EFFECT OF SURFACTANTS ON DROP BREAKAGE IN TURBULENT LIQUID DISPERSIONS

7/29/2019 EFFECT OF SURFACTANTS ON DROP BREAKAGE IN TURBULENT LIQUID DISPERSIONS

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Chenucal Engineering Science. Vol . 43. No. 3, pp. b49-654. 1988. 0009-2509!88 $3.00+0.00Printed in Great Britain. 80 1988 Pergamon J ournals L td.

EFFECT OF SURFACTANTS ON DROP BREAKAGE INTURBULENT LIQUID DISPERSIONS

ABRAHAM KOSHY, T. R. DAS and R. KUMAR*Department of Chemical E ngineering, Indian Institute of Science, Bangalore 560012, India(Received 1 September 1986; accepted for publ icati on 1 J une 1987)

Abstract-The existing models of drop breakage in stirred dispersions grossly overpredict the maximumdrop size when surface active agents are present inspite of using the lowered value of i nterfacial tension. It isshown that the difference in the values of dynamic and static interfacial tension, aids the turbulent stresses indrop breakage. When the difference is zero, e.g. for pure liqui ds and for high concentration of surfactants, theinfluence of the addition of surfactant is merely to r educe the interfacial tension and can be accounted for byexisting models. A modi fied model has been developed, where the drop breakage is assumed to be representedby a Voigt element. T he deforming stresses are due to turbulence and the difference between dynamic andstatic interfacial tensions. T he resisting stresses arise due to interfacial tension and the viscous flow inside thedrop. The model yields the existing expressions for d,,, as special cases. The model has been found to besatisfactory w hen tested against experimental results using the styrene-water-teepol system.

lNTRODUCTlONMechanical agitation is a comm only employed methodfor generating and maintaining a dispersion of oneliquid in another. The rate of transport processes insuch dispersions depends on the interfacial area,transfer coefficient and the state of mixing of the twophases. The interfacial area can be calculated from thesauter mean diameter, which has generally been foundto be directly proportional to the diameter of thelargest stable drop (d,,) existing in the stirred d isper-sion. A number of reports exist in literature whichpredict d,,, from the operating param eters of theequipment and system properties. Hinze (1955) sug-gested tha t a drop would break if the ratio of thedeforming inertial stress across its diameter and therestoring stress due to the interfacial tension, crossed acritical value. Shinnar (1961) used the above criterionand derived the following expression for d,,,

d max- = consta nt ( We)-.6D (1 )where We is the Weber number.

Sprow (1967) has suggested the same expression asabove and has found the value of the constant to bebetween 0.126 and 0.15. Lagisetty et al. (1986) havefound the value of the constant to be 0.125. Equation(1) has been employed by a numb er of investigatorsand Coulaloglou and Tavlarides (1976) have discussedthe various correlations available in literature, basedon eq. (1).

Equation (1) is applicable when the viscosity of thedispersed phase is small, since it does not take intoaccount the Row of the dispersed phase duringbreakage. The viscosity of the dispersed phase has beenreported to have a significant effect on drop size (Araiet al., 1977; Konno et al., 1982; Lagisetty et al., 1986).Apart from the interfacial tension which tends torestore the original drop shape, viscosity also tends tolower the rate of deformation of a drop. Thus an

increase in viscosity tends to increase the d,,, in astirred vessel. Lagisetty et al . (1986) have proposed aphenomenological model for drop breakage and havetested it not only for Newtonian liquids, but also forpower law fluids and Bingham plastics as dispersedphases. Their model reduces to Shinnar (1961) ex-pression, when the viscous p roperties of the dispersedphase are neglected.

Addition of a surfactant to the liquid-liquid disper-sion reduces the droplet size as in the case of emulsifi-cation. Th e m ain reason for this would be the reduc-tion of interfacial tension caused b y the surfactant. Toverify if existing models can adequately explain theeffect of surfactant on drop breakage, preliminaryexperiments were conducted in a stirred vessel. Lowviscosity dispersed phases were used, as all the modelsyield Sprows (1967) expression for these. Such acomparison is shown in Fig. 1 , which contains exper-imental results for two systems-one without a sur-factant a nd the other with it. The water-octanol systemis representative of one without a surfactant. For thissystem d maxvalues were measured as a function of rpsand are shown as solid circles. The system withsurfactant was water-styrene. It has an interfacialtension of 0.034 N/m when no surfactant is used.Teepol was added to water un til the interfacial tensionof the system came down to the same value as forwater-octanol (0.0083 N/m ). The values of d,,, forthis system ha ve been shown as solid triangles in thefigure. It is seen that the values of d,,, with thesurfactant are much lower than without surfactant,though the relevant system property, i.e. the interfacialtension is the same. The b roken line gives the values ofd,., calculated from Sprows expression using theconstant as 0.125. It is seen that this equation predictsthe values of d,,, for the water-octanol system ex-tremely well, but grossly overpredicts those for thewater-surfactant solution-styrene system, though theproperties influencing the drop volum e are the same.

649


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ABRAHAM KOSHY et aI.50

150

E 100CDPx

iiD50

0 I I I I I I I5 6 7 8 9 10 11 1Impeller speed (rps)Fig. 1. Comparison of experimental results of a surfactantand a pure system having the same interfacial tensions.Interfacial tension: 0.0083 N m I, Systems: water-octanol,experimental: 0; surfactant solution-styrene, experimental: A.Sprows equation - - - - - .

Experiments performed on other systems also indicatethat the existing models overpredict the maximumdrop size obtained in a stirred dispersion, when surfaceactive agents are present. This would indicate that thesurfactant not only acts through the reduction ofinterfacial tension but also influences in some otherfashion, which has not been considered by any of theexisting models. An attempt has been made in thepresent investigation to develop a model incorporatingthe effect of the surfactant.

DEVELOPMENT OF THE MODELThe recent model of Lagisetty et al. (1986) assumes

that the deformation of the drop can be represented bya Voigt element. The drop deformation is caused bythe external inertial stress arising out of the turbulentpressure fluctuations. The deformation is resisted bythe stress due to interfacial tension and the viscousstress (due to internal flow). Thus

t = 7s+7,. (2)

They used the following expression for t, and 5,~~=:f3(1-Q) for8< 1 (3)

=o for B 3 1and deTO = fix. (4)The stress due to interfacial tension is assumed to passthrough a maximum and then reach zero at 9 = 1.The model described above captures the grossessential features of the breakage process, but bypassesthe details of the flow both inside and outside thebreaking drop. Thus, the presentation of the appliedturbulent stress and the resisting stresses due tointerfacial tension and viscosity through a spring anddashpot assembly significantly simplifies the complexflow problem.

As the addition of the surfactant is not likely tochange the mechanism of breakage in a drastic way, thebasic features of the model of Lagisetty et al. (1986) canstill be retained while the role of surfactant is de-lineated in more detail. The surfactant molecules havea tendency to get adsorbed at the liquid-liquid inter-face, thereby reducing the interfacial tension. When apressure fluctuation due to an eddy is experienced bythe drop across its diameter, the drop starts deforming.The deformation most probably starts by the forma-tion of a depression on the drop interface and thisdepression propagates resulting in breakage. When thesurfactants are present at the interface, the pressurefluctuation apart from causing depression at theinterface, also removes the adsorbed surfactant mol-ecules thereby exposing a fresh interface. This freshinterface has dynamic interfacial tension which ishigher than the static interfacial tension. Thus, at thebase of the depression, the interfacial tension is higher.This difference in interfacial tension, causes a flowtowards the base and this adds to the flow alreadytaking place due to the pressure fluctuation. Thus, anextra stress is generated due to the difference indynamic and static interfacial tension, which adds tothe stress due to the turbulent pressure fluctuation.The assumed mechanism through which the extrastress gets generated has been shown in Fig. 2. Here

Appliedturbulent stress

La) Drop before interaction (b) Formation of thewith eddy. depression.Fig. 2. Generation of the extra stress due to difference in dynamic and equilibrium interfacial tensions.


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Effects of surfactants on drop breakage 651again we bypass the complex flow field and simplify theanalysis b y adding the extra stress to the inertial stress.The extra stress may be expressed as An/d, where Aa isthe difference between the dynam ic and static inter-facial tensions.

Equating the deforming and resisting stresses, weobtain

Od - CTr+- =dThe od value corresponds to the interfacial tension at

the freshly created interface. The difference between odand u is function of the surfactant concentration.

Hinze (1955) has given the following expression for rr cc P~U (d) (6)

ud) can be expressed in terms of parameters as-sociated with the stirred vessel (Coulaloglou andTavlarides, 1977) as

u2 (d) = C,C23d23. (7 )Further E = 0.4Q7N3D2. (8)Thus, r = Cp,N= D43d2/3. (9)Substituting this expression for r in eq. (5) we obtain

CpcN2DVd23 +%j? = %e(l-t,)+p%p (10)Equation (10) can be expressed in non-dimensionalform as

d0- = CWe(d/D)53+d?where PI is the non-dimensional time given by

Equation (11) may be written asd0

where(6 - 4) + a = dr j

(12)

(13)

a = CWe(d/D)53+

Equation (13) has been solved w ith initial condition8=0 at q=O.

For breakage to occur, the deformation (0) should beat least unity so that the interfacial tension cannotbring it back to the original state. Further, thisminimu m deformation for breakage should beachieved within the life time of an eddy, r. We cantherefore obtain maximum stable drop diameter, i f

q(tl = 1) = F;( -> .max (14)Coulaloglou and Tavlarides (1977) have given the lifeof an eddy as

T = d23/(ND23). (15)

Substituting the above expression in eq. (14) we obtain~(0 = 1) = (Re/We)(D/d,,)3 (16)

where Re = D2N p,/,u.Equation (13) has been integrated with C = 8(Lagisetty et al., 1986), obtaining the following ex-pression for d,,,

4

32 We(d,,,lD) 5/3+4(?!$)_l]

tan-l32 We(d,,,/D)53

= (Re/We)(d,,,/D)-3. (17)For pure liquids, trd = IT and u nder this condition, eq.(17) reduces to the proper limit, i.e. the equation givenby Lagisetty et al. (1986). Further, the equation isapplicable for Newtonian dispersed p hases, but can beeasily extended to non-Newtonian dispersed phases bysubstituting appropriate rheological expression in eq.(5). Thus, for power law liquid having the rheologicalexpression

=k g( >7 (18)and defining Reynolds number for any value of n as

H e, = D (N D) -P C2-3(3 + l/n )k

the equation for d,,,, when n = 213 works out to be20

32 We(d,,,/D)513= (Re We)32 (d,,,ax/D)-56.

EXPERIMENTALThe stirrer assembly employed in the present investi-

gation is shown in Fig. 3. A glass stirred vessel of0.135 m i.d. and 0.2 m height was equipped with fourequi-spaced baffles at its wall. Each baffle had a widthequal to l/lOth the vessel diameter. A six bladedRushton type impeller, shown in the figure, wasemployed for stirring. The impeller was normallylocated at the centre o f the liquid column and was runthrough a l/5 hp motor. The speed was controlledthrough a dimm erstat and measured through a digitaltachometer connected to the stirrer shaft through abelt and pulley arrangement.

To start a run, the continuous phase was firstcharged in the required quantity. The stirrer wasstarted and its speed adjusted to the required rpm. Thedispersed phase was then added. In all the experiments


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652 ABRAHAM KOSHY et al.

V. Vessel B. BaffleS. Shaft C. CouplingF. Frame M. MotorT. Tachometer Ii. Bearing houseI. Impeller Dimensions are in m

F ig. 3. Schematic diagram of stirr ing assembly.

reported here, the dispersed phase fraction was lessthan 0.02 to minimize coalescence. It took ab out anhour to reach steady state. After this period, sampleswere withdraw n and the diameters measured using amicroscope. There was no coalescence of drops duringwithdrawal and measurem ent because of the very lowdispersed phase fraction em ployed. A minimum of 200droplets were measured to decide on d,,,.

The dynamic interfacial tension was determinedthrough the photographic method of Andreas et al.(1938). A drop of the surfactant solution was formedfrom a capillary tip and was photographed at knownintervals of time. The drop shape varied as a functionof time because of the change in interfacial tensionbrought about by adsorption of the surfactant mol-ecules at the liquid-liquid interface. T he interfacialtension at each time was found by the method given byAndreas et a l. (1938). Interfacial tension was plotted asa function of time and extrapolated to zero time to

Cont. of surfactant solution (Kg/m?L1.C

Fig. 4. Effect of surfactant on dynamic and equilibriuminterfacial tension for water-teepokkstyrene system.obtain dynam ic values. Static interfacial tension valuewas obtained when the slope no longer changed as afunction of time. Static interfacial tension was alsoalternatively obtained by the drop weight method ofHarkins and Brown (1919). A typical set of bothequilibrium and dynamic values of interfacial tensionvs the surfactant concentration for the systemwater-teepol-styrene has been presented in Fig. 4. Itshould be noted that after a certain concentration ofsurfactant, the equilibrium and dynamic interfacialtensions become identical. The rheological par-ameters of the liquids were measured using a rotationalviscometer.

RESULTS AND DISCUSSION

Figure 5 presents two sets of experimental data inthe range of surfactant concentrations where thedynamic a nd equilibrium interfacial tensions differ.The system is styrene-water and the surfactant used isteepol. For points corresponding to the equilibrium

Fig. 5. Comparison ofexperimental results with present model when the dynamic and equilibrium interfacialtensions differ. E qui librium interfacial tension: 0.0253 N/m; AC : 0.0011 N/m; experimental: A; L agisetty etal. model:-.----.-; present modek -_ E qui librium interfacial tension: 0.011 N/m; Ao: 0.0014 N/m;experimental: l L agisetty et al. model: - - ~ --; present model: -p.


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Effects of surfactants on drop breakage 653

I I I I I I I Ic 5 6 7 8 9 10 11Impeller speed ( rps)

Fig. 6. Comparison of experimental results with those pre-dicted by the present model at zero and high concentrationsof the surfactant. System: water-styrene; interfacial tensionl0.034 N/m; experimental: A; present model -. System:water-teepol-styrene; interfacial tension: 0.0032 N/m; exper-imental: l present model p_interfacial tension value of 0.011 N/m the A5 is0.0014 N/m. The dotted line corresponds to the modelof Lagisetty et al. (1986). This line also represents theearlier models as they are special cases of the model ofLagisetty et al . It is clear that the existing modelssignificantly overpredict the values of d,, over thewhole range of rps studied. The present model, shownby the solid line, however, predicts the data quitesatisfactorily. Similar conclusions can be drawn fromthe other set of data presented in the figure. Here, thevalues of 5 and A5 are 0.0253 N/m and 0.0011 N/mrespectively. In this instance, the overprediction byearlier models is relatively small because of the lowvalue of A5 when compared to u.

It has been shown earlier in Fig. 4 that at zero andhigh concentrations of the surfactant, there is nodifference between dynamic and equilibrium values.To verify, if the model could be applied to theseextreme conditions also, experiments were conductedwith zero and high concentrations of the surfactant forthe water-styrene system. These results are presentedin Fig. 6. Here again, it is seen that the present modelexplains the data well both for zero and high concen-trations of the surfactant. The success of the model topredict the high concentration results furtherstrengthens the assumption that the difference be-tween the two interfacial tensions indeed plays animportant role in facilitating drop breakage.Eflect of Au on breakage of viscous drops

To study the breakage of viscous drops, a solution ofpolystyrene was employed as the dispersed phase andwater as the continuous phase. The polystyrene sol-ution was highly viscous and followed power lawcharacteristics with k = 4.1 and n = 2/3. The surfac-tant teepol was added to the aqueous phase to reducethe equilibrium interfacial tension value to0.0144 N/m. The A5 was found to be 0.0015 N/m. Theresults for this system are presented in Fig. 7. Alongwith the experimental points, predictions by the model

Impeller speed (rps)Fig. 7. Comparison of experimental results with the predic-tion from the present model for a power-law fluid. Dispersedphase: polystyrene. Equilibrium interfacial tension:0.0144 N/m; Acr: 0.0015 N/m; K: 4.1 kg/ms4j3; n = 2/3.Experimental: A; present model: __.have been shown as solid line. The model is found topredict the experimental results for this system also.Calculations were made by putting A5 = 0 instead of0.0015. The calculated values were the same as shownby the solid line. As the viscosity of the dispersed phaseis increased, the breakage is increasingly controlled byviscous forces and small changes in interfacial tensionwould not be expected to change the value of d,,,.

CONCLUSIONSThe breakage of drops in stirred dispersions is

influenced by the presence of surfactant not onlythrough the reduction of interfacial tension, but alsoby the generation of an interfacial tension gradientacross the drop. This results in an extra stress whichadds to the turbulence stress and hence results in theformation of smaller droplets. The effects are smallwhen the difference in dynamic and equilibrium inter-facial tension is small when compared to the equilib-rium value for low viscosity liquids. As the viscosity ofthe dispersed phase is raised the effect becomesincreasingly smaller and finally vanishes. It is possibleto predict the d,, values by adding this new stress tothe turbulence stress causing the drop breakage.

NOTATIONc, Cl constantsd drop diameter, md 23nid:32 Sauter mean diameter, - mCn,dfd InBX maximum drop diameter, mD impeller diameter, mk non-Newtonian viscosityn constant (power law)N imoeller soeed. rDs1 _ ,*Re Reynolds number, D (ND) - p


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654t time, s

ABRAHAM KOSHY er al.Arsi, K., Konno, M., Matunga, Y. and Saito, S., 1977, Effect ofT average time period, R dispersed phase viscosity on the maximum stable drop sizefor break-up in turbulent flow. J. Chem. Engng Jap. 10,

Greek&?PrFCL0CTGd5

T.

letterenergy dissipation rate per unit mass, m2/s3

I /

dimensionless timedensity of the continuous phase, kg/m3

viscous stress, N/m

viscosity, Ns/mconstantdimensionless strain

difference between the dynamic and static

static interfacial tension, N/mdynamic interfacial tension, N/m

inter-facial tensions, N/m

average value of the external inertial stress,N/m2elastic stress. N /m2

325-330.Coulaloglou, C. A. and Tavlarides, L. L., 1976, Drop sizedistribution and coalescence frequencies of liquid-liquiddispersion in flow vessels. A.1.Ch.E. J . 22, 289-297.Coulaloglou, C. A. and Tavlarides, L. L., 1977, Description ofinteraction Processes in agitated liquid-liquid dispersions.Chem. Engng Sci. 32, 1289-97.

Harkins, W. D. and Brown, F. E., 1919, The determination ofsurface tension (free surface energy) and the weight offalling drops: The surface tension of water and benzene bythe capillary height method. J . Am. Chem. Sot. 41,499-524.Hinze, J. O., 1955, Fundamen tals of the hydrodynamicmechanism of splitting up in dispersion process. A.1.Ch.E.J . 1, 289-295.on coalescence of dispersed drops in suspension polymerlz-ation of slyrene. J. Chem. Engng J ap. 15, 131-135.Lagisetty, 3. S., Das. P. K., Kumar, R. and Gandhi, K. S., 1986,Breakage of viscous and non-Newtonian droos in stirreddispersions. Chem. Engng Sri. 41, 65-72. -

Konno. M.. Arai, K. and Saito. S.. 1982. The effect of stabilizer

REFERENCES Shinnar, R., 1961, On the behaviour of liquid dispersions inmixing vessels. J . Fluid Mech. IO, 259-275.Andreas, J. M., Hauser, E. A. and Tucker, W. B., 1938, Sprow, F. 3., 1967, Distribution of drop sizes produced inBoundary tension by pendant method. J . Phys. Chem. 42, turbulent liquid-liquid dispersion. Chem. Engng Sci. 22,1001. 435442.

EFFECT OF SURFACTANTS ON DROP BREAKAGE IN TURBULENT LIQUID DISPERSIONS

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