Influence of sodium silicate on the rheological behaviour of clay suspensions—Application of the ternary Bingham model

Applied Clay Science, 3 {1988) 323-335

323

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

Influence of Sodium Silicate on the Rheological Behaviour of Clay Suspensions Application of the Ternary B i n g h a m Model L. GARRIDO, J. GAINZA and E. PEREIRA

Centro de Tecnologia de Recursos Minerales y Cerdmica (CETMIC), Camino Parque Centenario y 506-1897-Manuel B. Gonnet (Argentina) (Received October 22, 1986; accepted after revision January 15, 1988)

ABSTRACT Garrido, L., Gainza, J. and Pereira, E., 1988. Influence of sodium silicate on the rheological behaviour of clay suspensions--applicationof the ternary Bingham model. Appl. Clay Sci., 3: 323335. Several concentrated suspensions (51% w/w) of clay in water with different amounts of a deflocculant agent (sodium-silicate solution, J = 38-39 ° B~ ) were prepared. Flow curves from each suspension were obtained by means of a coaxial-cylinder viscometer. The suspensions with low or no content of deflocculant agent give flow curves exhibiting a high initial value of the shear stress. Furthermore, this stress is highly dependent on both the shear rate and time. This indicates the presence of viscous, elastic and plastic properties in the suspensions. At higher contents of deflocculant, these properties are attenuated. A quantitative and satisfactory explanation of this complex rheological behaviour is given through a mechanical model, the double ternary Bingham model. The parameters of the proposed model depend on the sodium-silicate content of the suspension.

INTRODUCTION

The rheological characteristics of clay suspensions are of industrial interest due to their influence on the slip-casting process. Also, the filtration characteristics, behaviour on drying and the dry strength of cast ware are controlled by the properties of the slip (Satava, 1977). Some types of suspensions and pastes are often depicted, from a rheological point of view, applying the plastic Bingham model. It cannot be applied here, because the shear stress of the suspensions examined varies with time. They could be partially characterized using four thixotropic coefficients (Weltmann, 1956), but we consider that these have only a weak physical meaning. Furthermore, in the literature concerning thixotropy, equations describing the complete thixotropic loop have always been lacking. 0169-1317/88/$03.50

© 1988 Elsevier Science Publishers B.V.

324

Therefore, to explain the rheological behaviour of our suspensions, we use here an equation which takes into account their viscous, plastic and elastic properties. The equation is derived from a mechanical model formed by a helical spring (Reiner, 1956) in series with a binary Bingham model as shown in Fig. 1. This last assembly, called the plastic Bingham model, is, in turn, a dashpot and skate arranged in parallel. Here, we assume that the spring represents the Hookean elastic behaviour, the dashpot the Newtonian viscous behaviour and the skate (friction or St. Venant model ) the constant resistance from solid friction (Coulomb's force ). Such a model was also called the ternary Bingham mechanical model (Persoz, 1969) because of these three typical factors. In brief, taking into account the relations between forces and elongations in such a model (Gainza et al., 1983) it can be expressed by: (1)

Q+rQ'-p=~l(Jl)'

where ~/=viscosity coefficient of the dashpot, (Jl)'=time derivative of the elongation, r = r e l a x a t i o n time=~l/E, E= "over-all" elastic modulus of the helical spring (Reiner, 1956), Q=pulling force, Q' = t i m e derivative of Q, p = constant friction resistance, or dynamics threshold of sliding of the skate (constant resistance of a perfect plastic body). Mutatis mutandi, through a tensorial conversion we can obtain a rheological equation for a material having viscous, plastic and elastic properties. (The mathematical basis is given in short in the Appendix. ) In the cylindrical Couette flow, this equation takes the form: a+ r/~-p=

~1;;

(2)

where a a n d ?, are tangential-radial physical components of the shear-stress tensor and velocity-deformation tensor, that is say, a 12 or aOr and e *~2, respectively (see Appendix), r = t i m e constant of the material (time of relaxation, traditionally), ~/=plastic viscosity in the steady state (hypothetical), p = extrapolated yield stress from downward part. of the flow curve.

.....

I

I

!

I

Fig. 1. Schematic representation of the double ternary Bingham model.

325 For a kind of flow that obeys: (3)

",;=at

where a is a constant called here acceleration of deformation. By integrating eq. 2 using eq. 3, one obtains:

a(~',) =a(0)

e-;"/~+p(l-e-;'/°~)-a~/T(1-e -;;/"~) + ii~',

(4)

where a(~T,)=a12=shear stress (Pa), ~',=rate of' shear ( s - l ) , a=acceleration of the shear rate ( s - 1 m i n - 1), a ( 0 ) = shear stress at ~"= 0 (Pa). A complete flow curve consist of two parts; the first part, called the upward curve, goes from ~,"=0 to ~;-';, --,M, where )'~Mis a top deformation velocity that is arbitrarily chosen. Here the "upward curve" obeys eq. 3 and, therefore, also eq. 4. The second part of the curve or "downward curve", runs from ~"= ~"Mto ~"= 0. The flow history for it is given by:

i'~- ~'~M- a t

(5)

where a has the same value as that in eq. 3. Applying eq. 5 in eq. 2 and integrating, we have: :' --" 0"(~"))= [O'(f'M)--I/~"M] e-(:"M-:")/"r"bP 1--e -- (.M .)/"¢ /

(6) + a,/T(1--e-(;"M- ;")/at) 4-'l]"

where a(];M)=shear stress at 3"='~"M (Pa), which must explain the "downward" part of the flow curve. A single ternary Bingham model is not in itself adequateto explain the flow curve, but the explanation of both "upward" and "downward" curves can be given through a "double ternary Bingham model" which is formed by assembling two ternary Bingham models in parallel. The resulting shear stress from such a model is the sum of individual shear stresses of each element (i.e., simple ternary Bingham model). Then: 2

a(;',)= ~ ai(;") i=l

(7)

where ai(~'), of course, obeys eq. 4 in the "upward curve" and eq. 6 in the "downward curve". There are eight rheological parameters of the material a, (o), ~L, ri, p~, where i = 1,2, which must be fitted from the experimental flow curve, but there are two practical restrictions to be applied thereto. Thus, at ~"= 0, in the "upward part" of the flow curve

326 TABLE I Constraints imposed on the rheological parameters (some are experimental and others come from extrapolations)

a~(0) +a2(0) p~+p~ ~1~+~1~lowerlimit ~h+ ~/2upper limit

0(i't *1

0~!i;( ''1

0~!i( *1

(1)

(2)

(3)

0.21q~ 0.31%~ 0.41%c 0.81~:i~. 1.16%~ 6.35%,

91.27 87.37 1 0 4 . 7 67.21 56.53 55.18 62.01 34.00 0.001 0.001 0.001 0.001 1.65 1.65 1.65 1.31

90.20 24.15 0.001 1.08

70.57 15.88 0.001 0.75

20.96 5.00 0.001 0.8

0.0 0.0 0.001 0.8

2.719 0.40 0.001 0.8

*~Numbers between parentheses indicate different measurements made with a fresh sample each time (see Fig. 2).

0"(0) ----0.1(0) +0"2(0 ) where 0"(0) is the e x p e r i m e n t a l s h e a r stress at ~)= O. T h e straight p a r t of the " d o w n w a r d c u r v e " allows, t h r o u g h a little m a t h e matical analysis, one to write: p ~
where p = P l +P2, and asd is the e x t r a p o l a t e d value at ~)= 0 from the s t r a i g h t section of t h a t curve. T h e n , by choosing p = P l + P 2 - - a~d, we have the second restriction. T h u s , the n u m b e r of adjustable p a r a m e t e r s is reduced to six. It is necessary to consider t h a t the analogous m e c h a n i c a l e l e m e n t s are just symbols, which c a n n o t be c o r r e l a t e d with the s t r u c t u r e of the material (Pierrad, 1969). However, since the e l e m e n t s are used to r e p r e s e n t the b e h a v i o u r of an actual material, in the e q u a t i o n s derived from t h e m we have r e s t r i c t e d the range of values of some p a r a m e t e r s by a s s u m i n g a physical m e a n i n g for t h e m . So, the viscosity ~/= ~/1+ r/2 m u s t be lower limit < ~ < u p p e r limit. T h e s e limits s h o r t e n the c o m p u t e r work. T h e y a n d the values of 0.(0 ) a n d p are s h o w n in T a b l e I. T h e adjustable p a r a m e t e r s were o b t a i n e d by using the s u b r o u t i n e D F M C G ( I B M Application P r o g r a m , 1970, S y s t e m 1360 Scientific S u b r o u t i n e s Package Version III, P r o g r a m m e r ' s M a n u a l , p. 225 ) to minimize the sum of squares of the deviations between e x p e r i m e n t a l and calculated values of the shear stress. We began the iterative p r o c e d u r e by a s s u m i n g initial values for the p a r a m e t e r s . EXPERIMENTAL

Equipment A H A A K E Rotovisco RV3 was used. T h e m e a s u r i n g sensor s y s t e m consists of a set of M V I P profiled coaxial cylinders.

327 The rotating inner cylinder, is Rb = 20.04 mm in radius and 60 mm in height. The fixed outer cup is Rc = 21 mm in radius. The ratio RJRc is 0.954. The required sample volume is about 60 cm 3. The sample temperature was stabilized at 25 + 0.1 ° C. A complete rheological curve was performed by using a time-linear program of rotor speed change, a -- 20 s - 1 m i n - 1.

Materials and the preparation of suspensions The clay examined comes from deposits at the Cuchilla de las Aguilas, formation at Barker, province of Buenos Aires, Argentina. It is a kaolinitic clay with very little micaceous material and quartz. The particle-size distribution determined with a Sartorius sedimentological balance, is shown by a cumulative curve in Fig. 2. A sodium-silicate solution with a density of 38-39 ° Bd and with a composition of 8.8 w / w % Na20, 28 w / w % SiO2 was used. The mechanical behaviour of concentrated clay suspensions depends on many factors. Thus, the methods of preparation of the suspension were normalized. A suspension of a density of 1.7 g / c m 3 was prepared by dispersing of 66.66 % w / w dry clay in water; it was mixed by means of a vane stirrer for 5 min to obtain a homogeneous suspension. Then, the weighted sodium silicate was added and the suspension was again stirred for 3 min. Before measurements, the suspension was left at rest in the measurement system for 15 min to reach the working temperature. Since the suspensions are very sensitive to shear, the orientation of the particles changes during the determination of the flow curve. This means that the

'/ tO0 90 80 70 60 50 40 30 20 10 i I~0

ii t i i 100 80 60

i 40

i

i 20

i 10

i 5

i 3

om

Fig. 2. Clay-particle size distribution.

:{2s measurement procedure will cause rheological properties of the system to change. Hence, only one flow curve was made with any one suspension. RESI 7LTSAND DISCUSSION Fig. 3 shows flow curves for a clay suspension of 66.7 % w/w without additive. Three different measurements were made each time using a fresh sample. Each flow curve is identified by a number between parentheses. The flow curves show a very sudden rise of shear stress at shear rates of practically zero. Further increases in the rate of shear yields a rapid fall of the shear stress. At rates of shear ~',beyond 20 s - 1, the curve is quasi-linear. From the straight part of the "down curve" we extrapolate a yield value which is a measure of the residual plastic behaviour of the suspensions. The tlow curves show a hysteresis loop between "upward" and "downward" curves. The shear stress for the "upward" part of the flow curve is higher than that corresponding to the "downward" part at a constant rate of shear. It can be seen that this behaviour is not reversible. A second cycle on the suspension, after a period of rest, would show important changes in the characteristic properties. Beazley ( 1964 ) and Liu and Phelps ( 1976 ) reported similar flow curves with clay suspensions in a deflocculated condition, and they discussed a mechanism to explain this typical behaviour. We use a similar description which is consistent with a flocculated suspension. The percent volume concentrations of clay and water per volume of suspension were 43.3 and 56.7. Since the particles are grouped in floes and the voids between those particles retain a great volume of water, the volume concentration of' the floes in the free water will be higher than 43.3% and the floes necessarily touch each other. At the beginning of motion, the mutual interference among the flocs and among the particles associated in floes yields a solid friction at the solid surface. Furthermore, large floes offer an inertial resistance when the layers try to move like shear planes (Couette flow). The velocity gradient or the rate of shear cannot be established, because large floes move like blocks. After a short interval and beyond a critical shear rate, the blocks are broken down and the retained water may be released. This water increases the content of free water in the suspension and the friction and inertial resistance decay rapidly. We are able to use the double ternary Bingham model here to describe the decreasing non-linear shear and the plastic properties shown, at low shear rates, by both upward and downward curves. The dots in Fig. 3 correspond to shear-stress values calculated by applying the parameters listed in Table II to eqs. 4 and 6. The agreement between the experimental shear stress and the calculated value is also given in Table II as a percent standard deviation, SD, for the complete curve.

329 ~- Pal 110 tO0

GO 50 40 30 20 (3)

I0 0 90 $0 ?O GO 50 1,0 30 20

)

10 0 LI

l

I

l

I

I

l

I

I

I

90 80 70 60 50 I,O 30 20

(1)

10 ,

0

20

,

&,O

,

i

,

60

~

tO0

,

120

,

1/40

i

1fro

,

1~10

Fig. 3. Experimental flow curves for 66.7%w/w clay suspension. Symbols indicate shear stresses by curve fitting (by eqs. 4 and 6) with the parameters given in Table II ( 0 upward curve; O downward curve). Numbers between parentheses correspond to different measurements made with a fresh sample each time. N

~. ] (aei--ai)/~eil 2 SD2

i=1

N where aei is the experimental shear stress at shear rate

~i, 0"iis the shear stress

330 TABLE II Parameters appearing in eqs. 4 and 6 Sodium silicate per dry clay

al(0) (Pa)

~h (Pas)

zl (rain)

p~ (Pa)

a2(0) (Pa)

~ (Pas)

r2 (min)

p~ (Pa)

SD (%)

58.43 57.27 63.15 35.08 66.19 55.34 14.55 0.00 2.35

0.1346 0.1406 0.1391 0.1205 0.0999 0.0553 0.0712 0.0215 0.0239

1.10 - l ° 1.10 lo 3.10 -7 1.10 -9 7.10 -9 0.0175 0.0126 0.0300 0.1048

46.43 46.72 46.41 13.33 4.58 4.31 3.37 0.00 0.28

32.84 30.10 41.56 32.18 24.01 15.33 6.41 0.00 0.37

1.10 -5 1.10 5 1.10 -5 8.10 5 1.10 -~ 0.0233 0.0178 0.0010 0.0090

8.84 6.56 6.54 12.78 1.16 0.79 2.82 1.05 5.27

10.10 8.46 15.60 20.66 19.57 11.56 1.63 0.00 0.12

0.5 0.5 0.6 2.1 3.1 1.0 3.1 8.8 3.6

(%~ w/w) 0(1) .1 0(2) *j 0(3) *l 0.21 0.31 0.41 0.81 1.16 6.35

*~Numbers between parentheses indicate different measurements made with fresh sample each time (see Fig. 2 ).

calculated through the model and the parameters given in Table II, and N is the number of pairs (aei,~)i) taken from both "up" and "down" curves ( N = 100 for each part).

Effect of sodium silicate on rheological parameters Fig. 4 reports flow curves for different amounts of sodium silicate. The deflocculant concentration is expressed in %o w/w sodium-silicate solution per dry clay. Numbers on Fig. 4 indicate the sodium-silicate concentrations present in the suspension. As expected, the high initial value a(0 ), the shear stress-shear rate relation and the area of the hysteresis loop decrease with increasing deflocculant concentration. They reach a minimum at 1.16 %o where the system is deflocculated. As the sodium concentration rises, both the initial peak and nonnewtonian behaviour increase. An excessive amount of ion sodium promotes flocculation instead of avoiding it. Although the curves show the same curvature for the two parts, it is interesting to note that with a low content of deflocculant, the stress for the downward curve appears below that of the upward. At concentrations higher than 1.16, the position is inverted, the stress for the downward part is higher than the corresponding stress for the upward part. We found that the double ternary Bingham model (eqs. 4 and 6) is very useful in describing the complex rheological behaviour of the suspensions examined. In Fig. 4, dots were obtained according to the model. Table II shows the parameters as a function of the sodium-silicate concentration. There is a

331 ~"(P'] I

:°o

60

3O

2O 10 I

I

I

I

I

I

I

I

o

o

80

70

60 o

.I

o

.I

1.15

i

I

I

I

I

~

i ~

I

I

I

I

0.21 i ~

1~

1~

1/0

1~

Is-1]

Fig. 4. Experimental flow curves for 66.7%w/w clay suspensions and different concentrations of sodium silicate. Symbols indicate shear stresses by curve fitting (by eqs. 4 and 6) with parameters given in Table II. ( • upward curve, C) downward curve. ) Numbers on the figure are the deflocculant concentrations expressed in %o w/w sodium silicate solution per dry clay.

good agreement beyond a concentration of 1.16%o. Furthermore, better agreement was obtained at lower concentrations. As can be seen in Table II, ~/andp behave like a ( 0 ) . T] increases with added sodium silicate. Up to a concentration of 1.16%o, z] is not significant in comparison with the time of the experiment ~M/a. Thus, the corresponding exponential terms in eqs. 4 and 6 contribute very little to a(~)). For a concentration of 6.35, Zl has increased so much that the exponential terms became important.

332 TABLE III Parameters of the single ternary B ingham model (equivalent to the proposed double model) Sodium silicate solution per dry clay (ci(, w/w)

a(0 ) (Pa)

0(1)" 0(2) "~ 0(3) "~ 0.21 0.31 0.41 0.81 1.16 6.35

91.27 87.37 104.71 67.21 90.21 70.75 20.96 0.00 2.72

q (Pas) 0.135 0.141 /).139 0.1206 0.0999 0.0789 0.0890 0.0223 0.0329

p ( Pa ) 56.23 55.18 62.01 34.00 24.15 25.88 5.00 0.00 0.40

(~)) ~ o m u p w a r d curve )',=1

~)=3

~:,=5

?"= 10

?;=20

0:1260 0.1370 0.1047 0.0480 0.0183 0.0181 0.0413 0.0319 0.1170

0.4010 0.4398 0.3194 0.1466 0.0537 0.0519 0.1228 0.0351 0.1279

0.7180 0,8071 0.5429 0.2473 0.0874 0.0830 0.2031 0.0416 0.1682

2.2389 2.1005 1.1581 0.5122 0.1658 0.1510 0.3995 0.0463 0.2198

2.9992 2.7990 3.3460 1.1177 0.3057 0.7171 0.7867 0.0576 0.4897

"1Numbers between parentheses indicate different measurements made with a fresh sample each time (see Fig. 2).

Inversely, z2, which is the significant relaxation time, decreases by adding sodium silicate up to a concentration corresponding to the deflocculated condition; beyond this point, z2 increases with the concentration. Starting from eqs. 4 and 7, we can define a single ternary Bingham model, which could be equivalent to the proposed double model, by: (a(0) - p + a~z0)exp ( - ; / / a z ) - a q z = K(~'~) where: "CO---- ( q l -~- ~2 ) ~'1 T 2 / ( ql ~'2 ~- ~2 ~'1 ) ~--"relaxation time for ~ = 0

and: 2

2

K(~')= ~ ( a i ( 0 ) - p , + a r l i z i ) exp i=1

(-~/az,)-a ~ rkT:i :=1

Using the values of the parameters given in Table II, we can obtain 3, for each ~,, by applying an iterative procedure to the equation ( a ( 0 ) - - p + a q Z o ) exp

(--7/az)-a~v-- g ( ~ ) ) = 0

This equivalent model has two disadvantages. The first is that the relaxation time is not a constant, but it depends on the strain rate ~' in a rather complicated way. Secondly, the iterative procedure is not sufficiently convergent for deformation velocities ~)higher than 20 s - 1. Nevertheless, this equivalent model explains the whole plasticity, the whole viscosity and the whole elasticity of the suspension. The latter will then be reflected by the relaxation time. Table III shows these whole properties for ~" below 20 s - 1 and for the upward part of the flow curve.

333 The relaxation time ~ reaches a minimum at intermediate concentrations of sodium silicate; near a concentration of 0.81c~c ~ depends on ~',in a way that is not yet sufficiently clear. CONCLUSION The rheological behaviour of concentrated suspensions of clay in water is satisfactorily explained by both the double ternary Bingham model and the single ternary Bingham model which is equivalent to it. The double model is useful to calculate exactly the shear stress under flow conditions similar to those that we used. Also, it has rheological parameters which are constant in the examined ;', region. The single model allows an easy description of the rheological properties: elasticity, plasticity and viscosity, for each suspension as a whole. However, such a model must be obtained from the parameters of the double model and thus is not useful for predictions and accurate calculations. Of course, the values of almost all the parameters change markedly when the deflocculant concentration increases. Thus, the initial stress a(0), which defines the plastic behaviour, the Newtonian viscosity contribution q, the residual grade of plasticity p and the area of the hysteresis loop that is a measure of the shear decreasing with time, reach a minimum at some point between 1.16tic and 6.35cic of sodium-silicate solution per dry clay. The relaxation time r of the single model that represents the whole elasticity of the suspension has a minimum at 1.16%c sodium silicate per dry clay. APPENDIX The constitutive relation of the ternary Bingham model is obtained by combining Oldroyd's (1950) and Bingham's plastic tensorial equations (Fredrickson, 1964). The equation for the co-deformational contravariant model is (Gainza et al., 1983 ):

2pe'J

( 1 + 2 1 - ~ ) (a i~

) = 2,1(1 +)~._,~ ) e

'~

(A1)

12(eOei;) I '/2 when: 1 i i 2 ~a) aj>~p

where: D c / D t denotes a convective time derivative; a ij is the extra stress tensor;

eiJ= l/2(vlj + vJi)

334 is the rate of deformation tensor, where v ij is the covariant derivative of v i with respect to the x i coordinate; 21 and 22 are material constants, known as relaxation time and retardation time; ~/is the coefficient of viscosity and p is a yield stress. In the flow between two rotating coaxial cylinders the cylindrical coordinates are:

xl=O,

x2mr,

xa=z

The physical components of the velocity vector are:

v~=reo(r),

v2=v:~=0

where to is the angular velocity, which is a function of r. Then we obtain for the physical components of the rate of deformation tensor: e~ , : e..22 : e 2 : ~: e,:~=e33=Oande~2

lOv 1 20x 2-

10w 2 r or ="

(A2)

where ~ denotes the r0(12) component of the strain rate. In a rotating axial cylinder viscometer, the measured component of the stress is 0.12. From eqs. A1 and A2 and by assuming 0.22=0 and )~2=0, we obtain the linearized equation for the physical component 0.12 of the stress tensor: 0 0 -12

a ~ + )~, - ~ - - P = ~ l ? '

(A3)

where O/Ot indicates a partial time derivative. The experimental results carried out with concentrated aqueous clay suspensions indicate that the normal stress can be neglected. This justifies the assumption a 22-- 0. In steady shear flow (in which a 12 and ~)are constant with time), the codeformational contravariant Bingham ternary model (eq. A1 ) predicts the stress components a ~2, a~l; all other stress components vanish. In order to reach the steady shear flow we can apply to the system a normal stress a equal and opposite to a ~1, given by a = 2t I )~~ ?" When a'2 is constant with time, eq. A3 for the shear stress component becomes:

a~-'=p+ tlf, and that is the equation of the plastic Bingham model.

(A4)

335 REFERENCES Beazley, K.M., 1964. Breakdown and build up in China clay suspensions. Trans. Br. Ceram. Soc., 63: 451-471. Fredrickson, A., 1964. Principles and Applications of Rheology. Prentice Hall, Englewood Cliffs, N.J., 179 pp. Gainza, J., Garrido, L. and Pereira, E., 1983. Criterios para la selecci6n de modelos mec~nicos representativos del comportamiento reol6gico de suspensiones acuosas de arcilla. Comunication presented at XIIas Jornadas sobre investigaciones en Ciencias de la Ingenier~a Qulmica y Qulmica Aplicada. Tucum£n, Argentina, March 21-25. Liu, V. and Phelps, G., 1976. Influencia da distribuicao granulometria nas propiedades reolSgicas de barbotinas de argilo-minerais corn alta concentracao de s61idos. Ceramica, 22 (90): 231-243. Oldroyd, J.G., 1950. On the formulation of rheological equations of state. Proc. R. Soc. London, A 200: 123. Persoz, B. (Editor), 1969. La Rh~ologie. Masson, Paris, 186 pp. Pierrad, J.M., 1969. ModUles et fonctions visco-~lastiques Lin~aires. In: B. Persoz (Editor), La Rh~ologie. Masson, Paris, pp. 20. Reiner, M., 1956. Phenomenological macrorheology. In: F. Eirich (Editor), Rheology, Vol. I. Academic Press, New York, N.Y., pp. 9-61. Satava, V., 1977. Th~orie de la fluidification des barbotines c~ramiques et optimalisation du proc~d~ de coulage. Industrie Ceram., 707: 433-437. Weltmann, R., 1956. Rheology of pastes and paints. In: F. Eirich (Editor), Rheology, Vol. III. Academic Press, New York, N.Y., pp. 189-248.