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Rheological Behavior of Kaolin and Montmorillonite Suspensions at Low Concentrations
Journal of Colloid and Interface Science 244, 405– 409 (2001) doi:10.1006/jcis.2001.7926, available online at http://www.idealibrary.com on
Rheological Behavior of Kaolin and Montmorillonite Suspensions at Low Concentrations V. N. Kislenko1 and R. M.Verlinskaya Lviv Polytechnic State University, 12 Bandera St., Lviv 79013, Ukraine Received April 30, 2001; accepted August 17, 2001; published online November 9, 2001
The rheological behavior of kaolin and montmorillonite suspensions at low concentrations in water and polymer solutions has been investigated. An influence of the polymer concentration on the viscosity of suspension for the kaolin suspension in the presence of diethylenetriaminomethylated polyacrylamide and for the montmorillonite suspension in the presence of polyacrylic acid has been demonstrated. The dependence between the shear stress and the cross-sectional area of particles and the number of particles in a unit volume of the suspension has been shown. Mathematical equations for the number of aggregates in the unit volume of suspension and the number of initial particles in aggregate at the different polymer concentrations in mixture are proposed. °C 2001 Elsevier Science Key Words: rheology; kaolin; montmorillonite suspension; polymer solution.
INTRODUCTION
Rheological properties of suspensions are important in various industrial processes, such as ceramics and pharmaceuticals (1, 2). Rheological measurements allow one to obtain information on particle interactions in suspension and their macroscopic structure. Investigation of silica suspensions in poly(ethylene oxide) (3) or polyvinyl alcohol solutions (4, 5) at 1–2% silica concentration in suspension showed that silica particles are flocculated. An increase in Aerosil concentration in suspension at pH 7–9 leads to a gradual transition from Newtonian to pseudo-plastic flow (5). Rheological measurements of Aerosil (fumed silica) particles in polyacrylamide solution in glycerine showed that the size of silica particles did not influence the viscosity results (6). The information concerning the rheological behavior of suspensions at low concentrations in polymer solution is very limited.
diameter 5 × 10−6 m and montmorillonite with average particle diameter 8 × 10−6 m were used. The particle diameter was determined on a UEMV-100 electron microscope. A water solution of polyacrylic acid with molecular mass 1.6 × 106 and diethylenetriaminomethylated polyacrylamide (DTAA) with molecular mass 1.4 × 105 and substitution degree 36% were used. A water solution of DTAA was prepared as described in (7). A water suspension of kaolin with concentration 262 g/l and pH 7 was diluted by distilled water or DTAA solution with pH 7 and mixed 15 min before the rheological experiment. We used the montmorillonite suspension and polyacrylic acid solution at pH 2.5. Rheological experiments were carried out by using Rheotest. Typical curves, obtained in experiments, are presented in Fig. 1. The intercept on the ordinate axis, Pc , and the slope of the tangent of the straight line, η0 , have been calculated. The adsorption isotherm of polyacrylic acid on the montmorillonite particles was obtained at montmorillonite concentration 13–28 g/l and pH 2. The mixture of suspension with polymer was stirred for 1 h at 20◦ C. The polymer concentration in solution was determined by the potentiometric method after centrifugation of the dispersed phase at a rotation rate of 8 × 103 min−1 , 12 × 103 g, for 20 min. Kinetics experiments show that the equilibrium state was reached after 1–2 min of mixing (Fig. 2). RESULTS AND DISCUSSION
Investigation of the relationship between η0 and the concentration of the suspension showed that it is linear at kaolin concentrations from 30 to 150 g/l and at montmorillonite concentrations from 1 to 40 g/l (Figs. 3 and 4). Therefore, in these concentration regions the suspension is Newtonian and the viscosity of the suspension can be described by the equation
EXPERIMENTAL
η0 = ηo (1 + ϕc),
Commercial Glukhovetsky kaolin and Zakarpatsky montmorillonite were washed with distilled water to remove the chloride ions, and a crude fraction was separated by sedimentation over 10 days. Water suspensions of kaolin with average particle
where ηo is the viscosity of the dispersion medium, c is the volume fraction, and ϕ is a constant. The value of Pc is the constant at low suspension concentration (up to 80 g/l for kaolin and 15 g/l for montmorillonite). The negative values of Pc can be bound with the known phenomenon when the hydrodynamic resistance of liquid decreases in the
1
To whom correspondence should be addressed.
405
[1]
0021-9797/01 $35.00
° C 2001 Elsevier Science
All rights reserved
406
KISLENKO AND VERLINSKAYA
FIG. 1. Dependence of shear stress on shear rate of montmorillonite suspension with 4.5 g/l polyacrylic acid at montmorillonite concentrations 37.4 (1), 18.7 (2), 9.4 (3), and 3.7 g/l (4).
presence of a low concentration of the polymers or solid particles as compared with the pure liquid. Then it rises sharply at more concentrated suspensions. Therefore, we suggested that, at low concentrations of suspensions, when the distance between particles is large, the value of Pc depends on the properties of particles such as the cross-sectional area of the particle. Really, measurements of Pc of latices, obtained from the synthetic caoutchouc, factory, Yaroslavl, Russia, and pigment suspensions, obtained from the dyestuff factory, Dniepropetrovsk, Ukraine, with the known average diameter of particles in the region of concentrations, when the values of Pc were constant, show (Fig. 5) that the relation between Pc and the particle section is linear according to the equation Pc = a1 + b1 log(Sh ),
[2]
where a1 and b1 are constants and Sh is the cross-sectional area of the partricle (in m2 ). The correlation coefficient was 0.939. a1 = 8.4 ± 2.2 Pa, and b1 = 1.1 ± 0.2 Pa, min. If the value of b1 = 1, the value of a1 can be calculated according to the equation a1 = [Pc − log(Sh )]/n = 7.3 ± 0.9,
[3]
FIG. 3. Plot of η0 (1) and Pc (2) versus kaolin concentration in water.
When the suspension concentration is higher and the distance between particles is shorter, the value of Pc depends on the concentration of dispersed phase raised to a power close to 2 (Fig. 5). Therefore, we suggest that, in this concentration region, Pc depends on the number of particle collisions. Really, the relationship between Pc and the number of particles in the unit volume of suspension, N , is linear according to the following equation, obtained with the use of Eq. [3], Y = a2 + b2 log N 2 ,
[4]
where Y = log[Pc − 7.3 − log(Sh )] and a2 and b2 are constants. As Fig. 6 shows, this dependence is linear. Correlation coefficients are 0.979 and 0.997 for kaolin and montmorillonite suspensions, correspondingly. The value of b2 is close to 1 ± 0.1, and the value of a2 is close to 23 ± 6 for both cases. If we suggested the value of b2 = 1, the value of a2 can be calculated
where n is the number of experimental points.
FIG. 2. Kinetics curve of polyacrylic acid adsorption on the montmorillonite particles at polymer concentration 1.34 g/l, montmorillonite concentrations 13.8 g/l, and 20◦ C.
FIG. 4. Plot of η0 (1) and Pc (2) versus montmorillonite concentration in water.
407
KAOLIN AND MONTMORILLONITE SUSPENSIONS
FIG. 5. Dependence of Pc on the hydrodynamic section of particle (in m2 ) for different latices and pigment suspensions.
FIG. 7. Plot of η0 (1) and Pc (2) versus TDAA concentration in the kaolin suspension with concentration 233 g/l.
according to the equation a2 = [log{Pc − 7.3 − log(Sh )} − log(N 2 )]/n,
[5]
where n is the number of experimental points. In this case the value of a2 is equal to 23.2 ± 0.8 and 20.7 ± 1.2 for kaolin and montmorillonite suspension, correspondingly. A rheological investigation of the kaolin suspension in the DTAA solution with different polymer concentrations showed that the value of η0 is practically constant and the value of Pc decreases when the polymer concentration increases (Fig. 7). According to Eq. [1], the volume fraction of the dispersed phase does not change in this case. At the same time, the flocculation of dispersed particles takes place (8). We can suggest two mechanisms of aggregate formation from kaolin particles in the presence of polymer. The first occurs when the aggregate construction is linear. In this case, the crosssectional area of the aggregate practically equals the initial par-
ticle section. Therefore, we can calculate the number of aggregates in the unit volume of suspension according to the following equation, obtained from Eq. [4]: Na = 10[log{Pc −7.3−log(Sh )}+23.2]/2 .
[6]
The number of particles in the aggregate equals n a = No /Na ,
[7]
where No is the number of initial particles in the unit volume of the unflocculated suspension. Figure 8 (curves 1, 3) demonstrates that the number of aggregates in the unit volume of suspension decreases and the number of initial particles in the aggregate increases when the polymer concentration increases. That is close to results obtained in ref. 8. The second mechanism suggests that the aggregate is spherical. In this case the volume of one aggregate equals va = c/Na ,
[8]
and the hydrodynamic section of the aggregate can be described by the equation Sh = π[(3c)/(4π Na )]2/3 .
[9]
From Eqs. [4] and [9] we obtained 2/3 10log[ Pc −7.3−log{π ((3c)/(4π Na )) }]/2 − Na = 0.
FIG. 6. Dependence of Pc on the number of particles in the unit volume of suspension for kaolin suspension (1) and montmorillonite suspension (2) when plotted according to Eq. [4].
[10]
Equation [10] allows one to calculate the number of aggregates in the unit volume of the suspension (Fig. 8, curve 2) and the number of initial particles in the aggregate (Fig. 8, curve 4).
408
KISLENKO AND VERLINSKAYA
FIG. 10. Plot of η0 versus polyacrylic acid concentration at the montmorillonite concentrations 9.4 (1), 18.7 (2), and 28 g/l (3). FIG. 8. Dependence of the aggregate number in the unit volume of suspension (1, 2) and the number of initial particles in the aggregate (3, 4) on the TDAA concentration at kaolin concentration 233 g/l calculated according to Eq. [6] (1, 3) and Eq. [10] (2, 4).
As Fig. 8 shows, the difference between two mechanisms of aggregation is not great. The rheological behavior of the montmorillonite suspension in the presence of polyacrylic acid differs from the kaolin suspension. Values of Pc and η0 pass through the maximum when the polymer concentration increases (Figs. 9, 10). Therefore, the volume fraction of the dispersed phase changes when aggregates have been formed.
The volume fraction of the dispersed phase can be calculated according to the equation c = (η0 − ηop − ηom − ηop ϕp cp )/(ηom ϕm )
[11]
where p and m are indexes of polymer and montmorillonite for values of Eq. [1] and cp is the equilibrium polymer concentration in solution. The values of the equilibrium polymer concentration in solution can be found from the adsorption isotherm. The adsorption isotherm of polyacrylic acid on the montmorillonite particles (Fig. 11) does not depend on the montmorillonite concentration in suspension. The experimental data on adsorption can be smoothed by Langmuir’s equation (Fig. 12) to calculate the values of cp , with the initial polymer concentration cp /A = 1/Am + kd /ka 1/cp ,
[12]
where Am is the maximum adsorption and kd /ka is the ratio of desorption and adsorption constants.
FIG. 9. Plot of Pc versus polyacrylic acid concentration at the montmorillonite concentrations 9.4 (1), 18.7 (2), and 28 g/l (3).
FIG. 11. Adsorption isotherm of polyacrylic acid on the montmorillonite particles at montmorillonite concentrations 13.8 (1) and 24.6 g/l (2).
409
KAOLIN AND MONTMORILLONITE SUSPENSIONS
FIG. 12. Dependence of polyacrylic acid adsorption at montmorillonite particles on the equilibrium polymer concentration when plotted according to Eq. [12] at the montmorillonite concentrations 13.8 and 24.6 g/l.
The correlation coefficient equals 0.913, 1/Am = 57 ± 16 g/g, and kd /ka = 10.7 ± 1.4 l/g. The equilibrium polymer concentration can be found from A = F − (F 2 − Am co /cd )1/2 ,
[13]
where F = 1/2(co /cd − kd /ka Am /cd − Am ), co is the initial polymer concentration, and cd is the concentration of montmorillonite, and cp = co − Acd .
[14]
Equations [11], [13], and [14] allow one to find the equilibrium polymer concentration in the flocculated montmorillonite
suspension at different initial polymer and montmorillonite concentrations. Calculation of the number of aggregates in the unit volume of suspension at 18.7 g/l montmorillonite concentration by using the first model, Eq. [6], showed that it is less than 1. The number of initial particles in aggregate according to Eq. [7] practically equals the initial particle number in the unit volume of suspension. Therefore, this model does not describe the rheological behavior of the montmorillonite suspension. The results of the calculation of the number of aggregates in the unit volume of suspension, Eq. [10], the number of initial particles in the aggregate, Eq. [7], and the radius of aggregate using the second model are demonstrated in Fig. 13. At the low polymer concentration, the flocculation of suspension proceeds quite well. An increase of the polymer concentration leads to an increase of the number of aggregates in the unit volume of suspension and to a decrease of the size of aggregate. These results are confirmed by the investigation of the number of aggregates of the kaolin suspension in the presence of polymer by nephelometric method (8). The suspension is stabilized by the polymer at the large polymer concentration. A use of both models for the montmorillonite concentration of 28 g/l in the suspension leads to a decrease of aggregate number in the unit volume of suspension less than 1. Evidently, the suspension is structured in this case, and these models do not describe the rheological behavior of the suspension at high concentrations. The difference in rheological behavior between kaolin and montmorillonite suspensions stipulates evidently for the structure and the charge of the particle surface. Really, the montmorillonite suspension flocculates with the formation of very great aggregates in the presence of DTAA in solution. At the same time, the flocculation of kaolin suspension in the DTAA solution proceeds more slowly and the size of aggregates is small. Therefore, the change of the number of aggregates in the unit volume of suspension and the number of initial particles in aggregate at the different polymer concentration in the mixture can be calculated according to Eqs. [7] and [10] on the basis of the experimental data on the rheological behavior of the suspension. REFERENCES
FIG. 13. Plot of the number of aggregates in the unit volume of suspension (1), the number of initial particles in the aggregate (2), and the radius of aggregate (3) versus polyacrylic acid concentration calculated according to Eqs. [9] and [10].
1. Tadros, Th. F., in “Solid/Liquid Dispersions.” (Th. F. Tadros, Ed.), Chapter 1. Academic Press, London, 1987. 2. Tadros, Th. F., Adv. Colloid Interface Sci. 12, 141 (1980). 3. Eisenlauer, J., and Killmann, E., J. Colloid Interface Sci. 74, 108 (1980). 4. Tadros, Th. F., J. Colloid Interface Sci. 64, 36 (1978). 5. Heath, D., and Tadros, Th. F., J. Colloid Interface Sci. 93, 320 (1983). 6. Otubo, Y., and Watanabe, K., Colloids Surf. 50, 341 (1990). 7. Verlinskaya, R. M., Kislenko, V. N., and Berlin Ad. A., J. Appl. Chem. (Russia) 9, 1505 (1998). 8. Kislenko, V. N., and Verlinskaya, R. M., J. Colloid Interface Sci. 216, 65 (1999).
Rheological Behavior of Kaolin and Montmorillonite Suspensions at Low Concentrations V. N. Kislenko1 and R. M.Verlinskaya Lviv Polytechnic State University, 12 Bandera St., Lviv 79013, Ukraine Received April 30, 2001; accepted August 17, 2001; published online November 9, 2001
The rheological behavior of kaolin and montmorillonite suspensions at low concentrations in water and polymer solutions has been investigated. An influence of the polymer concentration on the viscosity of suspension for the kaolin suspension in the presence of diethylenetriaminomethylated polyacrylamide and for the montmorillonite suspension in the presence of polyacrylic acid has been demonstrated. The dependence between the shear stress and the cross-sectional area of particles and the number of particles in a unit volume of the suspension has been shown. Mathematical equations for the number of aggregates in the unit volume of suspension and the number of initial particles in aggregate at the different polymer concentrations in mixture are proposed. °C 2001 Elsevier Science Key Words: rheology; kaolin; montmorillonite suspension; polymer solution.
INTRODUCTION
Rheological properties of suspensions are important in various industrial processes, such as ceramics and pharmaceuticals (1, 2). Rheological measurements allow one to obtain information on particle interactions in suspension and their macroscopic structure. Investigation of silica suspensions in poly(ethylene oxide) (3) or polyvinyl alcohol solutions (4, 5) at 1–2% silica concentration in suspension showed that silica particles are flocculated. An increase in Aerosil concentration in suspension at pH 7–9 leads to a gradual transition from Newtonian to pseudo-plastic flow (5). Rheological measurements of Aerosil (fumed silica) particles in polyacrylamide solution in glycerine showed that the size of silica particles did not influence the viscosity results (6). The information concerning the rheological behavior of suspensions at low concentrations in polymer solution is very limited.
diameter 5 × 10−6 m and montmorillonite with average particle diameter 8 × 10−6 m were used. The particle diameter was determined on a UEMV-100 electron microscope. A water solution of polyacrylic acid with molecular mass 1.6 × 106 and diethylenetriaminomethylated polyacrylamide (DTAA) with molecular mass 1.4 × 105 and substitution degree 36% were used. A water solution of DTAA was prepared as described in (7). A water suspension of kaolin with concentration 262 g/l and pH 7 was diluted by distilled water or DTAA solution with pH 7 and mixed 15 min before the rheological experiment. We used the montmorillonite suspension and polyacrylic acid solution at pH 2.5. Rheological experiments were carried out by using Rheotest. Typical curves, obtained in experiments, are presented in Fig. 1. The intercept on the ordinate axis, Pc , and the slope of the tangent of the straight line, η0 , have been calculated. The adsorption isotherm of polyacrylic acid on the montmorillonite particles was obtained at montmorillonite concentration 13–28 g/l and pH 2. The mixture of suspension with polymer was stirred for 1 h at 20◦ C. The polymer concentration in solution was determined by the potentiometric method after centrifugation of the dispersed phase at a rotation rate of 8 × 103 min−1 , 12 × 103 g, for 20 min. Kinetics experiments show that the equilibrium state was reached after 1–2 min of mixing (Fig. 2). RESULTS AND DISCUSSION
Investigation of the relationship between η0 and the concentration of the suspension showed that it is linear at kaolin concentrations from 30 to 150 g/l and at montmorillonite concentrations from 1 to 40 g/l (Figs. 3 and 4). Therefore, in these concentration regions the suspension is Newtonian and the viscosity of the suspension can be described by the equation
EXPERIMENTAL
η0 = ηo (1 + ϕc),
Commercial Glukhovetsky kaolin and Zakarpatsky montmorillonite were washed with distilled water to remove the chloride ions, and a crude fraction was separated by sedimentation over 10 days. Water suspensions of kaolin with average particle
where ηo is the viscosity of the dispersion medium, c is the volume fraction, and ϕ is a constant. The value of Pc is the constant at low suspension concentration (up to 80 g/l for kaolin and 15 g/l for montmorillonite). The negative values of Pc can be bound with the known phenomenon when the hydrodynamic resistance of liquid decreases in the
1
To whom correspondence should be addressed.
405
[1]
0021-9797/01 $35.00
° C 2001 Elsevier Science
All rights reserved
406
KISLENKO AND VERLINSKAYA
FIG. 1. Dependence of shear stress on shear rate of montmorillonite suspension with 4.5 g/l polyacrylic acid at montmorillonite concentrations 37.4 (1), 18.7 (2), 9.4 (3), and 3.7 g/l (4).
presence of a low concentration of the polymers or solid particles as compared with the pure liquid. Then it rises sharply at more concentrated suspensions. Therefore, we suggested that, at low concentrations of suspensions, when the distance between particles is large, the value of Pc depends on the properties of particles such as the cross-sectional area of the particle. Really, measurements of Pc of latices, obtained from the synthetic caoutchouc, factory, Yaroslavl, Russia, and pigment suspensions, obtained from the dyestuff factory, Dniepropetrovsk, Ukraine, with the known average diameter of particles in the region of concentrations, when the values of Pc were constant, show (Fig. 5) that the relation between Pc and the particle section is linear according to the equation Pc = a1 + b1 log(Sh ),
[2]
where a1 and b1 are constants and Sh is the cross-sectional area of the partricle (in m2 ). The correlation coefficient was 0.939. a1 = 8.4 ± 2.2 Pa, and b1 = 1.1 ± 0.2 Pa, min. If the value of b1 = 1, the value of a1 can be calculated according to the equation a1 = [Pc − log(Sh )]/n = 7.3 ± 0.9,
[3]
FIG. 3. Plot of η0 (1) and Pc (2) versus kaolin concentration in water.
When the suspension concentration is higher and the distance between particles is shorter, the value of Pc depends on the concentration of dispersed phase raised to a power close to 2 (Fig. 5). Therefore, we suggest that, in this concentration region, Pc depends on the number of particle collisions. Really, the relationship between Pc and the number of particles in the unit volume of suspension, N , is linear according to the following equation, obtained with the use of Eq. [3], Y = a2 + b2 log N 2 ,
[4]
where Y = log[Pc − 7.3 − log(Sh )] and a2 and b2 are constants. As Fig. 6 shows, this dependence is linear. Correlation coefficients are 0.979 and 0.997 for kaolin and montmorillonite suspensions, correspondingly. The value of b2 is close to 1 ± 0.1, and the value of a2 is close to 23 ± 6 for both cases. If we suggested the value of b2 = 1, the value of a2 can be calculated
where n is the number of experimental points.
FIG. 2. Kinetics curve of polyacrylic acid adsorption on the montmorillonite particles at polymer concentration 1.34 g/l, montmorillonite concentrations 13.8 g/l, and 20◦ C.
FIG. 4. Plot of η0 (1) and Pc (2) versus montmorillonite concentration in water.
407
KAOLIN AND MONTMORILLONITE SUSPENSIONS
FIG. 5. Dependence of Pc on the hydrodynamic section of particle (in m2 ) for different latices and pigment suspensions.
FIG. 7. Plot of η0 (1) and Pc (2) versus TDAA concentration in the kaolin suspension with concentration 233 g/l.
according to the equation a2 = [log{Pc − 7.3 − log(Sh )} − log(N 2 )]/n,
[5]
where n is the number of experimental points. In this case the value of a2 is equal to 23.2 ± 0.8 and 20.7 ± 1.2 for kaolin and montmorillonite suspension, correspondingly. A rheological investigation of the kaolin suspension in the DTAA solution with different polymer concentrations showed that the value of η0 is practically constant and the value of Pc decreases when the polymer concentration increases (Fig. 7). According to Eq. [1], the volume fraction of the dispersed phase does not change in this case. At the same time, the flocculation of dispersed particles takes place (8). We can suggest two mechanisms of aggregate formation from kaolin particles in the presence of polymer. The first occurs when the aggregate construction is linear. In this case, the crosssectional area of the aggregate practically equals the initial par-
ticle section. Therefore, we can calculate the number of aggregates in the unit volume of suspension according to the following equation, obtained from Eq. [4]: Na = 10[log{Pc −7.3−log(Sh )}+23.2]/2 .
[6]
The number of particles in the aggregate equals n a = No /Na ,
[7]
where No is the number of initial particles in the unit volume of the unflocculated suspension. Figure 8 (curves 1, 3) demonstrates that the number of aggregates in the unit volume of suspension decreases and the number of initial particles in the aggregate increases when the polymer concentration increases. That is close to results obtained in ref. 8. The second mechanism suggests that the aggregate is spherical. In this case the volume of one aggregate equals va = c/Na ,
[8]
and the hydrodynamic section of the aggregate can be described by the equation Sh = π[(3c)/(4π Na )]2/3 .
[9]
From Eqs. [4] and [9] we obtained 2/3 10log[ Pc −7.3−log{π ((3c)/(4π Na )) }]/2 − Na = 0.
FIG. 6. Dependence of Pc on the number of particles in the unit volume of suspension for kaolin suspension (1) and montmorillonite suspension (2) when plotted according to Eq. [4].
[10]
Equation [10] allows one to calculate the number of aggregates in the unit volume of the suspension (Fig. 8, curve 2) and the number of initial particles in the aggregate (Fig. 8, curve 4).
408
KISLENKO AND VERLINSKAYA
FIG. 10. Plot of η0 versus polyacrylic acid concentration at the montmorillonite concentrations 9.4 (1), 18.7 (2), and 28 g/l (3). FIG. 8. Dependence of the aggregate number in the unit volume of suspension (1, 2) and the number of initial particles in the aggregate (3, 4) on the TDAA concentration at kaolin concentration 233 g/l calculated according to Eq. [6] (1, 3) and Eq. [10] (2, 4).
As Fig. 8 shows, the difference between two mechanisms of aggregation is not great. The rheological behavior of the montmorillonite suspension in the presence of polyacrylic acid differs from the kaolin suspension. Values of Pc and η0 pass through the maximum when the polymer concentration increases (Figs. 9, 10). Therefore, the volume fraction of the dispersed phase changes when aggregates have been formed.
The volume fraction of the dispersed phase can be calculated according to the equation c = (η0 − ηop − ηom − ηop ϕp cp )/(ηom ϕm )
[11]
where p and m are indexes of polymer and montmorillonite for values of Eq. [1] and cp is the equilibrium polymer concentration in solution. The values of the equilibrium polymer concentration in solution can be found from the adsorption isotherm. The adsorption isotherm of polyacrylic acid on the montmorillonite particles (Fig. 11) does not depend on the montmorillonite concentration in suspension. The experimental data on adsorption can be smoothed by Langmuir’s equation (Fig. 12) to calculate the values of cp , with the initial polymer concentration cp /A = 1/Am + kd /ka 1/cp ,
[12]
where Am is the maximum adsorption and kd /ka is the ratio of desorption and adsorption constants.
FIG. 9. Plot of Pc versus polyacrylic acid concentration at the montmorillonite concentrations 9.4 (1), 18.7 (2), and 28 g/l (3).
FIG. 11. Adsorption isotherm of polyacrylic acid on the montmorillonite particles at montmorillonite concentrations 13.8 (1) and 24.6 g/l (2).
409
KAOLIN AND MONTMORILLONITE SUSPENSIONS
FIG. 12. Dependence of polyacrylic acid adsorption at montmorillonite particles on the equilibrium polymer concentration when plotted according to Eq. [12] at the montmorillonite concentrations 13.8 and 24.6 g/l.
The correlation coefficient equals 0.913, 1/Am = 57 ± 16 g/g, and kd /ka = 10.7 ± 1.4 l/g. The equilibrium polymer concentration can be found from A = F − (F 2 − Am co /cd )1/2 ,
[13]
where F = 1/2(co /cd − kd /ka Am /cd − Am ), co is the initial polymer concentration, and cd is the concentration of montmorillonite, and cp = co − Acd .
[14]
Equations [11], [13], and [14] allow one to find the equilibrium polymer concentration in the flocculated montmorillonite
suspension at different initial polymer and montmorillonite concentrations. Calculation of the number of aggregates in the unit volume of suspension at 18.7 g/l montmorillonite concentration by using the first model, Eq. [6], showed that it is less than 1. The number of initial particles in aggregate according to Eq. [7] practically equals the initial particle number in the unit volume of suspension. Therefore, this model does not describe the rheological behavior of the montmorillonite suspension. The results of the calculation of the number of aggregates in the unit volume of suspension, Eq. [10], the number of initial particles in the aggregate, Eq. [7], and the radius of aggregate using the second model are demonstrated in Fig. 13. At the low polymer concentration, the flocculation of suspension proceeds quite well. An increase of the polymer concentration leads to an increase of the number of aggregates in the unit volume of suspension and to a decrease of the size of aggregate. These results are confirmed by the investigation of the number of aggregates of the kaolin suspension in the presence of polymer by nephelometric method (8). The suspension is stabilized by the polymer at the large polymer concentration. A use of both models for the montmorillonite concentration of 28 g/l in the suspension leads to a decrease of aggregate number in the unit volume of suspension less than 1. Evidently, the suspension is structured in this case, and these models do not describe the rheological behavior of the suspension at high concentrations. The difference in rheological behavior between kaolin and montmorillonite suspensions stipulates evidently for the structure and the charge of the particle surface. Really, the montmorillonite suspension flocculates with the formation of very great aggregates in the presence of DTAA in solution. At the same time, the flocculation of kaolin suspension in the DTAA solution proceeds more slowly and the size of aggregates is small. Therefore, the change of the number of aggregates in the unit volume of suspension and the number of initial particles in aggregate at the different polymer concentration in the mixture can be calculated according to Eqs. [7] and [10] on the basis of the experimental data on the rheological behavior of the suspension. REFERENCES
FIG. 13. Plot of the number of aggregates in the unit volume of suspension (1), the number of initial particles in the aggregate (2), and the radius of aggregate (3) versus polyacrylic acid concentration calculated according to Eqs. [9] and [10].
1. Tadros, Th. F., in “Solid/Liquid Dispersions.” (Th. F. Tadros, Ed.), Chapter 1. Academic Press, London, 1987. 2. Tadros, Th. F., Adv. Colloid Interface Sci. 12, 141 (1980). 3. Eisenlauer, J., and Killmann, E., J. Colloid Interface Sci. 74, 108 (1980). 4. Tadros, Th. F., J. Colloid Interface Sci. 64, 36 (1978). 5. Heath, D., and Tadros, Th. F., J. Colloid Interface Sci. 93, 320 (1983). 6. Otubo, Y., and Watanabe, K., Colloids Surf. 50, 341 (1990). 7. Verlinskaya, R. M., Kislenko, V. N., and Berlin Ad. A., J. Appl. Chem. (Russia) 9, 1505 (1998). 8. Kislenko, V. N., and Verlinskaya, R. M., J. Colloid Interface Sci. 216, 65 (1999).