

entrainment for this flow would corne nom the central region, forming a distributed m m

flow. At the base and the interface between the Grenophyric and Nontic loyers, there would

be an inward flow of the cold layer (Figure 98). This flow will have a low velocity since the

Reynolds number in this area would be very smail. At the intaface, the inflow at the base of

the granophyre layer would be stronger than the outward fiow fiom entrainment so it would

dominate and drag some of the mafc magma with it. This would produce a weak circulation

zone, which rnight cause some mwng in the Norite at the interfiace. The thickness of the

bottom, horizontai boundary layer is thick enough to allow the sulphides droplets that entered

the layer achieve a full terminal velocity while settling. However, the particles that occur

close to the upper edge of the boundary layer could be easily re-entrained into the convecting

magma, as the position of this edge fluctuates. Therefore, adequate time is required before

the magma chamber crystallizes if most of the sulphides are to be trapped in the boundary

layer.

F i p n 91). Possible corneaion in the Smdbury magma layen (Bdaer, f000, pucoad communicition).

In the experirnentq it was observeci that the particles filled the artificial dots cafved in the

tank floor. Therefore, if there were cracks or embayments in the chamber floor, as was the

case in the Sudbury Structure, the sulphides most likely would filter down into these. The

convection would rffect the deposition pattern on the floor. Since the fîow dong the wall is

very strong, the sulphides would slide away fiom the wds and deposit closer to the center of

the base. In case of the Sudbury deposit, the floor of the structure resembles a basin rather

than a sloping surface, which would enhance the sliding, thus increasing the accumulation

towards the center. Since there was no outer heat source present during development of the

Sudbury Structure, the sedimentation would not resernble the pattern of the perfomed

experiments.

in the experiment involving injection of the slightly heavier fluid, it was demonstratecl that

the replenishment of the magma chamber by hot dense magma would likely to lead to zoning

in the chamber. If the new input takes fonn of a turbulent fountain, as was the case in the

test, extensive mixing will occur between the new magma and the hctionated magma. The

mixture of the two is denser than the ambient fluid and will move downward leading to the

developmeat of a hybrid loyer at the bottom of the chamber.

In the thermosyphon phase following the intrusion phase, the particles were allowed to

convect and deposit next to and inside the inlet. Similarly, in magma chambers, the

convection occwing between the injections of new magma, would allow the heavy sulphides

to accumulate close to the feeder, if this were acting as a heat source. A new pulse of magma

might cany some of the d e d and circulating particles up to the chamber roof if there was

enough overpreswin, a new chamber could open above the original chamber and the new

pulse of magma could transport the sulphides to the new location (Voisey's Bay example).

The conceptual mode1 of the Voisey's Bay deposit (Figun 99) involves flow of magma in a

sub-horizontal fader that was rapiâ, possibly turbulent. The flow carried sulphide droplets.

Once the magma enter4 the main intrusion, its velocity decreased causing the sulphides to

settie (Naldrett et al 1 9%).

Howeveq the -riment involving injection of densa fluid containing the mica particles did

not co&m this hypothesis. The simulated intrusion was laminar and the resuîting foumwi

did not rise very high. The flow spread out on the tank floor entraining some of the trapped

ambient fluid. The ambient and injected fluids did not mix, and the particles were not

transferred into the ambient liquid. One would assume that since the convection in the

denser fluid was laminar, the particles would easily settle. Nonetheless, the mica flakes were

convecting for several days before part of the particles accumulated on the container bottom.

The rest of the particles remained in suspension, separating h o three main zones (Figure

88). There were no particles close to the walls or at the interface between the fluids.

'Tl~erefore, even in a case of the laminar flow, sulphide dropiets wiil neeci a substantial

amount of time before they sediment to the floor. Additionally, convection might be a

mechanism that would enhance the settling in the natural situation

CONCEPTUAL MODEL FOR

VOISEY'S BAY Ni - CU - CO DEPOSIT 9

Figure 99, Conceptuai mode1 for Voisey's Bay deposit showing levds o f erosion in different parts o f the dcposit ( A f k Naid- et. al, 1996).

Dwing the thctmosyphon phase in the experiments, the convection affected the fiuid residing

in the tubing ~ 0 ~ e c t e d to the inlet of the tank. The particles were ckculating there and

depositing on the lower waîi of the sub-horizontal tube. The geometry of the naturai

magmatic system is much more complicateâ thpn the container and the tubing used in

experiments. However. a thermosyphon would likely occur in a feeder dyke to a magma

chamber. The difference is that the crystals or the sulphide droplets would accumulate faster

in the thinnest section of the feeder dyke. in the experiment, the width of tubing was smailer

than the inlet, which served as a hot spot. Since it provided a heat source, intense

entrainment occurred in the inlet. The flow swept some of the panides fiom the tank floor

dom along the wall of the inlet and imo the tubing. The strong upward flow carried some of

the particles back into the container. In the thin section of the dyke, there is no strong

thermosyphon; therefore, the suiphides would likely remain in that section instead of being

entrained in the upflow. An example of this type of deposition is Ovoid Deposit, Voisey's

Bay (Figure 100), where the Troctolite forming the feeder to the ovoid comprise 25950%

sulp hides.

X I X X

1-0 Borehole Trace

Figure 1W. West -facing geoiogical section through the Ovoid Dcposit, Voisey's Bay (Linc 1300E).

It is intereshg to speculate about what might occur if the order of injection was changed in

experiments, and a significantly heavier fluid containhg mica particles was injected into a

lighter fluid first, and then, &et the fluids had been convecting, a slightly densa fiuid was

injected into the mixture. From the experiment, it was observeci that the heavier fluid

t'iowing d o m to the floor sweeps some of the particles towards the inlet. In naturai systems,

the sienificantly heavier fluid would be a primitive basaltic magma carrying oulphides. In

this case, as the magma entend the chamber, it wouldn' t mix with its surroundiags due to its

higher density and lower viscosity. Some of the sulphides and olivine ctystals would settle,

as they did in the experiment, al1 over the chamber floor. The next infiow of magma, which

is oniy slightly denser thon the magma in the lower chamber, goes through both of the

magmas if there is suscient momentum. It wouid then entrain some of the sulphides

carrying them up to the roof Upon flowing down back to the floor, it would swap sulphides

close to the chamber walls moving them towards the feeder.

5. CONCLUSIONS

It was shown that the fluid dynamics of the chambers has an important effect on the

movement of sulfide droplets (or aystals of sulfide minerals) in convecting magma.

Although the experiments were c h e d out in a simplifieci system, a plot of settling and

convective velocities versus the viscosity change showed similar slopes for the natural

magmatic systems and the experiments. From the observation of the mica particles in the

convecting environment several conclusion can be drawn with respect to natural magma

chambers:

in the higher viscosity fluids, convection forces the droplets into the bottom boundary

layer. The boundary Iayer is usually suficiently thick to allow the sulphides droplets that

entered the layer achieve a full terminal velocity while settling.

a Crystallization and growth of olivine crystals might afEect the time that the sulphides take

to settle.

a In magma chambers heated Born below, the largest accumulation of sulphides is Iikely to

occur directly above the heat source. This is caused by the shear drag of the tlow along

the floor. The higher the dope of the inclined floor in the chamber, the larger is the

accumulation around the feeder.

The experiments confirmeci that the sedimentation pattern is strongly influenced by the

viscosity. The higher the viscosity of the convecting fluid, the more pronounced is the

tendency for sulphides to concentrate above the source of kat. Additionally, with

increaseâ viscosity, the vertical boundary layer on the c h b e r walls becomes larger.

Consequently, the floor-settling pattern is affkted by the sliding of dmplets on the floor

away from îhe wails.

Since some of the particles concentrated at the interface between convection cells, large

accumulations of disseminated sulphides might be found concentrated in zones within an

intrusion.

Multiple injection of den= magma will likely lead to zoning in the chamber. If the

viscosity difference between the injected and the resident magmas is hi& no extensive

mixing occurs.

Injection of new, denser magma that has sufficient momentum would produce a fountain

that mixes to a certain degree with ail of the magma that it moves through. The

downfiow of this denser melt will drag sulphides that have already been deposited on

floor closer to the feeder.

REFERENCES

Atkinson, B. K., (1984). Subcritical crack growth in geologic materials. Journal of

Geophysical research, 89,407741 14.

Baines, W. D. and Chu, V.H. (1996). Jets and plumes. Environmental Hydraulics. 7-6 1.

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APPENDIX

Rcpresentatîve figure for putide counting (SO% giycerol).