1122
Ind. Eng. Chem. Res. 1997, 36, 1122-1129
Creaming Behavior of Solids-Stabilized Oil-in-Water Emulsions Nianxi Yan and Jacob H. Masliyah* Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6
Creaming behavior of oil-in-water emulsions stabilized by kaolinite clays was studied. The clays were treated with asphaltenes resulting in clays having different contact angles. It was found that the emulsion creaming velocity decreased and that the volume of the creamed emulsions increased with increasing clay concentration at the oil droplet surface. At a given initial clay concentration in the aqueous phase, a plot of the emulsion creaming velocity versus the square of the oil droplet diameter did not follow any rational hindered settling equation. At a constant clay concentration at the oil droplet surface, however, a plot of the emulsion creaming velocity versus the square of the effective oil droplet diameter gave a straight line passing through the origin. A model for creaming of solids-stabilized oil-in-water emulsions was developed, and it is able to predict the creaming velocity of the emulsions quite well. Introduction Sedimentation of a suspension of particles under the action of gravity has been studied extensively due to its importance in practical applications such as oil sands extraction, solid-liquid separation, particle size measurement, dewatering of coal slurries, clarification of waste water, and processing of drilling and mining fluids containing rocks and mineral particles of various sizes (Novotny, 1987; Prunet-Foch et al., 1991; Glasrud et al., 1993; Yan and Masliyah, 1993). The problem that has received the most attention is that of sedimentation of monosized spheres at very small particle Reynolds numbers. The settling behavior of suspensions is very complex, and a literature survey shows that the efforts to predict from first principles the settling behavior of particles numbering from a few to several thousands has only been moderately successful. In some concentration ranges, theory and experiment correlated very well, but these ranges were at the extreme ends of the concentration spectrum. Early research on multiphase flow has been conducted by Hamielec and his colleagues. They were among the earlier workers who developed numerical methods to solve the Navier-Stokes equations for axisymmetric flows around spheres and around circular cylinders (Hamielec et al., 1967a,b; Hamielec and Raal, 1969). The total drag around spherical particles in an assemblage for different Reynolds numbers was also investigated, and particle interaction was accounted for using a “surface-interaction method” (LeClair and Hamielec, 1968). The agreement between their predicted drag coefficients and the experimental data for packed and fluidized beds was quite satisfactory. Owing to the significance of the subject, there have been numerous experimental and theoretical investigations on the sedimentation of a single particle. One of the earliest of these studies is that of Stokes’ analysis. The sedimentation velocity Uo of a single rigid spherical noninteracting particle with diameter d can be determined by equating the gravitational force with the opposing hydrodynamic drag force, as given by Stokes’ law, i.e.
Uo )
gd2(F1 - F2) 18µ
(1)
* Phone: (403) 492-4673. Fax: (403) 492-2881. Email:
[email protected]. S0888-5885(96)00360-0 CCC: $14.00
where F1 and F2 are the densities of the particle and the medium, respectively. Here, µ is the viscosity of the medium and g is the acceleration due to gravity. The above simple treatment applies only to extremely dilute suspensions of noninteracting particles at very low Reynolds numbers. The problem becomes more complicated for concentrated suspensions. Since then, research has focused on extending Stokes’ law by considering nonspherical rigid particles, drops and bubbles, non-Newtonian fluids, nonzero Reynolds numbers, the presence of a wall near a particle, and the interaction between particles. A theoretical relationship between the sedimentation velocity of nonflocculated suspensions and particle concentration (or volume fraction φ) that is applicable to relatively low volume fractions (φ < 0.1) has been provided by Maude and Whitmore (1958a) and by Batchelor (1972). Batchelor (1972) derived the following expression for the mean settling velocity U of a particle in a suspension
U ) Uo(1 - 6.55φ)
(2)
where φ is the volume fraction of the dispersed phase. Equation 2 suggests that the sedimentation velocity of a particle in a diluted suspension decreases linearly with increasing the volume fraction of the dispersed phase. The sedimentation velocity of a particle in a concentrated suspension is always less than the settling velocity of a single particle in isolation. This is partly because the downward movement of particles causes an equal volumetric flow rate of the displaced fluid relative to which the particles must move. Furthermore, for a given relative velocity, the average velocity gradients, and hence shear stresses, will be greater in a concentrated suspension. If the particles are all uniform, they will settle with equal velocities, and therefore, there will be few interparticle collisions or near collisions. Although various forms of expressions have been suggested for the calculation of settling velocity as a function of dispersed phase volume fraction, one of the simplest relationships is the hindered settling equation suggested by Richardson and Zaki (1954)
U ) Uo(1 - φ)n
(3)
For oil droplet creaming in an aqueous phase at very low Reynolds numbers, eq 3 can be written as © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1123
U)
gd2(Fs - Fo) (1 - φo)n 18µ
(4)
where Fs and Fo are the densities of the aqueous phase and the oil phase, respectively. Here, µ is the viscosity of the aqueous phase, and φo is the oil volume fraction. No theoretical value can be assigned to n, but experimental results showed that n varies between 4 and 12, depending on the system (Al-Naafa and Sami Selim, 1992). For noninteracting hard spheres at low Reynolds numbers, a value of 4.65 is normally assigned to n. The sedimentation velocity, and consequently the value of n, is further influenced by the shape, roughness (Chang et al., 1979), and Dorn potentials (Levine et al., 1976) of the particles. The presence of an electric double layer becomes more significant as the particle concentration increases and the particle size decreases (less than 100 µm). It is very likely that the high value of n ) 8 obtained by Maude and Whitmore (1958b) for 2040 µm emery powder in water and that of n ) 10.5 obtained by Richardson and Miekle (1961) for 4-7 µm alumina particles in water are due in part to electrokinetic effects. Values of n as high as 48 for flocculated kaolinite clays have been reported (Dollimore and Horridge, 1971; Davies and Dollimore, 1976). In order to accomodate the vaule of Richardson and Zaki of n ) 4.65 normally associated with large smooth spheres, several researchers introduced a modified hindered settling equation of the form (Steinour, 1944; Michaels and Bolger, 1962; Fouda and Capes, 1977, 1979)
U ) Uo(1 - Kφ)n
(5)
where K is a hydrodynamic volume factor. This modification assumes the presence of immobile liquid surrounding the particles. The presence of a liquid layer increases the effective concentration of the particles and their effective diameter and thereby affects the settling velocity of the suspension. In other words, the inclusion of K (K g 1) has a similar effect to having n g 4.65. For large smooth spheres without an encapsulating immobile liquid layer, K has the value of unity and eq 5 becomes that of the Richardson and Zaki correlation. For fine particles, the value of K can be as high as 3 for flat mica particles. Unfortunately, no uniquely definable relationship between the hydrodynamic volume factor K with the particle shape and/or size and with the electrokinetic properties of the particles has yet emerged from previous studies. Despite the experimental and theoretical studies on the settling behavior of dispersions, the sedimentation of solid-liquid or liquid-liquid dispersions cannot be as yet fully predicted. In the present study, we shall present the effects of clay particle adsorption at the oil droplet surface on the creaming behavior of claysstabilized emulsions. An emulsion creaming model is proposed on the basis of the creamed emulsion volume and the clay concentration at the oil droplet surface. To our knowledge, no previous studies have been conducted for this type of system. The Model In a recent study, Yan and Masliyah (1994) found that when oil is dispersed into water containing clays, a solids-stabilized oil-in-water emulsion is obtained, and the clays partition between the oil droplet surface and
Figure 1. Photographs of the creamed clays-stabilized emulsions prepared with different initial clay concentrations. (a, top) Ct ) 4 kg/m3; (b, middle) Ct ) 35 kg/m3, focused on clays in-between the oil droplets; (c, bottom) Ct ) 35 kg/m3, focused on the top surface of the oil droplets.
the aqueous phase. In the present study, it is observed that the emulsion creaming velocity decreases and the creamed emulsion volume increases significantly with increasing equilibrium clay concentration at the oil droplet surface. The increased volume of the creamed emulsion is 10-50 times that of the clays adsorbed at the oil droplet surface. Visual observations under a microscope show that oil droplets of the creamed emulsion nearly contact each other when the clay concentration at the oil droplet surface is low as shown in Figure 1a. At high clay concentrations, however, the oil droplets stay apart with a significant layer of claywater suspension in-between them as is shown in Figure 1b,c. The photograph of Figure 1b was taken with the focus plane on the clays in-between the oil droplets, while Figure 1c was obtained with the focus plane on the top of the oil droplet surface. The above mentioned
1124 Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997
Figure 2. Pictorial diagram showing an oil droplet surrounded by adsorbed clays and its associated clay-water suspension layer.
observations suggest that as the emulsion creaming proceeds, the oil droplets move along with the adsorbed clays and their associated immobile aqueous layer surrounding each of the oil droplets, such that an effective oil volume fraction should be used to describe such a creaming process. As a result, the dispersed oil droplets should have a larger effective diameter, higher effective density, and volume fraction. The effective volume of the oil phase, Veff, can be expressed as
Veff ) KVo
(6)
where K is a hydrodynamic volume factor which is a function of the clay concentration at the oil droplet surface and Vo is the volume of oil used in preparing the emulsion. Dividing both sides of eq 6 by the total volume of the prepared emulsion, Vt, yields
φeff ) Kφo
(7)
where φeff and φo are the effective oil volume fraction during the creaming process and the oil volume fraction for preparing the emulsion, respectively. By definition, we have φeff ) Veff/Vt and φo ) Vo/Vt. Figure 2 shows a schematic diagram of an oil droplet of diameter d covered with adsorbed clays and its associated clay-water suspension layer. During the creaming process, a layer of clay-water suspension encapsulates the oil droplet to form a drop having an effective diameter deff, which is given from eq 6 as
deff ) K1/3d
(8)
The effective density of the oil droplet can be expressed as
Feff )
πd2Cs + VoFo + (Veff - Vo)(RcFc + RwFw) (9) Veff
where Fc, Fo, and Fw are the densities of clays, oil, and water, respectively. Here, Rc and Rw are the volume fraction of clays and that of water in the clay-water suspension encapsulating the oil droplets, respectively. The sum of Rc and Rw is unity. Substituting eq 6 into eq 9 yields
Feff )
6Cs Fo 1 + + 1 - (RcFc + RwFw) Kd K K
(
)
(10)
Making use of effective quantities, eq 4 can then be expressed as
U)
g(Fs - Feff)d2eff (1 - φeff)n 18µs
(11)
where Fs and µs are the density and the viscosity, respectively, of the separated clay-water suspension. Equation 11 represents the creaming velocity of solids-stabilized oil droplets where a hydrodynamic volume factor, K, is incorporated to account for the effective dispersed phase volume fraction together with an effective oil droplet diameter and an effective dispersed phase density. It can be seen from eq 11 that by keeping the quantities (Fs - Feff), (1 - φeff)n, and µs constant, one should expect to have the creaming velocity U be proportional to the effective diameter 2 squared, deff . In the absence of clays, Cs ) 0 and K ) 1, and eq 11 becomes that of Richardson and Zaki as given by eq 4. It will be shown later that the effective oil droplet properties are uniquely determined by the clay concentration at the oil droplet surface and the relevant physical properties of the individual components, e.g., oil, water, and clays. Experimental Section Modification of Clay Particles with Asphaltenes. In the present study, kaolinite clay particles (Hydrite UF) from Georgia Kaolin Company, Inc. were used as the stabilizing solids. The equivalent spherical diameter of the dry clay particles was 0.2 µm. The procedure for modifying the clay particles was similar to that described by Menon and Wasan (1986) and by Yan and Masliyah (1994). Asphaltenes were first extracted from Alberta Athabasca bitumen by adding excess hexane to the bitumen. The volume ratio of hexane to bitumen was 4:1. The mixture of bitumen and hexane was stirred in a beaker for 30 min and left undisturbed for 2 h. The asphaltenes precipitated to the bottom of the beaker, and then they were filtered out and dried at room temperature for 24 h. A known amount of asphaltenes was then dissolved in a 1:1 volume toluene/ n-heptane (heptol) mixture. Kaolinite clay particles (Hydrite UF) (10 g/L) were added to the heptol mixture containing the asphaltenes, and the mixture was stirred for 24 h. Finally, the treated clay particles were filtered out and were left to dry at room temperature for 24 h. The contact angle, θ, of the treated clay particles was measured through the water phase using the compressed disc method as reported by Yan and Masliyah (1993). The treated clays having a contact angle of 90° were used for all the creaming experiments presented here. Emulsion Preparation. Reverse osmosis water from Continental Water Systems (ROSLW1001) was used for preparing the emulsion. A known amount of the treated clay particles (Wt) was first added to a given volume of water and sheared using a homogenizer (Gifford-wood Model 1-LV) for 30 min at 4000 rpm. This initial clay concentration in water is denoted by Ct. The emulsion was prepared by adding a known volume of oil to the prepared clay in water suspension and shearing the mixture using the same homogenizer at a predetermined speed for 10 min. The total volume of the oil and the water was 600 mL. A light mineral oil (Bayol-35) was used as the dispersed phase. It has a density of 780 kg/m3 and a viscosity of 2.4 mPa‚s at 25 °C. Unless otherwise specified, the oil volume fraction, φo, of the prepared emulsion was 0.2. Photomicrographs of the creamed emulsion oil droplets were analyzed using an image analyzer (Buehler, Omnimet-TM). The Sauter mean diameter was used to quantify the average size of the oil droplets.
Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1125
Figure 4. Variation of emulsion creaming interface height with time at different initial clay concentrations in aqueous phase.
Figure 3. Adsorption isotherms for clay particles at different contact angles.
Determination of Clay Partitioning between Oil and Water. Once an emulsion was prepared, it was left to cream in a separating funnel until no further reduction in the height of the creamed emulsion took place. The volume of both the creamed emulsion (Ve) and the separated clay-water suspension (Vw) was measured using a graduated cylinder. The weight of the clays in the separated clay-water suspension was determined by drying the suspension in an oven at 200 °C for 24 h. The equilibrium clay concentration in the separated clay-water suspension is given by
Cw )
Ww Vw
(12)
where Ww is the weight of the clays in the separated clay-water suspension. For the creamed emulsion, it is assumed that the concentration of the nonadsorbed clays in the water entrained between the emulsion oil droplets is the same as that in the separated clay-water suspension. The total weight of the clays associated with the oil is then given by
Wo ) Wt - CwVwo
(13)
where Vwo is the volume of clay-water suspension added prior to emulsification. Since the clay particles reside at the oil-water interface (Yan and Masliyah, 1994), the equilibrium clay concentration at the oil droplet surface is given by
Cs )
Wo Wo d ) A Vo 6
(14)
where A is the total oil-water interfacial area and Vo is the volume of oil for preparing the emulsion. Figure 3 shows the variation of the equilibrium clay surface concentration, Cs, with the equilibrium clay concentration in the aqueous phase, Cw, for clays having
different contact angles for an oil droplet diameter of 75 µm. All the data points fall on their respective sigmoidal curves, indicating that multilayer adsorption is involved. Comparison between the adsorption curve for θ ) 40° and that for θ ) 143° shows a marked difference in the shape of the isotherms and the level of the clay adsorption. For a given Cw, the value of Cs is much lower for θ ) 40° than that for θ ) 143° where the clay particles are more hydrophobic. On the other hand, in order to attain the same value of Cs, the value of Cw needs to be much higher for θ ) 40° than that for θ ) 90°. The apparent density of an oil droplet with its adsorbed clays is given by
Fa )
FoVo + Wo Vo + Wo/Fc
(15)
The viscosity of the separated clay-water suspension, µs, was measured using a coaxial cylinder viscometer (Contraves Rheomat 115). A double-gap bob and cup measuring system was used. Emulsion Creaming. Batch creaming experiments were conducted at room temperature in a vertical rectangular Plexiglass container having internal dimensions of 40 × 8.2 × 1.7 cm. The vertical alignment of the settler was ensured by adjusting the three screw nuts located at its base using a spirit level before each run. The prepared emulsion was poured into the container, and the height of the rising interface between the creamed emulsion and the separated clay-water suspension was recorded as a function of time. The creaming velocity was then obtained from the initial slope of each plot. Results and Discussion Effect of Initial Clay Concentration on Emulsion Creaming at Constant d and Oo. The rising interface between the creamed emulsion and the separated claywater suspension was distinct when the oil volume fraction was above 0.1 and the initial clay concentration was higher than 3 kg/m3. Consequently, for φo > 0.1, the interface could be tracked very accurately. Below φo of about 0.1, the interface was not distinct as creaming proceeded. Figure 4 shows the variation of the creaming emulsion interface height with time for emulsions having different initial clay concentrations,
1126 Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 Table 1. Dependence of Cs, µs, and Ga on Cta Ct (kg/m3) Cs × 104 µs × 103 (Pa‚s) Fa (kg/m3) a
4 1.5 1.07 792
7 2.52 1.11 800
15 6.46 1.13 832
20 9.66 1.06 857
25 12.4 1.04 879
30 14.8 1.05 899
35 17.1 1.07 917
θ ) 90°, φo ) 0.20, d ) 75 × 10-6 m and temperature ) 25 °C.
Figure 6. Dependence of hydrodynamic volume factor on the clay surface concentration.
of effective oil droplet volume. Equation 16 can be rewritten as
Figure 5. Dependence of Ve/Vt on the clay surface concentration.
Ct. It can be observed that the emulsion creaming velocity decreases rapidly with an increase in Ct. Two types of plots are obtained, depending on the initial clay concentration, as shown in Figure 4. For Ct < 25 kg/ m3, H initially increases linearly with time but eventually veers off to a constant value. For Ct > 25 kg/m3, the initial emulsion creaming velocity is very low but the creaming velocity of height versus time initially increases with time, reaching a maximum, and then decreases, thus exhibiting an S-shaped curve. This type of plot is similar to the settling plot of flocculated suspensions as reported by Michaels and Bolger (1962). Table 1 shows the dependence of the equilibrium clay concentration at the oil droplet surface, Cs, the viscosity, µs, and the apparent density, Fa, of the separated claywater suspension on the initial clay concentration, Ct. It is clear that the viscosity of the separated clay-water suspension does not change appreciably with Ct. However, both Cs and Fa increase considerably with Ct. From the final height of the interface between the creamed emulsion and the separated clay-water suspension shown in Figure 4, the volume of the creamed emulsion, Ve, can be obtained for each of the creaming experiments. The clay concentration at the oil droplet surface for each of the creaming experiments can be obtained from our previous clay-partitioning experimental data as shown in Figure 3. A plot of Ve/Vt versus Cs is shown in Figure 5. It can be seen that at φo ) 0.2 a plot of Ve/Vt versus Cs gives a straight line. Also shown in Figure 5 are data points of Ve/Vt versus Cs at other φo values. From the conceptual model, the volume of the creamed emulsion can be divided into the effective volume of the oil phase which can be expressed as KVo (K g 1) and the void between the effective oil droplet units which can be expressed as Ve, i.e.
Ve ) KVo + Ve
(16)
where K is a hydrodynamic volume factor which is a function of clay concentration at the oil droplet surface and is the voidage of the creamed emulsion in terms
Ve Kφo ) Vt 1 -
(17)
From the intercept of Ve/Vt versus Cs line of Figure 5 at Cs ) 0, a value of 0.267 for φoK/(1 - ) is obtained. Because of the fact that in the absence of clays Veff ≡ Vo, K is unity when Cs is equal to zero. Therefore by setting φo to 0.2, an value of 0.25 is obtained. From eq 17, the hydrodynamic volume factor, K, can then be expressed as
K)
0.75 Ve φo Vt
(18)
A plot of K versus Cs for φo ) 0.2 is shown in Figure 6. As would be expected, a straight line passing through the origin is obtained. It is interesting to note that plots of K versus Cs for other φo values collapse to the φo ) 0.2 straight line. A linear fit for K variation with Cs of Figure 6 gives
K ) 1 + 776Cs
(19)
Equation 19 indicates that the hydrodynamic volume factor, K, is linearly proportional to the equilibrium clay concentration at the oil droplet surface, Cs. When Cs is equal to zero, K is unity. By knowing the value of K, all the effective oil droplet properties, such as the effective oil volume fraction φeff, the effective oil droplet diameter deff, and the effective oil droplet density, Feff, can be obtained. Effect of Oil Droplet Diameter on Emulsion Creaming. Making use of the creaming experimental data, eq 4 suggests that for a given oil volume fraction, φo, a plot of Uµs/(Fs - Fa) versus d2 would give a straight line passing through the origin. Figure 7 shows such a plot for different initial clay concentrations in the aqueous phase, Ct. For Ct ) 3 and 6 kg/m3, plots of Uµs/ (Fs - Fa) versus d2 are indeed approximately straight lines, however, they do not pass through the origin. On the other hand, plots for Ct ) 10 and 15 kg/m3 give curved lines. The reason for this unexpected behavior is as follows. Although appropriate corrections have been made for the physical properties, the plots are for constant initial clay concentration in the aqueous phase. As clays partition between the oil-water interface and
Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1127
Figure 7. Dependence of Uµs/(Fs - Fa) on d2 at different Ct values. Table 2. Dependence of Cs on the Oil Droplet Diameter for a Given Value of Ct and for Oo ) 0.2 d × 106 (m) Cs × 104 (kg/m2)
Ct ) 3.0 kg/m3 98 128 160 1.71 2.10 2.45
203 2.87
230 3.11
282 3.52
Ct ) 6.0 kg/m3 d × 106 (m) 44 74 75 88 90 104 111 159 220 Cs × 104 1.65 2.59 2.61 2.97 3.03 3.40 3.59 4.78 6.22 (kg/m2) d × 106 (m) Cs × 104 (kg/m2) d × 106 (m) Cs × 104 (kg/m2)
36 2.27
Ct ) 10 kg/m3 52 70 98 3.12 4.05 5.47 Ct ) 15 kg/m3 40 67 3.68 5.93
128 6.96 115 9.84
150 8.02
210 11.0 170 14.3
centration at the oil droplet surface. If one is to accept the concept that the characteristics of an oil droplet, defined by its effective diameter and density, are influenced by the degree of clay adsorption, and hence Cs, then one should not expect to have a proportionality between Uµs/(Fs - Fa) and d2 when Cs is not kept the same. In order to investigate the dependence of the emulsion creaming velocity on the oil droplet diameter at a constant Cs value, one may change the oil droplet diameter by altering the homogenizing speed in accordance with the variation of the initial clay concentration in the aqueous phase during the emulsion preparation. This can be done by combining the clay adsorption isotherm and clay mass balance equation to arrive at a relationship between the initial clay concentration in the aqueous phase and the oil droplet diameter. The clay adsorption isotherm is given by (Yan and Masliyah, 1994)
Cs k1Cw ) Cm (1 - kmCw)(1 - kmCw + k1Cw)
(20)
where Cs and Cw are the equilibrium concentrations of clay particles at the oil droplet surface and in the aqueous phase, respectively. Cm is the monolayer coverage of the clay particles at the oil droplet surface. k1 and km are the equilibrium constants for the first layer and the subsequent layers, respectively. The values of Cm, k1, and km for a clay contact angle of 90° are 2.39 × 10-4 kg/m2, 3.50 m3/kg, and 0.362 m3/kg, respectively (Yan and Masliyah, 1994). The mass balance of clays in the emulsion is given by
(Ct - Cw)Vwo ) Cs
6Vo d
(21)
Substituting φo ) Vo/(Vo + Vwo) into eq 21 yields
d)
Figure 8. Dependence of the emulsion creaming velocity on the oil droplet diameter and on the clay surface concentration for θ ) 90° and φo ) 0.2.
the aqueous phase, starting with the same initial clay concentration in aqueous phase, Ct, would mean different values of clay concentration at the oil droplet surface, Cs, when different oil droplet diameters are generated during the emulsion preparation. This is simply due to the fact that at a given oil volume fraction, φo, the available oil droplet surface area is inversely proportional to the oil droplet diameter. Consequently, for a given value of Ct, each data point has a different Cs value as shown in Table 2, leading to different oil droplet characteristics. Figure 8 shows the dependence of the emulsion creaming velocity on the oil droplet diameter and the equilibrium clay concentration at the oil droplet surface. It can be observed that the emulsion creaming velocity decreases with increasing clay con-
6Cs φo Ct - Cw 1 - φo
(22)
At a given Cs value, the equilibrium value of Cw can be obtained from eq 20. Then for a given oil volume fraction, φo, eq 22 represents the relationship between Ct and d. During the emulsion preparation stage, the oil droplet diameter was controlled by altering the homogenizing speed according to the variation in Ct, so as to maintain a constant value of Cs for different Ct values. The experimental creaming plots were then converted to creaming velocities at constant Cs values. The creaming velocity as given by eq 11 is governed by the effective physical properties φeff, deff, and Feff together with the hydrodynamic volume factor K. All of the aforementioned quantities are uniquely determined by the clay concentration at the oil droplet surface, Cs, and the physical properties of oil, water, and clays as given by eqs 7, 8, 10, and 19. Making use of eq 2 11, the variation of the creaming velocity with deff is shown in Figure 9. Each curve is provided for a constant Cs value. As φo is kept the same for the data of Figure 9, all the physical properties as well as the K value are constant for a given Cs value. Figure 9 clearly shows that at a constant value of Cs, U is proportional 2 to deff in accordance to the proposed model. Indeed, as deff is a function of d and Cs only, a plot of U versus d2 will also give a linear relationship at a constant Cs. If
1128 Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997
Figure 9. Dependence of the emulsion creaming velocity on 2 deff at constant Cs values.
Figure 11. Comparison of the emulsion creaming velocity between the experimental data and the predicted values from eq 23.
tal data is shown in Figure 11. It can be seen that the predictions agree quite well with the experimental data. Conclusions
2 Figure 10. Dependence of U/deff on the clay surface concentration.
one is to plot U versus d2, a similar plot to that of Figure 9 would emerge. However, the individual straight lines will have different slopes. Making use of the creaming velocity plots of Figure 2 9, U/deff is plotted against Cs as shown in Figure 10. It 2 can be seen that U/deff decreases somewhat linearly with Cs for Cs > 2.5 × 10-4 kg/m2. For Cs < 2.5 × 10-4 2 kg/m2, however, U/deff increases sharply with a decrease in Cs. Experimental data showed that when Cs was below a monolayer coverage given by 2.39 × 10-4 kg/m2 (Yan and Masliyah, 1994), the emulsion was not stable, and the oil droplets tended to coalesce with each other as emulsion creaming proceeded. As a result, 2 higher values of U/deff are obtained for Cs < 2.5 × 10-4 2 kg/m due to coalescence. From the experimental results discussed above, it is clear that the clay concentration at the oil droplet surface has a significant effect on the creaming behavior of the solids-stabilized emulsions. Substituting eqs 7 and 8 into eq 11, the model equation for the emulsion creaming velocity is given by
U)
g(Fs - Feff)K2/3d2 (1 - Kφo)n 18µs
(23)
where K ) 1 + 776Cs. Curve-fitting the experimental data with eq 23, n is found to be 2.93. A comparison between the predictions from eq 23 and the experimen-
The creaming behavior of oil-in-water emulsions was studied by using treated kaolinite clays as the emulsion stabilizer. Experimental data showed that the emulsion creaming velocity decreased and the volume of the creamed emulsion increased with the clay concentration at the oil droplet surface. At a given initial clay concentration in the aqueous phase, a plot of the emulsion creaming velocity versus the square of the oil droplet diameter did not follow any rational settling equation. The adsorbed clays and their associated immobile clay-water suspensions surrounding each of the oil droplets changed the physical properties of the oil phase during the emulsion creaming process, whereby effective oil phase properties should be used in predicting the emulsion creaming velocity. A conceptual model was proposed whereby an oil droplet was considered to be surrounded by adsorbed clays and their associated clay-water suspension layers. The conceptual model leads to a modified Richardson and Zaki hindered settling equation, where
g(Fs - Feff)K2/3d2 (1 - Kφo)2.93 U) 18µs with K ) 1 + 776Cs. Acknowledgment This project was financially supported by a strategic grant from the Natural Sciences and Engineering Research Council of Canada. Initial experimental testings were carried out by Ms. Cheryl Kurbis to whom the authors are grateful. Nomenclature A ) total surface area of oil droplets, m2 Cm ) monolayer surface coverage of clays at the oil droplet surface, kg/m2 Cs ) equilibrium clay concentration at the oil droplet surface, kg/m2 Ct ) initial clay concentration in aqueous phase, kg/m3 Cw ) equilibrium clay concentration in aqueous phase, kg/ m3 d ) diameter of oil droplets or particles, m
Ind. Eng. Chem. Res., Vol. 36, No. 4, 1997 1129 deff ) effective diameter of oil droplets, m k1 ) equilibrium constant for the first adsorption layer, m3/kg km ) equilibrium constant for the second and successive adsorption layers, m3/kg K ) hydrodynamic volume factor t ) creaming time, s U, Uo ) creaming velocity for emulsion and for single oil droplet, respectively, m/s Ve ) volume of the creamed emulsion, m3 Veff ) effective volume of the oil phase, m3 Vo ) volume of oil used in preparing the emulsion, m3 Vt ) total volume of the prepared emulsion, m3 Vw ) volume of the separated clay-water suspension, m3 Vwo ) volume of clay-water suspension initially added for emulsification, m3 Wo ) weight of clays in oil phase, kg Ww ) weight of clays in water, kg Wt ) weight of total clays initially added to water, kg Greek Letters Rc, Rw ) volume fraction of clays and that of water in the clay-water suspension, respectively (Rc + Rw ) 1) ) voidage of the creamed emulsion in terms of effective oil droplet volume θ ) contact angle measured across the water phase, (deg) µ ) viscosity of the continuous phase, Pa·s µs ) viscosity of clay-water suspension, Pa·s Fa ) apparent density of oil phase with adsorbed clays, kg/ m3 µs ) viscosity of clay-water suspension, Pa·s Fa ) apparent density of oil phase with adsorbed clays, kg/ m3 Fc ) density of clays, kg/m3 Feff ) effective density of oil droplet, kg/m3 Fo ) density of oil phase, kg/m3 Fs ) density of clay-water suspension, kg/m3 Fw ) density of water, kg/m3 φ ) volume fraction of dispersed phase φeff ) effective oil volume fraction φo ) oil volume fraction used for preparing the emulsion
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Received for review June 24, 1996 Revised manuscript received September 17, 1996 Accepted September 17, 1996X IE960360O
X Abstract published in Advance ACS Abstracts, February 15, 1997.
