Die Ressourcenuniversität. Seit 1765. Wettability at elevated temperatures FIRRE UNITECR 2011,...

Die Ressourcenuniversität. Seit 1765.

Wettability at elevated temperaturesFIRRE

UNITECR 2011,

October 30 – November 2, Kyoto

Prof. C. G. Aneziris

[email protected]

Topics• Surface and interfacial energies

– Gibbs equation– Dupré equation

• Wetting behaviour of ideal solid surfaces – Young equation– Microscopic and macroscopic contact angles– Effect of system size

• High-temperature wettability of non ideal surfaces– Equipment– Microstructure-assisted– Electro-assisted

• Contribution of wettability on melt corrosion of refractories– Penetration of slag into refractories– Dissolution of refractories into slag– Molten slag viscosity– Crystallite growth processes

2

3

Surface and interfacial energies *

Solid / Liquid / Vapour System: the total free energy of the system F the surface area

defined by GIBBS (1961) for SOLIDS:

the work needed for reversible creation of a solid surface S at constant strain by breaking bonds to increase the number of solid atoms (or molecules) in contact with a vapour V,

SV = solid surface energy

inVTSV

F

,,

2m

J

Creation of a solid surface (shaded) by cleavage *

T – temperature V – volume ni – number of moles of component i

Eustathopoulos, N. et all (1999): Wettability at high temperatures. Pergamon: Amsterdam et all.

4



defined by GIBBS (1961) for SOLIDS:

the work needed for creation of a solid surface S without increasing the number of surface atoms by purely elastic strain of the solid in contact with a vapour V,

SV = solid surface tension

d

d SVSVSV

m

N

Creation of a solid surface (shaded) by elastic deformation*

= macroscopic elastic strain


5

Surface and interfacial energies


Defined by GIBBS (1961) for LIQUIDS:

the work needed for reversible creation of additional surface of a liquid L in contact with a vapour V,

LV = liquid surface energy

the reversible stretching of a liquid surface is identifical to a reversible creation of new surface; the liquid can increase its surface area only by the addition of new atoms to the surface,

LV = liquid surface tension

inVTLV

F

,,

T – temperature V – volume ni – number of moles of component i

2m

J

LVLV

m

N

6


Solid / Liquid / Vapour System: interface of two non-reactive phases = interfacial energy

Wc = the work of cohesion in a pure liquid or pure solid

defined by DUPRÉ the work of adhesion (1869):

the reversible work needed for cleavage on the boundaries of two non-reactive phases (liquid and solid),

Wa = the work of adhesion

SLLVSVaW

SL – solid/liquid interfacial energy

SVS

c

LVL

c

W

W

2

2

7

Example: Melt filtration

a) Metal melt without filtration

b) Filtration

c) Filtrated metal

Aneziris, Jung, SFB 920 proposal 2011

8Janke, D.; Raiber, K.: Grundlegende Untersuchungen zur Optimierung der Filtration von Stahlschmelzen. Technische Forschung Stahl, Luxemburg: Amt für amtliche Veröffentlichungen der Europäischen Gemeinschaften, 1996. – ISBN 92-827-6458-3

9

slsgAW lg

lg2KW

lg slsgKA WWG

Pslsg coslg

)1(coslg PG

Work of adhesion to separatetwo phases

Work of cohesion to createtwo new surfaces

(1)

(2)

(3)

(4)

(5)

Equations for filtration of non metallic inclusions

(5)

10

Z SV

SL

LV

liquid

vapour

solid

r

z

Displacement of a triple line around its equilibrium position that allows derivation of the Young equation.*

Wetting behaviour of ideal solid surfaces (the solid surface is vertical and TL is perpendicular to the plane of the fig. and assume to be a straigth line;the total length of TL is constant during its displacement, as in the case of a meniscus formed on a verticalplate)


The surface free energy Fs of the system caused by a small displacement z of the solid/liquid /vapour triple line.

The radius r of the triple line region is much larger than the range of atomic or molecular interactions in the system.

For metallic and ionocovalent ceramics:

The variation of interfacial free energy Fs per unit length of triple line (small linear displacement z):

The equilibrium conditions:

leads to Young equation:

11

LV

SLSV

cos

nmtonmr 1021

zzFzFzzF LVSVSLsss cos

0

zd

Fd s

ZSV

SL

LV

liquid

vapour

solid

r

z

Displacement of a triple line around its equilibrium position that allows derivation of the Young equation.*


Conditions: solid surface flat, undeformable, perfectly smooth, chemically homogeneous

liquid non-reactive, does not completely cover the solid vapour phase

contact angle between liquid surface and solid surface,scale of wetting behaviour of the liquid

The equilibrium value of the contact angle obeys the classical equation of YOUNG (1805):

12

LV

SLSV

cos

LV

13

Perfect wetting liquid – = 0°

Wetting liquid – < 90°

Non-wetting liquid – > 90°

Non-wetting liquid – = 180°

drop

local nanometric (microscopic) contact angle macroscopic contact angle M *

14

SV

SL

LV

M

liquid

vapour

solid

r

z

cr

Z


The energy of an atom lying on a given interface inside a sphere of radius rc is different to the energy of an atom at the same interface far from the triple line.

The three relevant interfacial energies SV, SL, LV close to and far from the triple line are different and this difference increase with the range atomic interactions.

Sessile drop configuration during wetting: effect of system size *

drop size r increase with rc the relevant contact angle is no longer Young contact angle Y but the microscopic contact angle

concept of line energy the increase R of the drop base radius R leads to an increase of the triple line length

the triple line can be treated as an equilibrium line defect with a specific excess free energy

The variation of interfacial free energy during wetting in the sessile drop configuration is:

The equilibrium conditions:

leads to:

for R < 100 nm

15

Solid

Liquid

R

R

Top view of a sessile drop during spreading.*

RRRRRF LVSVSLs 2cos22

0

Rd

Fd s

LVYeq R

coscos


Solid / Liquid / Vapour System: effect of the curvature of the liquid/vapour surface *

defined by LAPLACE (1805) for LIQUIDS and VAPOURS:

the curvature at each point Q of the Liquid / Vapour surface in the gravitational field

16

21

11

RRPP LV

QV

QL

PLQ – pressure on the liquid side of the surface

PVQ – pressure on the vapour side of the surface

LV – liquid surface energyR1, R2 – principal radii at point Q

The principal radii of curvature R1 and R2 at a point Q on a curved liquid surface. *

The total free energy change F can be calculated when a liquid surface initially in a horizontal position (z* = 0, = 90°) is raised (or depressed) to form a meniscus of height z*, corresponding to a contact angle .

The contact angle can be determined by minimizing F as a function of z*.

For a triple line of unit length, the total free energy change F is (Neumann and Good, 1972):

– A 0 90°

+ A 90 180°

17

Meniscus rise on a vertical wall when < 90° (a) and depression when > 90° (b).*

solid

solid

vapour

vapour

liquid

liquid

21

21

21

21

21

2sin1sin2sin12sin131

A

l

F

cLV

LV

SLSVA


The total free energy change F can be calculated when a liquid surface initially in a horizontal position (z* = 0, = 90°) is raised (or depressed) to form a meniscus of height z*, corresponding to a contact angle .

The contact angle can be determined by minimizing F as a function of z*.

For any rise z*of the meniscus, z* and are related by:

+ z* 0 90°

– z* 90 180°

The capillary length lc is the maximum rise of a liquid on a perfectly wetted vertical plate.

18

Meniscus rise on a vertical wall when < 90° (a) and depression when > 90° (b).*

solid

solid

vapour

vapour

liquid

liquid

21

2

gl LVc

21

21

21

sin1sin12

*

c

LV lg

z

lc – capillary length – liquid densityg – gravity


19

Solid / Liquid / Vapour System: metastable and stable equilibrium contact angles *

After spreading of a liquid droplet:

(a) metastable equilibrium: Young angle Y

conditions: only displacements of the triple line parallel to an undeformable Solid / Vapour surface

(b) stable equilibrium: dihedral angles 1, 2, 3

conditions: deformation of the solid close to triple line as displacement h

defined by SMITH (1948):

(c) total equilibrium: equilibrium at the triple line and along the whole Solid / Liquid interface are attained

conditions: unchanging curvature at any point of the Solid / Liquid interface (a small liquid droplet on the surface of another immiscible liquid)

321 sinsinsin LVSLSV

(a)*

(b)*

(c)*


Solid / Liquid / Vapour System: metastable and stable equilibrium contact angles *

The stable equilibrium in terms of the three dihedral angles 1, 2, 3 can be obtained by regarding the displacement h of the triple line as two elementary displacements, one perpendicular to the intersectionsof the Liquid / Vapour surface (h1) and one perpendicular to the intersection of the Solid / Liquid interface (h2).

Assuming isotropic Solid / Vapour and Solid / Liquid surface and interfacial energies, the interfacial free energy change Fs for the displacements h1 and h2 is:

The equilibrium conditions: ,

leads to: and

defined by SMITH (1948):

20

0

1

hd

Fd s

12 sinsin SLSV

1112 sinsin hhF SLSVs

2123 sinsin hhF LVSVs 0

2

hd

Fd s

13 sinsin LVSV

321 sinsinsin LVSLSV

Displacement of the triple line around ist equilibrium position when the solid is deformable.*

360321

21

Formation of a wetting ridge h at the triple line.*


The wetting of low viscosity liquid drops on solid substrates can occour in 3 stages:

rapid stage: the macroscopic contact angle approaches the YOUNG angle Y, the area of the Solid / Liquid interface and the Liquid /

Vapour surface are determined

slower stage: the stable local equilibrium according to the SMITH equation

much longer time stage: the total equilibrium i.e., a constant curvature on the whole Solid / Liquid interface is obtain

The rapid and the slower stages will take several minutes or hours.

22

A. Non-reactive Solid / Vapour couples

23

B. Reactive Solid / Vapour couples Chemical dissolution with low influence on


LV – liquid surface energy+

first stage: 10-2 s spreading without reaction; the macroscopic contact angle approaches

the YOUNG angle Y,

second stage: the chemical dissolution is affecting the macroscopic contact angle; in case of

liquid Sn / solid Bi remains the interface solid/liquid in the first 5 s

macroskopic flat and then arises at the triple point; diffusion is taking place,

the melt volume is increasing and the spreading diameter is increasing.

kTCC eqi 1)(RT

vmsl

(Gibbs-Thomson-Equation with Ci equilibrium concetration with curvature, Ceqequilibriuem concetration of a flat interface, k curvature and Vm molar volume of solid)

24

B. Reactive Solid / Vapour couples Chemical dissolution with low influence on



third stage: the total equilibrium i.e., a constant curvature on the

whole Solid / Liquid interface is obtained.

In case of liquid Sn/Bi solid at 245 °C the chemical equilibrium

is reached after 100 s with 7 % change of the spreading radius.

25

C. Reactive Solid / Vapour couples Chemical dissolution with high influence on



0lglg

0 )()(cos)(cos

tGt

t

(Momentary wetting angle)

Wetting behaviour for real, microstructured surfaces

26

High-temperature wettability (B)

Wetting behaviour for real, microstructured surfaces: the apparent contact angle W on a rough surface

Defined by WENZEL (1936):

For a smooth surface:For a rough surface:

28

YW r coscos W – apparent contact angler – roughness ratioY – macroscopic YOUNG contact angle

1r1r

The roughness leads to more wetting of a good wetted surface and less wetting of a „bad“ wetted surface

Aneziris, C. G.; Hampel, M.: Microstructured and Electro-Assisted High-Temperature Wettability of MgO in Contact with a Silicate Slag-Based on Fayalite. Int. J. Appl. Ceram. Technol., Vol. 5, No. 5, 2008, pp. 469-479

On real surfaces may exist a wide range of practically stable apparent contact angles:

„Advancing contact angle“: when the drop volume , the contact line appears to be pinned W = maximum

„Receding contact angle“: when the drop volume , the contact line appears to be pinned W = minimum

„Contact angle hysteresis“: difference between „advancing“ and „receding“ contact angle

29

Influence of roughness of solid surface to wetting:

increase of the actual surface and

pinning of the triple line by sharp edges

On rough, hydrophilic surfaces:

in contact with large drops the WENZEL equation is mainly fulfill

30

)1(cos1cos * s

2* )1(cos1cos s

On microstructured hydrophobic surfaces (surface pattern):

the main parameter that determaines the contact angle is the fraction of solid s actually in contact with the liquid (not the surface roughness)

(Cassie and Baxter equation)

(Bico, Marzolin and Quere equation)

Cassie, A., Baxter, S., Trans. Farraday Soc, 40, (1944) 546

Shinozaki, N., Kaku, H., Mukai, K., “ Influence of pores on wettability of zirconia ceramic by molten manganese”, Trans. JWRI, Vol 30 (2001)

31

s 0.05 s 0.64

s 0.25

Bico, J., Marzolin, C., Quere, D., „Perl drops“, Europhysics Lett., 47 (2), (1999)

Effect of an electrical potential on the wettability: corrosion resistance of refractories

Applications of electrical voltage:

at room temperature: – Electro Wetting on Dielectric (EWOD)– the movement of a microdroplet with reducing contact

angle based on the YOUNG-LIPPMANN equation:

the shape of a liquid drop on a surface is determined by: the composition of the liquid and the composition and morphology of the surface

an electric potential is applied across the liquid drop and the solid substrate: ions and dipoles redistribute in the liquid, in the solid, or in both depending on the relative material properties hydrophobic surface to behave an a hydrophilic manner

32

LVYV d

V

2coscos

20

V – contact angle at a voltage VY – macroscopic YOUNG contact angle0 – dielectric constant in vakuum – dielectric constant of the layerV – the voltaged – the thickness of layerLV – the Liquid/Vapour surface tension


Kinetic quantification of the wetting process: between silicate slag and silicate refractories

Kinetic equation:

activation energy for three kinetic stages:

(a) initiation of wetting stage(b) development and spreading stage(c) penetration and reaction stage

Liquid drops on vertical an inclined surface:(at room temperature)

B0 = ratio of gravitional to surface tension forces:

B0 indicates D and/or

34

RT

QK

t

d

0lnlnd – diameter of the slag wetting areat – timeK0 – constantQ – activation energyR – gas constantT – absolute temperature

LV

gDB

sin2

0

– liquid densityg – acceleration of gravityD – equivalent drop diameter – surface inclination angleLV – Liquid/Vapour surface tension


Kinetic quantification of the wetting process: between silicate slag and silicate refractories

Static work of adhesion of surface inclination:

Dynamic work of adhesion of surface inclination:(at room temperature)

a high work of adhesion = good wetting a low work of adhesion = poor wetting

Inclination constant k:

k at the is directly proportional to WLV,

35

cos1 LVSLW

R – reciding contact angle at

A – advancing contact angle at

– surface inclination angleLV – Liquid/Vapour surface tensionm – mass of the liquidr* – radius of the base of the dropletg – acceleration of gravity

ARLVLVW coscos,

*,21

2

sin

r

mgWk LV


Experimental: sample preparation

Raw material: - commercially fused magnesia (bulk density= 3,52 g/cm³, grain size > 100 µm, d50= 25 µm)- temporary pressing additive (1wt% liquid ligninsulfonate)

Mixing: - at room temperature

Forming: - uniaxial pressing at 150 MPa- cylindrical sampels (d= 50 mm, h= 25 mm)

Sintering: - electrical furnace in air- 1.700 °C, 6 h

Grinding: - surface roughness for samples

Microstructuring: - CO2 laser (laser pulse energy 20 mJ, 100 ms laser pulse duration)

- three different stripe pattern- distance of laser beam 150 µm, 300 µm

36


Experimental: influence of the roughness of MgO-surfaces of the contact angle

ground-MgO surface laser-treated MgO-surface

37

Ground-MgO surface.*** Laser-treated MgO surface, distance of laser beam 300 µm.***

Cross-section of MgO-ground surface.*** Cross-section of laser-treated MgO surface, distance of laser beam 300 µm.***

pores between 5 and 30 µm

XRD-Analysis:MgOCa3Mg(SiO4)2

pores stripe area

XRD-Analysis:MgOCa3Mg(SiO4)2

38

Heating microscope, IKGB TU Bergakademie Freiberg

Experimental: influence of the roughness of MgO-surfaces of the contact angle

Heating microscope: macroscopic YOUNG angle Y as a function of temperature

the roughness , the contact angle higher wetting of the microstructured samples at lower temperature leads to higher adhesive work

Surface1116 °C, 30 s

r Wenzel

according to Wenzel- equation

90 ° 60 ° 30 °

Grinded 67,91,2 ° 1 67,9 ° 1112 °C 1120 °C 1138 °C

300 µm laser 58,31,6 ° 1,35 59,4 ° 1100 °C 1115 °C 1158 °C

150µm laser 42,71,8 ° 1,9 44,3 ° 1102 °C 1112 °C 1160 °C

39

YW r coscos

Contact angles at 1116 °C.*** Contact angles as a function of temperature.***

Experimental: influence of the applied voltage of the contact angle

Heating microscope: macroscopic YOUNG angle Y as a function of temperature and voltage

Assumption: The dielectric constant and the thickness of the electro formed layers have the same value for twodifferent applied voltages.

40


according to Young-Lippmann equation

Grinded –35 V

57,81,5 ° 52,8 °

Grinded –17,5 V

64,31,2 ° 65,4 °

Grinded +35 V

87,41,7 °

2

1

2

0102

coscoscoscos

V

V

Contact angles at 1116 °C.***

Heating microscope images of MgO samples with applied voltages, above -35 V (contact angle 57,8 °1,5 °), below +35 V (87,4 °1,7 °), 1116 °C, 30 s).***

-35 V57,8 °

+35 V87,4 °

0 – contact angle with no voltage1 – contact angle at the applied voltage V1

2 – contact angle at the applied voltage V2

Experimental: influence of the applied voltage of the phases of slag

Heating microscope: phase formation of the slag in air and in argon atmosphere

Applying positive voltage:

change of the slag phase composition with insitu formation of MgFe2O4

Applying negative voltage:

formation of the interface layer between slag drop and the MgO

41

Surface Phases of slag in air

GrindedFe3O4, Fe2O3, SiO2 (Christobalite),Ca2Fe1,2Mg0,4Si0,4O5

Phases of slag in argon

Grinded Fe3O4, (Fe, Mg)2 SiO4, Fe2SiO4

Grinded –35 V

Fe3O4, (Fe, Mg)2 SiO4, Fe2SiO4

Grinded +35 V

Fe3O4, (Fe, Mg)2 SiO4, Fe2SiO4, MgFe2O4

XRD, X-ray diffraction of the frozzen slag.***

SEM-image, -35 V, 1116 °C, 6.000s, slag, interface layer, MgO.***

slag

layer

MgO

Experimental: influence of the applied voltage of the interface layer

Heating microscope: thickness and phase evolution of the interface layers between MgO and slag

The phase composition of the interface layers is a function of the applied voltage.

Applying negative voltage: the voltage , the thickness of interface layer

42*** Aneziris, C. G.; Hampel, M.: Microstructured and Electro-Assisted High-Temperature Wettability of MgO in Contact with a Silicate Slag-Based on Fayalite. Int. J. Appl. Ceram. Technol., Vol. 5, No. 5, 2008, pp. 469-479

SurfaceThickness of layer after 6.000 s, 1116 °C , [µm]

Thickness according to Young-Lippmann equation, [µm]

Phases

Grinded 130-180Fe3O4, MgFe2O4, SiO2 (Christobalite),(Fe, Mg)2SiO4, MgO(0,91)FeO(0,09), MgO (Periclas)

Grinded –35 V

120-230 130-210Fe3O4, (Fe, Mg)2 SiO4, MgFe2O4, MgO(0,91)FeO(0,09), MgO (Periclas)

Grinded –17,5 V

90-145 82-158 Same as –35 V

Grinded +35 V

117-147 ---Fe2SiO4, SiO2 (Christobalite), (Fe, Mg)2 SiO4, MgFe2O4, MgO (Periclas)

XRD, X-ray diffraction.***

2

12

1

2

0102

coscoscoscos

d

d

V

V

Experimental: influence of the roughness and the applied voltage of the contact angle

Heating microscope: macroscopic YOUNG angle Y as a function of time and voltages at high temperature

With increasing of time:

contact angles

Applying voltage („+“ or „-“):

higher contact angles after 6.000 s of all „electro-assisted“ samples

43


1116 °C , 2.400 s

1116 °C, 6.000 s

Grinded 67,91,2 36,40,5 36,20,5

300µm laser 58,31,6 29,91,1 28,80,9

150µm laser 42,71,8 25,91,1 22,51,2

Grinded –35V

57,81,5 47,13,1 47,02,2

Grinded –17,5V

64,31,2 45,01,5 45,01,2

Grinded +35V

87,41,7 62,52,1 62,41,8

Contact angles as a function of time.***

Experimental: influence of the roughness of MgO-surfaces of the activation energy Q

Heating microscope: spreading diameters of the slag as a function of temperature, time and voltages

low contact angle (high spreading diameter) leads to a low activation energy Q

the porous stripes of the „300 µm laser“ sample contribute to lowest activation energy Q

SurfaceTime [s]

60 150 330 630 930

Grinded

1116 °C1132 °CQ [kJ/mol]

23,230,5169,8

24,330,9148,6

25,430,9124,0

26,931,391,9

27,231,281,5

300 µm laser

1116 °C1132 °CQ [kJ/mol]

21,922,928,1

22,623,113,7

23,123,22,7

23,423,52,7

23,623,72,2

150 µm laser

1116 °C1132 °CQ [kJ/mol]

21,223,868,8

21,523,967,4

21,724,166,7

22,724,342,8

23,024,540,1

Kinetic stages (a) (b) (c)

44

Spreading diameters as a function of temperature and time, activation energies and kinetic stages.***

Q – activation energyd1 – spreading diameter at temperature T1 and time t1

d2 – spreading diameter at temperature T2 and time t2

Kinetic stages:(a) initiation of wetting stage(b) development and spreading stage(c) penetration and reaction stage

21

2

2

1

1

11

lnln

TT

td

td R

Q

Experimental: influence of the roughness of the MgO-surfaces on inclined surfaces

Heating microscope: advancing A and receding

R angles of the slag as a function of inclination; inclination constant k

Laser microstructured MgO surface, 300 µm:

rolling angle * 24,3 °

advancing angle A 99,9 °

receding angle R 22,2 °

45

Rolling angle at 24,3 °, advancing angle at 99,9 °, and receding angle at 22,2 ° of a laser-treated MgO surface with a laser beam distance of 300 µm.***

1116 °C; 24,3 °

1116 °C; 99,9 °

1116 °C; 22,2 °

Experimental: influence of the roughness of the MgO-surfaces on inclined surfaces

Heating microscope: advancing A and receding

R angles of the slag as a function of inclination; inclination constant k

Roughness of the laser-treated samples:

highest inclination constant k

high adhesion work

46


1116 °C 1116 °C

Grinded

k [N/m]

=0 °67,9

=3,2 °

A: 87,1 °

R: 82,3 °0,087

*=19 °

A: 101,9 °

R: 18,9 °0,406

300 µm laser

k [N/m]

=0 °58,3

=2,5 °

A: 89,4 °

R: 75,1 °0,069

*=24,3 °

A: 99,9 °

R: 22,2 °0,576

150 µm laser

k [N/m]

=0 °42,7

=2,9 °

A: 50,6 °

R: 40,1 °0,063

*=22,2 °

A: 71,3 °

R: 14,3 °0,434

Young contact angles, advancing (A) and receding (

R) angles as a function of inclination angle (), rolling angles (*) as well as calculated inclination constant k. ***

*,21

2

sin

r

mgWk LV

47

Sobczak, N., Nowak, R., Radziwill, W., Budzioch, J., Glenz, A., Experimental complexof high-temperature behaviour of molten metals in contact with refractory materials,Mat. Sc. Techn., 2007

High-temperature wettability (C)

48


49


50


51


52Sobczak, N., Nowak, R., Radziwill, W., Budzioch, J., Glenz, A., Experimental complexof high-temperature behaviour of molten metals in contact with refractory materials,Mat. Sc. Techn., 2007

53Sobczak, N., Nowak, R., Radziwill, W., Budzioch, J., Glenz, A., Experimental complexof high-temperature behaviour of molten metals in contact with refractory materials,Mat. Sc. Techn., 2007

54


55

Penetration of slag into refractories

Dissolution of refractories into slag

Molten slag viscosity

Crystallite growth processes

Contribution of Wetting on Melt Corrosion of Refractories

56

Penetration of slag into refractories:

capillaries (open pores, microcracks) = initial

the penetration rate dl/dt of slag into a capillary expressed by POISEULLE:

brick temperature has a large effect on the penetration depth l trought is effect on

influence of the cristallite shape and crystallite growth (microstructure) during penetration by a liquid

influence of the microstructure (grain size, porosity) during penetration by a liquid:

l

Pr

dt

dl

8

2

r – capillary radiusP – capillary sucking pressure – dynamic viscosity of the slagl – slag penetration deptht – time

2cos2 SLgb gb – grain boundary interface energy

SL – Solid / Liquid interface energy – dihedral angle

57

Penetration of slag into refractories: influence of the microstructure (grain size, porosity)

the liquid can penetrate into grain boundaries:

the liquid can appear along all three grain edgesas a continously connected phase:

liquid can only partially penetrate along grain boundaries:

no penetration:

02 orSL

gb

603 orSL

gb

1206031 orSL

gb

1201 orSL

gb

gb – grain boundary interface energySL – Solid / Liquid interface energy – dihedral angle

Penetration of slag into refractories: influence of the brick temperature

the temperature decrease away from the hot face the slag viscosity increase the slag is to viscous to penetrate

the slag penetration can be suppressed by increasing slag viscosity or contact angle or by decreasing the surface tension:

a temperature gradient from a cool outside surface to the hot (contact) face can limit penetration

58Lee, W.E., Zhang, E.: Melt corrosion of oxide and oxide-carbon refractories. International Materials Reviews, Vol. 44, No. 3, 1999, pp. 77-104

Schematic diagramm of liquid (slag) penetration in typical kiln lining.**

rP

cos2

– slag surface tension t – time – wetting or contact angle r – capillary radius – dynamic viscosity of the slagl – slag penetration depthl

Pr

dt

dl

8

2

l

r

dt

dl

4

cos

trl

22 cos

(a)**

(b)**

(c)**

59

r

kTD

6

D – ionic diffusivityk – Boltzmann‘s constantT – absolute temperature r – radius of the diffusing species – dynamic viscosity of the slag

Lee, W.E., Zhang, E.: Melt corrosion of oxide and oxide-carbon refractories. International Materials Reviews, Vol. 44, No. 3, 1999, pp. 77-104

Crystallite growth processes: precipitation and growth from satured solution= reverse process to corrosion indirect dissolution

Phases form from the liquid at temperature or on cooling: analysis via thermodynamic calculations (GIBBS energy minimisation modules)

Tend to high dissolution rate:

components of a solid with the highest solubility particles with high specific surface area (small radius of curvature, angular shaped protuberances) pressure at particles/particles contact (necks)

… leads to a general rounding of the microstructur.

Equilibrium shap of the crystals:

- considering their interfacial energies with the liquid phase isotropic interfacial energy spherical shap anisotropic interfacial energy shaps by the WULFF

constructionFor example: MgO – spheres Mullite – needle like or cuboidal

Al2O3 – prismatic CA6 – elongated tabular

60

Dissolution and redeposition leads to general rounding of angular crystals.**


Crystallite growth processes: precipitation and growth from satured solution= reverse process to corrosion indirect dissolution

Effect of local composition changes (phase separation, impurity segregation) lead to changes in the equilibrium form of the crystal morphology so that these shapes may not necessarily occur for these phases in complex refractory-slag systems.

Cr2O3 liquid into solid MgO: angular MgO(-Cr2O3) crystal morphologies

Crystallite growth processes tend to bee defined by the rate determinig step:

growth of Al2O3: controlled by the rate of reaction at the liquid/alumina interface

growth of MgO: controlled by mass transport diffusion through the boundary layer phase

Slag penetration into a refractory can lead to (subsatured slag species at lower temperature):

solid state diffusion of slag species into a grain phase

exsolution (precipitation) on coolingFor example: exsolved precipitation in refractories include Cr2O3 in MgO grains in MgO-Cr2O3 bricks

and (Mg, Fe, Mn)O in MgO grains in doloma


62

Wetting and Micro-hydrodynamicsWetting and Micro-hydrodynamics

Thank you very much for the attentionThank you very much for the attention

Penetration of slag into refractories: rate of corrosion

Corrosion rate = f (T, refractory/liquid/interface composition, liquid density, viscosity, diffusivity, degree of agitation, …)

Active corrosion: - reaction product is soluble or dissociates directly in the liquid slag

destruction of the refractory

Passive corrosion: - reaction product is a solid phase forms a layer on the refractory

reduce the overall rate of corrosion of the refractory- possible corrosion rate steps:

- chemical reactions forming the layer,- diffusion through the layer, or- diffusion through the slag

For example: - formation of a dense MgO layer in MgO-graphite refractories- formation of a MgAl2O4 spinel layer in alumina refractories by MgO containing slags- formation of a dicalcium silicate C2S layer on MgO-dolomite refractories by silica containing

slags

Selective corrosion: - only certain phases in the solid are attackedFor example: - decarburisation of carbon containing refractories

dissolution of carbon in the molten steel decarburised refractory layer is wetted by the slag penetration and spalling of the decarburised layer 63


Appendix

Penetration of slag into refractories: other physiochemical effects

a) microstructural effects where a smooth surface and material: dens material may resist porous material may not resist

b) slag line attack

c) velocity of slag flow (Marangoni effect): turbulent flow tends to pull out the fine grains in the brick by erosion (physical wear)


Appendix


Appendix

Dissolution of refractories into slag:

Direct dissolution: - atoms from the solid dissolve directly into the liquid melt

- can be reaction or interface controlled

the diffusivity of reaction products is faster then the rate of chemical reaction at the interface

Rate of corrosion:

crystal orientation, grain boundary phases, grain shape are neglected

stirring of the melt has no apparent effect on dissolution rate

66

mo

c CA

AKJ

J – dissolution rate [g/cms]K – rate constantAc – actual area of refractory [cm²]Ao – apparent area of refractory [cm²]Cm – concentration of reactant in the melt [g/cm³]


Appendix


Direct dissolution: - atoms from the solid dissolve directly into the liquid melt

- can be transport or diffusion controlled

the diffusivity of reaction products is slower the rate of chemical reaction at the interface

Rate of corrosionby NERNST:

Boundary layer thickness:

if the solid is unsaturated with component of the liquid then solid solution may occur

the liquid phase diffusion of the product through the melt boundary layer is consitered

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ms CCDJ

J – dissolution rate [g/cms]D – diffusion coefficient [cm²/s]Cs – saturation concentration of refractory in the melt [g/cm³]Cm – concentration of reactant in the melt [g/cm³] – effective boundary layer thickness [cm²]

dc/dx – concentration gradient over the interface dxdc

ms CC


Appendix

Growth of solid interlayer between refractory and slag leads to indirect dissolution; t1<t2.**


Indirect dissolution: - growth of solid interlayer between refractory and slag


stirring the melt or rotating the refractory sample (slab), enhances the rate of indirect dissolution by reducing the thickness of liquid boundary layer

For laminar conditions the rate of corrosion:

A flat slab held vertically in the melt: the rate of corrosion depends on the boundary layer thickness the boundary layer thickness is limited by: degree of convective flow, liquid viscosity, mean diffusion coefficient, container size

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414

1

5,0 xCCDJ Dg

ms

J – dissolution rate [g/cms]D – diffusion coefficient [cm²/s]Cs – saturation concentration of refractory in the melt [g/cm³]Cm – concentration of reactant in the melt [g/cm³] – density difference between saturated and bulk melt [g/cm³] – dynamic viscosity [poise]g – gravitational constant [cm/s²]x – distance from the leading edge of the slab [cm]


Appendix


Indirect dissolution: - growth of solid interlayer between refractory and slag


stirring the melt or rotating the refractory sample (slab), enhances the rate of indirect dissolution by reducing the

thickness of liquid boundary layer

For forced convectionrate of corrosion:

J=0, if the refractory oxid has been saturated in the slag

to minimise J (Cs-Cm) must be minimised,

For example: if the MgO content in the slag, the corrosion of periclas -refractories

Cm=0 (Cs-Cm) = maximum, J= maximum

69

3

12

1

09,3 DxU

ms CCDJ

J – dissolution rate [g/cms]D – diffusion coefficient [cm²/s]Cs – saturation concentration of refractory in the melt [g/cm³]Cm – concentration of reactant in the melt [g/cm³] U – bulk velocity of the fluid [cm/s] – kinematic viscosity [cm²/s]=3,09(x/U)1/2(D/)1/3 – effective boundary layer thicknessx – distance from the leading edge of the slab [cm]

Appendix

70

TBAT exp

– viscosityT – absolute temperatureA, B – parameters depending only on the melt composition

Appendix

Die Ressourcenuniversität. Seit 1765. Wettability at elevated temperatures FIRRE UNITECR 2011,...

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