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Formation and Charaterization of Submicrometer Oil-in-Water (O/W) Emulsions, Using High-Energy Emulsification Isuru N. Seekkuarachchi,† Kuniaki Tanaka,‡ and Hidehiro Kumazawa*,† Department of Chemical Process Engineering, UniVersity of Toyama, Toyama 930-8555, Japan, and Plant Equipment Department, Sugino Machine Limited, Toyama 936-8577, Japan
Submicrometer emulsions were generated by a high-pressure wet-type jet mill and a motionless mixer called the Ramond Supermixer. Kerosene and liquid paraffin were used as the dispersed phase, aqueous sucrose and poly(ethylene glycol) solutions of PEG 400 to PEG 20000 were used as the continuous phase, and sodium dodecyl sulfate was used as a surfactant. The droplet size distribution, the Sauter mean diameter (d32), and the geometric standard deviation of the droplet size distribution (σg) were investigated under various combinations of the operating variables. The analysis of time-scale parameters contributed to an understanding of droplet deformation and possible re-coalescence. The relationship between the maximum droplet diameter and d32 was determined to be a function of the ratio of the viscosity of the dispersed phase to the viscosity of the continuous phase (K). Empirical correlations were constructed for d32 and σg, and a larger similarity was determined to exist within the correlations, irrespective of the emulsifier that was used. Mechanistic models were developed to describe the droplet formation in view of droplet breakage phenomena with negligible re-coalescence. Separate models were proposed for both the turbulent inertia sub-range and the viscous subrange. For the viscous sub-range, a plot of the critical Weber number versus K revealed a rapid increase of droplet diameter at K < 0.05, regardless of the emulsifier. Introduction Emulsions that have narrow droplet size distributions, with an average droplet diameter of
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Figure 5. Influence of ηc on d32 at different W for φ ) 0.1, ηd ) 3.61 mPa s: (a) wet-type jet mill, P ) 50 MPa, n ) 2; (b) wet-type jet mill, P ) 150 MPa, n ) 2; (c) RSM, N ) 10, VL ) 1.243 m/s, n ) 10; and (d) RSM, N ) 10, VL ) 0.871 m/s, n ) 10.
42.4 mPa s. To compare the polydispersity of the distributions obtained under various process conditions, the geometric standard deviation of the droplet size distribution (σg) was calculated by assuming all distributions are described apparently by a log-normal distribution. With the wet-type jet mill, σg increased from 1.05 to 1.33 at n ) 2, and, at n ) 15, σg increased from 1.02 to 1.13 as ηd increased from 0.96 mPa s to 61.0 mPa s. With the RSM, σg increased from 1.03 to 1.41 at n ) 2 and from 1.02 to 1.18 at n ) 15 for the same range of ηd. At small n and low ηd, narrow distributions were obtained with the RSM, whereas at high ηd, more narrow distributions were obtained with the wet-type jet mill. A few previous researches reported a similar increase of droplet diameters with increasing ηd; however, all the studies were limited to the range of micrometer-sized droplets.11,14 Effects of the Viscosity of the Continuous Phase and the Molar Mass of Stabilizer. The effects of ηc on d32 at φ ) 0.1 and ηd ) 3.61 mPa s at various stabilizers are shown in Figure 5. Figures 5a and 5b were drawn for the wet-type jet mill at n ) 2 and pressures of P ) 50 MPa and P ) 150 MPa. Figures 5c and 5d were drawn for the RSM at n ) 10 and N ) 10, for VL ) 0.870 m/s and VL ) 1.243 m/s. All plots were made at ηc e 72 mPa s. For any stabilizer, d32 decreased with increasing ηc. The rate of decrease was changed in the range of 6 mPa s e ηc e 15 mPa s, where a comparatively higher rate of decrease was obtained for ηc e 6 mPa s. This range coincides with the range at which a sudden increase of ηc with increasing Cs is obtained, as shown in Figure 2. A rapid increase of ηc with increasing Cs was obtained beyond ηc ) 15 mPa s; even so, this exerted less influence on decreasing d32. Aqueous solutions of sucrose and PEG 400, with closer W values, gave similar d32. The value of d32 increased as W increased. Also, for both emulsifiers, similar effects of ηc and W on d32 were obtained, resulting in a negligible effect of the method of producing submicrometer emulsions under any continuous-phase conditions. To illustrate the effects of ηc and W on droplet size distributions, Figure 6 was drawn for the wet-type jet mill at φ ) 0.1, ηd ) 3.61 mPa s, n ) 1, and P ) 50 MPa for aqueous
solutions of sucrose, PEG 600, PEG 2000, and PEG 20000. For ηc e 72 mPa s, log-normal distributions were obtained. As ηc increased from 2 mPa s to 72 mPa s, σg decreased from 1.10 to 1.02 for aqueous solutions of sucrose, from 1.11 to 1.02 for aqueous solutions of PEG 600, from 1.12 to 1.04 for aqueous solutions of PEG 2000, and from 1.15 to 1.04 for aqueous solutions of PEG 20000. As ηc exceeded a value of 72 mPa s, d32 shifted to larger droplet side, resulting in droplet size distributions with a tail at smaller diameter range. Similar plots could be given for the RSM. Schulz and Daniels,16 who studied hydroxyl propyl methylcellulose as a surfactant, showed that a surfactant with low molar mass at higher contents, along with low homogenization pressure, could sufficiently produce submicrometer emulsions. In the stabilization studies with milk protein as a surfactant and glycol and PEG 20000 as stabilizers, Tech and Schubert8 found that, compared to glycol, PEG 20000 resulted in destabilization of emulsion. They attributed the results to the intermolecular bonding between polymer and stabilizer, which resulted in an isotropic/anisotropic phase separation. In our study, we used a typical surfactant; thus the effects of process conditions could be studied clearly by eliminating such ambiguities. In addition, we obtained more-uniform dependencies of droplet diameter on ηc and the molar mass of stabilizer. Sugiura et al.17 observed an increase of droplet diameter with increasing ηc during microchannel emulsification. Here, the dispersed phase is forced into the continuous phase through the microchannel and an increase of ηc restricted such flow, and the change of hydrophobicity reduces the wetting of terrace, thus opposing droplet formation. In their study, the flow conditions are laminar. The magnitude of the driving force of droplet collisions is dependent on the laminar flow. An increase of ηc leads to a higher driving force, forcing the liquid film between approaching droplets to drain, and hence droplets coalesce each other. In turbulent flow fields such as in ours, driving forces are rather complicated. The effect of ηc on the thin film drainage will be discussed
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Figure 6. Influence of ηc on the droplet size distribution for the emulsion prepared by wet-type jet mill at φ ) 0.1, ηd ) 3.61 mPa s, P ) 50 MPa, and n ) 1: (a) ion-exchanged water and aqueous solutions of sucrose, (b) PEG 600, (c) PEG 2000, and (d) PEG 20000.
later. Such different mechanisms of droplet formation could lead to different dependencies of the droplet diameter on the process conditions. Effect of the Volume Fraction of the Dispersed Phase. Figure 7 indicates the variation of d32 with φ, as parameters of ηc and W, for ηd ) 3.61 mPa s in Figure 7a and 7c and at ηd ) 42.4 mPa s in Figures 7b and 7d. Figures 7a and 7b were drawn for the wet-type jet mill at n ) 2 and P ) 50 MPa, whereas Figures 7c and 7d were drawn for the RSM at n ) 10, N ) 10, and VL ) 1.119 m/s. At low ηd and ηc conditions, d32 increased as φ increased. For ηc > 15 mPa s and low ηd, d32 exhibited less dependency on φ. At high ηd (such as ηd ) 42.4 mPa s) and either at low or high ηc, d32 became independent of φ. No significant difference of the dependency of d32 on φ was
obtained at two emulsifiers. Figure 8 was drawn under similar conditions to those of Figure 7 and ηc ) 2.68 mPa s (sucrose). For the wet-type jet mill, at low φ, log-normal distributions were obtained. As φ increases, slight shifting from true log-normal nature was observed. For the RSM at low ηd, all log-normal distributions were observed, and at high ηd, a shift of log-normal nature was observed only at φ ) 0.6. The distributions obtained by the RSM exhibited fine log-normal distributions, compared to that obtained with the wet-type jet mill, under the given process conditions. In the wet-type jet mill, as φ increased from 0.02 to 0.6, σg decreased from 1.40 to 1.04 at ηd ) 3.61 mPa s and from 1.61 to 1.03 at ηd ) 42.4 mPa s. Narsimhan and Goel,18 while studying the coalescence rate of SDS-stabilized oil-in-water (O/W) emulsions, determined that
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Figure 7. Influence of φ on d32 at different ηc and W values: (a) wet-type jet mill, P ) 50 MPa, n ) 2, ηd ) 3.61 mPa s; (b) wet-type jet mill, P ) 50 MPa, n ) 2, ηd ) 42.4 mPa s; (c) RSM, N ) 10, VL ) 1.119 m/s, n ) 10, ηd ) 3.61 mPa s; and (d) RSM, N ) 10, VL ) 1.119 m/s, n ) 10, ηd ) 42.4 mPa s. Symbol legend is the same as that given in Figure 7.
although the droplet sizes increased with φ, the coalescence rate decreased, because of the suppression of turbulence intensity with increasing φ. Although an increase of d32 was considerably low here, compared to their data, a similar reduction of turbulence was unavoidable. Floury et al.5 obtained a rapid increase of d32 with φ, because of the reduction of the availability of surfactant, and at large P and φ, d32 became independent of φ. In our study, no specific influence of P on the relation between d32 and φ was observed. Effect of Processing Pressure of Wet-Type Jet Mill. The effect of P on d32 at n ) 1 and φ ) 0.1, with ηc, W, and ηd as parameters, was illustrated in Figure 9. Except at low W but high ηc, d32 decreased as P increased. However, at low W but high ηc, an increase of d32 with increasing P was obtained for P g 150 MPa. At ηd ) 3.61 mPa s, PEG 20000 with ηc ) 8.0 mPa s, gave a local minimum at P ) 100 MPa. For any dispersed phase substance, log-normal distributions were obtained at P e 150 MPa, and at P ) 250 MPa, a tail in small droplet diameter range was observed. At ηd ) 0.96 mPa s and ηd ) 42.4 mPa s, σg varied from 1.11 to 1.03 and from 1.3 to 1.04, as P increased from 50 MPa to 150 MPa. Pressure provides the energy required for emulsification and an increase of pressure corresponds to an increase of turbulent shear forces through eddies. These eddies lead to the droplet disruption and small droplets are obtained with increasing P. Moreover, the viscous energy dissipation will lead to a local temperature increase. Local shear becomes further intensified, and the droplet breakage becomes more efficient. Fine droplets produced by turbulent shear forces are then stabilized by the adsorption of emulsifier or through hydrodynamic stabilization. As P increases, the surface adsorption rate of surfactants increases. Therefore, an increase of P resulted in not only small droplets due to higher turbulence, but also stable droplets due to high surface concentration of adsorbed surfactant. Such combined effects resulted in the formation of small and stable droplets.
Marie et al.6 found a decrease of d32 with increasing P. An increase of W results in a deterioration of hydrodynamic stabilization, and, thus, a destabilization of droplets occurs. Therefore, for materials with large W (such as PEG 20000), the droplets produced even under high pressures were destabilized. Floury et al.,5 who were studying high-pressure homogenization stabilized by whey protein, found no significant influence of P on either d32 or droplet size distribution. Floury et al.19 obtained a reduction of d32 with increasing P, followed by an increase of d32. At high pressures, bio-polymeric surfactants such as whey proteins were denatured, because of high shear stresses and temperature, which leads to poor stabilization. Mohan and Narsimhan7 and Narsimhan and Goel18 noted an increase of droplet coalescence efficiency due to high collision frequency induced by high turbulent forces, leading to large droplets with an increase of P. Immiscible liquid systems with a surfactant as a foreign material dissolved in either phase result in a considerable decrease of interfacial tension with increasing pressure, whereas that in pure systems is not dependent on pressure.20 The surfactant takes more space around the droplet as in the continuous phase, leading to an increase in volume with increasing interfacial area. Thus, thermodynamically, this corresponds to a decrease of interfacial tension with increasing pressure.20,21 As a separate study of emulsification, we passed only the continuous phase through emulsifier, and then the interfacial tension with respect to the dispersed phase was analyzed. No significant difference of interfacial tension compared to that obtained without pressurization, was observed. The entire ranges of ηc, W, and ηd were analyzed. This suggested a negligible influence of P on the interfacial tension. Because it is impossible to analyze the effect of P on the interfacial tension during the real emulsification in the chamber of emulsifer, we will refrain from further comments on this effect. Effect of Number of Mixing Units of the Ramond Supermixer. Figure 10 was plotted at φ ) 0.1, ηd ) 7.96 mPa s, and
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Figure 8. Influence of φ on the droplet size distribution at ηc ) 2.68 mPa s (sucrose): (a) wet-type jet mill, P ) 50 MPa, n ) 2, ηd ) 3.61 mPa s; (b) wet-type jet mill, P ) 50 MPa, n ) 2, ηd ) 42.4 mPa s; (c) RSM, N ) 10, VL ) 1.119 m/s, n ) 10, ηd ) 3.61 mPa s; and (d) RSM, N ) 10, VL ) 1.119 m/s, n ) 10, ηd ) 42.4 mPa s.
VL)0.932 m/s, with n, ηc, and W as parameters. Under any process conditions, d32 decreased as N increased. At low ηc and n, submicrometer emulsions were obtained only at large N, whereas at n g 3, submicrometer emulsions were obtained even at high ηc and W. For any process conditions, the effect of n on d32 became negligible at n > 15. At any ηd, log-normal distributions were obtained for N ) 6, 8, and 10. At small N, some deviation from true log-normal nature was observed, and especially at high ηd, where a comparatively long tail in a small droplet range was observed. With an increase of N, the mixing length, as well as the residence time, of the droplets becomes longer, which results in high pressure decreases. The energy dissipation was enhanced, resulting in greater droplet breakage. Some researchers found that the effect of N on the droplet size diminished with an increase of N and there existed a maximum of N to obtain effective droplet distruption.10,14,22 This can be attributed to the reduction of driving force for the droplet disruption, which is the difference between the local average droplet diameter and the equilibrium diameter. However, in our study, no such effect
was observed, and both SDS and stabilizers were prominent to give small droplet sizes, even at large N, through effective stabilization. Effect of Superficial Liquid Velocity in the Ramond Supermixer. The influence of VL on d32, taking n, ηc and W as parameters, at φ ) 0.1, N ) 10, and ηd ) 3.61 mPa s, was shown in Figure 11. At any n and ηc, d32 decreased as VL increased. At high ηc, and any ηd and VL, log-normal distributions were obtained. For example, at n ) 5, ηc ) 72.0 mPa s (sucrose), and ηd ) 3.61 mPa s, as VL increased from 0.435 m/s to 0.746 m/s, σg decreased from 1.06 to 1.03 and remained unchanged at VL > 0.746 m/s. At ηd ) 42.4 mPa s with the same n and ηc, σg decreased from 1.08 to 1.03 and remained unchanged at VL > 0.746 m/s. The increase in VL results in a higher turbulent intensity, which obviously enhances the droplet disruption. A similar reduction was observed by Al Taweel and Walker.10 At any ηc, W, and VL > 0.870 m/s, the effect of n on d32 became negligible. Also at low ηc, such as ηc ) 6.31 mPa s (sucrose) and VL g 0.870 m/s, the effect of VL on d32 became negligible. With an increase of W, the limiting values of VL
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Figure 9. Influence of P on d32 at different ηc, W, and ηd values for φ ) 0.1 and n ) 1.
Figure 10. Influence of N on d32 at different ηc, W, and n values at ηd ) 7.96 mPa s, φ ) 0.1, and VL ) 0.932 m/s.
and n shifted to low values. For example, at ηc ) 71.0 mPa s of PEG 6000, the effects of VL and n were diminished for VL g 0.746 m/s and n g 10. As VL increases, the turbulent intensity increases. The increase of turbulence enhances the collision frequency between droplets. On the other hand, as the velocity increases, the average residence time of droplets in the emulsification chamber reduces. Thus, the duration of droplet collisions reduces. This results in a lower coalescence probability. The coalescence frequency is the product of collision frequency and coalescence probability. The two opposite effects
Figure 11. Influence of VL on d32 at different ηc, W, and n values for ηd ) 3.61 mPa s, φ ) 0.1, and N ) 10.
are counteracted and eventually the coalescence frequency reduces with increasing velocity. This led to a reduction of droplet diameters with increasing liquid velocity, as shown in Figure 11. At low and moderate VL, the droplet breakage becomes the limiting factor. However, large collisions result in droplet coalescence at high VL, leaving the coalescence to be the limiting factor. At high VL, the dynamic equilibrium is reached, and the further increase of VL serves merely to maintain the dynamic equilibrium. As discussed under the effect of N, an increase of W results in rapid coalescence, leaving the effect of VL being flattened at low VL and n. Effect of Number of Passages. Figure 12 indicates the effect of n on d32 at different ηc and W for φ ) 0.1 and ηd ) 3.61 mPa s. Figures 12a and 12b were drawn for the wet-type jet mill at P ) 50 MPa and P ) 150 MPa, respectively. Figures 12c and 12d were drawn for the RSM at N ) 10 MPa, for values of VL ) 0.746 m/s and VL ) 1.181 m/s, respectively. At the wet-type jet mill, the value of d32 decreased gradually as n increased, and at any P and n g 10, the effect of n on d32 became less important. An increase of n results in a higher turbulent intensity, which ultimately leads to the droplet disruption. A negligible effect of n at n g 5 was only obtained at ηc ) 25.0 mPa s for aqueous solutions of PEG 20000. For the RSM, a continuous decrease of d32 with increasing n was obtained at VL e 0.807 m/s. It is evident that the energy dissipation is quite high in the wet-type jet mill, which leads to a limitation on the minimum droplet, which can be achieved with increasing n. Energy dissipation in the RSM is not adequate to obtain the minimum droplet size, especially at low VL. Higher energy dissipation at VL ) 1.181 m/s, resulted in no effect of n on d32 for n > 15. At high W and ηc, such as at ηc ) 75.0 mPa s in aqueous solutions of PEG 6000, the effect of n diminished at n ) 10. Extended droplet coalescence frequency at high W overcomes the droplet disruption effect. Similar to that observed in Figure 12b, an aqueous solution of PEG 20000 with ηc ) 25.0 mPa s resulted in a constant value of d32 for n g 5. The effects of n on the droplet size distributions are plotted in Figure 13 at ηc ) 72.0 mPa s (sucrose) and φ ) 0.1. Figures
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Figure 12. Influence of n on d32 at different ηc and W values for ηd ) 3.61 mPa s and φ ) 0.1: (a) wet-type jet mill, P ) 50 MPa, (b) wet-type jet mill, P ) 150 MPa, (c) RSM, N ) 10, VL ) 0.746 m/s; and (d) RSM, N ) 10, VL ) 1.119 m/s.
13a and 13b refer to the wet-type jet mill at P ) 50 MPa, for ηd ) 3.61 mPa s and ηd ) 42.4 mPa s, respectively. Figures 13c and 13d refer to the RSM at VL ) 0.808 m/s and N ) 10, for ηd ) 3.61 mPa s and ηd ) 42.4 mPa s, respectively. A value of n ) 0 represents the emulsion obtained by the Ramond stirrer. A rapid decrease of droplet diameters and the width of the size distribution was obtained by passing the pre-emulsion through either the wet-type jet mill or RSM. Log-normal distributions were obtained under all process conditions. Even at high ηd, sharp distributions were obtained under the wet-type jet mill, compared to that with the RSM. For the wet-type jet mill at ηd ) 3.61 mPa s, with an increase of n from 1 to 5, σg decreased from 1.04 to 1.02, and remained constant for n > 5. At ηd ) 42.4 mPa s, with an increase of n from 1 to 10, σg decreased from 1.06 to 1.03, and remained constant for n > 10. For the similar conditions of ηd at the RSM, σg decreased from 1.06 to 1.03 and from 1.13 to 1.05 with an increase of n from 1 to 10, and afterward remained constant for n > 10. Analysis of Time-Scale Parameters. Time-scale parameters of the droplet diameter, surfactant, and eddies were introduced, to describe the effect of physical properties of constituents in the emulsion.23 Also, the analysis of these parameters gave an insight into whether droplet breakage and coalescence are possible or not. The average residence time (trec) of the droplets in the emulsification chamber is defined as VMMN/QL for the RSM, and dor/Vor for the wet-type jet mill. For the RSM at N ) 10, trec decreased from 2.5 × 106 µs to 0.9 × 106 µs while VL increased from 0.373 m/s to 1.243 m/s. For the wet-type jet mill, trec decreased from 3.0 × 103 µs to 1.0 × 103 µs while P increased from 50 MPa to 250 MPa. The life span of an eddy (ted) is defined as the ratio of eddy size to velocity gradient across the eddy. For the inertia sub-range, ted ) [Fc/ (wFe)]1/3dmax2/3, where dmax is the maximum droplet diameter. For the viscous sub-range, ted can be considered to be simply equivalent to wFe2/ηe. The time needed for droplet deformation (tdef) was defined as the ratio of droplet internal viscosity to external stress minus
the Laplace pressure. For droplet deformation under inertial and viscous turbulent fields, tdef can be described separately as
tdef,in )
ηd Fe(wd32)
tdef,vis )
2/3
ηd 2 1/2
( ) wη e V
σ d32
(3)
(4) σ d32
At φ ) 0.1 and ηc ) 1.0 mPa s, where Figures 3a and 3b were drawn, tdef and ted increased in the following ranges as ηd increased from 0.91 to 61.0 mPa s. For the RSM, at w ) 5.50 × 104 W/kg, tdef,vis ) 10.1-70.2 µs, ted,vis ) 30.6-90.2 µs; at w ) 7.72 × 104 W/kg, tdef,vis ) 5.0-40.8 µs, ted,vis ) 8.352.1 µs; and at w ) 10.1 × 104 W/kg, tdef,vis ) 2.1-20.2 µs, and ted,vis ) 2.8-20.8 µs. For the wet-type jet mill, at w ) 1.26 × 109 W/kg, tdef ) 0.07-0.35 µs, ted ) 0.3-0.7 µs; at w ) 4.43 × 109 W/kg, tdef ) 0.02-0.06 µs, ted ) 0.1-0.4 µs; and at w ) 9.49 × 109 W/kg, tdef ) 0.007-0.04 µs, ted ) 0.050.08 µs. Note that, in the wet-type jet mill at low ηd, tdef and ted were calculated for the viscous sub-range and at high ηd for the inertia sub-range. As would be expected from equations, both tdef and ted increased as ηd increased, and decreased as w increased. In all cases, trec is much longer than tdef, which gives sufficient time for deformation of droplets while passing through the emulsification chamber. Also, ted is longer than tdef, so that eddies formed in the turbulent field exist sufficiently long enough to cause droplet deformation and subsequent disruption. In addition, it was observed that the kinetic energy of eddies (equal to Fc1/3w2/3dmax11/3, for the inertia sub-range) was sufficiently higher than the surface energy of droplets. However, at large ηd, the times tdef and ted became comparable. Under such conditions, energy-bearing eddies were incapable of deforming newly formed droplets, and some coalescence could be assumed.
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Figure 13. Influence of n on the droplet size distribution at ηc ) 72.0 mPa s (sucrose) and φ ) 0.1: (a) wet-type jet mill, P ) 50 MPa, ηd ) 3.61 mPa s; (b) wet-type jet mill, P ) 50 MPa, ηd ) 42.4 mPa s; (c) RSM, VL ) 0.808 m/s, N ) 10, ηd ) 3.61 mPa s; and (d) RSM, VL ) 0.808 m/s, N ) 10, ηd ) 42.4 mPa s.
Stabilization that was achieved by delaying the drainage time of interfacial film between two approaching droplets was appraised recently, because of the expanding industrial usage of stabilizers. Both the rate of film thinning and the drainage time of the film are strongly dependent on the presence of surfactant in the continuous phase. In the prevailing conditions of intense turbulence, the adsorption time of free surfactant molecule (tads) by convective transport can be given as23
tads )
10Γ d32CSDS
( ) ηc Few
1/2
(5)
The surface excess concentration of surfactant (Γ) was obtained by balancing the moles of surfactant in the continuous phase before and after each run of emulsification.
Γ)
d32(1 - φ)(CSDS,ini - CSDS,fin) 6φ
(6)
Typically, CSDS,ini . CSDS,fin, and CSDS,fin can be neglected.
Assuming a random orientation through the available space, the average time elapsed between consecutive droplet collisions can be given as
( )
2 1 d32 Fc tcol ) 15φ w
1/3
(7)
Equation 7 was obtained for droplet collision under the inertia turbulent field and the corresponding equation can be obtained for the viscous field. ηd has a little effect on tads and tcol. For example, under conditions where Figure 3a and 3b were drawn, the following average values of tads and tcol were obtained at any ηd. For RSM, at w ) 5.50 × 104 W/kg, tads) 10.3 µs and tcol ) 28.3 µs; at w ) 7.72 × 104 W/kg, tads ) 5.4 µs, tcol ) 8.0 µs; and at w ) 10.1 × 104 W/kg, tads ) 2.7 µs, tcol ) 3.1 µs. For the wet-type jet mill, at w ) 1.26 × 109 W/kg, tads ) 0.05 µs, tcol ) 0.2 µs; at w ) 4.43 × 109 W/kg, tads ) 0.02 µs, tcol ) 0.17 µs; and at w ) 9.49 × 109 W/kg, tads ) 0.007 µs, and tcol ) 0.08 µs. For
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all cases, tads < tdef and tads < tcol. Sufficient time is available for the completion of adsorption of the surfactant on newly formed droplets, and, thus, stable emulsions are obtained. The parameters tads, tdef, and tcol are affected by ηc. Timescale parameters were calculated to illustrate the effect of ηc for the conditions under which Figures 5b and 5d were drawn. Here, ηc varies over a range of 1.0-70 mPa s. For the RSM, the following values are obtained: for sucrose, tads ) 10.313.2 µs, tdef,vis ) 12.0-9.8 µs, and tcol,vis ) 28.3-32.4 µs; for PEG 600, tads ) 10.0-12.8 µs, tdef,vis ) 11.1-7.3 µs, and tcol,vis ) 31.0-37.0 µs; for PEG 2000, tads ) 9.7-12.1 µs, tdef,vis ) 10.5-4.8 µs, and tcol,vis ) 33.0-41.0 µs. Similarly, for the wettype jet mill, the following values are obtained: for sucrose, tads ) 0.05-0.3 µs, tdef ) 0.2-0.08 µs, and tcol ) 0.25-0.7 µs; for PEG 600, tads ) 0.03-0.25 µs, tdef ) 0.1-0.06 µs, and tcol ) 0.3-0.8 µs; for PEG 2000, tads ) 0.02-0.2 µs, tdef ) 0.080.04 µs, and tcol ) 0.5-1.1 µs. Here, time parameters were obtained for the inertia sub-range at low ηc and the viscous subrange at high ηc. These values showed that, with increasing ηc, tads and tcol increased and tdef decreased. In all cases, ted and tres are considerably larger than tads, tdef, and tcol, so that sufficient time and energy are available for the droplet deformation. At low ηc, tad < tdef , tcol. Therefore, newly formed droplets are easily covered with surfactants, leaving less chance for immediate coalescence due to droplet collision. At large ηc, tdef < tad , tcol. Because tdef < tad, droplets will not be immediately covered with surfactants after formation. However, less chance is available for droplets to coalesce because of the collision, because tcol . tad. Finally, stable droplets are able to be obtained. As W increased, tads and tdef decreased and tcol increased. The presence of bulk material at the vicinity of the droplet surface will promote the droplet deformation process. The aforementioned analysis was performed using emulsions with small φ. As φ varied over a range from 0.02-0.4, the effects of φ on time-scale parameters were calculated under similar conditions where Figure 7a and 7c were drawn, except n ) 1. For the RSM, the following values were calculated: for sucrose at ηc ) 1.0 mPa s, tads ) 11.6-9.8 µs, tdef,vis ) 12.811.9 µs, and tcol,vis ) 35.0-10.5 µs; at ηc ) 2.68 mPa s, tads ) 12.0-10.1 µs, tdef,vis ) 12.4-11.1 µs, and tcol,vis ) 38.0-12.1 µs; at ηc ) 15.91 mPa s, tads ) 12.2-10.5 µs, tdef,vis ) 12.310.5 µs, and tcol,vis ) 41.0-13.1 µs, at ηc ) 25.0 mPa s, tads ) 12.6-11.0 µs, tdef,vis ) 12.0-10.0 µs, and tcol,vis ) 48.0-14.2 µs. Similarly, for the wet-type jet mill, the following values were calculated: at ηc ) 1.0 mPa s, tads ) 0.08-0.03 µs, tdef ) 0.15-0.13 µs, and tcol ) 0.32-0.17 µs; at ηc ) 2.68 mPa s, tads ) 0.06-0.01 µs, tdef ) 0.11-0.09 µs, and tcol ) 0.41-0.21 µs; at ηc ) 15.91 mPa s, tads ) 0.03-0.008 µs, tdef )0.090.07 µs, and tcol ) 0.50-0.28 µs; at ηc ) 25.0 mPa s, tads ) 0.009-0.001 µs, tdef ) 0.06-0.04 µs, and tcol ) 0.6-0.31 µs. The effect of φ on tcol is comparatively large, and tdef, is almost independent of φ. For all cases, except at ηc ) 25.0 mPa s for the RSM, tad < tdef < tcol. For φe0.4, stable droplets could be assumed, based on the analysis of time parameters. As φ increased, tcol became smaller, resulting in an increase of droplet-droplet collisions within the available space. As φ increases, the collision frequency increases, which is due to the close packing of small droplets within a confined space. This resulted in a higher coalescence frequency. In addition, because of the closer packing, a rapid increase of ηe was obtained (data not shown here). The effect of an increase of ηe can be considered to be the same as the effect of ηc. That is, an increase of ηe results in a resistance for drainage of the intervening film between droplets. Thus, an increase of φ may
result in a reduction of droplet diameters. The counterbalance of these two effects resulted in less dependence of d32 on φ, especially at small φ values, as shown in Figure 7. In addition, the probability of droplets not being subjected to the maximum energy input can further increase the coalescence frequency. Hence, the droplet coalescence, followed by the disruption, becomes the limiting factor in emulsification at large φ and low ηd. For high molar mass stabilizers, more numerous droplet coalescences resulted in a sudden increase of d32 with φ (see Figure 7 for PEG 6000, PEG 20000). At high ηd, droplets exhibits more solid nature, and the effect of φ becomes apparently negligible. Thus, the hydrodynamic stabilization becomes predominant. Coalescence Probability. Coalescence in liquid-liquid dispersions involves not only the approach of droplets, but also drainage and eventual rupture of the intervening film in the continuous phase. Thus, it is strongly dependent on the hydrodynamic force, which pushes the droplets against each other as well as on the surface forces such as van der Waals force. Several models on the film drainage were proposed by previous researchers, and the regime of drainage could be distinguished, depending on the rigidity and mobility of interfaces.24-26 The systems where the drainage is controlled predominantly by the motion of the film surface and the contribution of the additional flow within the film due to the pressure gradient being much smaller, are referenced to be “partially mobile”.24 The continuous phase with soluble surfactants, such as that in this study, can be considered to be partially mobile interface systems. By balancing the pressure variation in the film and the thinning rate at quasi-creeping flow conditions for head-to-head approaching droplets, the following expression was derived.24,27
t)
η dF t 16(π)
1/2
( )( d32 σ
3/2
)
1 1 h h0
(8)
Here, h and h0 designate the film thickness at the time when spontaneous film rupture occurs and the intervening film thickness at initial contact, respectively. The hydrodynamic force governing the collision will be predominantly inertia or viscous, and can be calculated as follows:
Fin ) Few2/3d328/3
(9)
()
Fvis ) 1.5πηcd322
w V
1/2
(10)
For droplets at small separations, the attractive van der Waals force (FvdW) becomes effective, and this enhances the film drainage.26
FvdW )
Ad32 24h
(11)
Assume Ft ) Fin (or Fvis) + FvdW. The value of h0 can be taken to be 0.2d32.28 The coalescence will begin to occur when the film thickness exceeds a critical rupture thickness (hc).
hc )
( ) Ad32 16πσ
1/3
(12)
The time at which h ) hc can be called the drainage time of the intervening film (tdra). The coalescence probability (CP) then can be written as
384
Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006
( )
CP ) exp -
tdra ted
(13)
ηc largely affects the value of tdra and CP. Some numerical values obtained under φ ) 0.1, ηd ) 3.61 mPa s, and n ) 1, with increasing ηc from 1 mPa s to 70 mPa s, are listed below. For the RSM, at N ) 10, VL ) 0.746 m/s, tdra ) 34-41 µs, and CP ) 0.31-0.30 for sucrose; tdra) 37-44 µs and CP ) 0.310.30 for PEG 400; tdra ) 40-47 µs and CP ) 0.28-0.29 for PEG 600; tdra ) 42-49 µs and CP ) 0.29-0.28 for PEG 2000. For the wet-type jet mill at P ) 150 MPa, tdra ) 0.51-1.3 µs, CP ) 0.23-0.16 for sucrose, tdra ) 0.55-1.4 µs, P ) 0.230.14 for PEG 400, tdra ) 0.6-1.6 µs, CP ) 0.22-0.17 for PEG 600, and tdra ) 0.71-1.71 µs, CP ) 0.31-0.24 for PEG 2000. To eliminate coalescence, tdra must be long enough to avoid film rupture, that is tdra > ted, and therefore CP must be 21.8 mPa s or ηc > 15 mPa s, the effect of φ became negligibly small, compared to that for low ηc and ηd. Nevertheless, in all cases, φ gave the least effect on d32. Mechanistic Model for d32. For fully turbulent flow conditions, the fluid induced the force of either shear or inertia, leading to disruption of a droplet, depending on the direction of the fluctuating eddies influencing the droplet and the ratio of the droplet diameter to the turbulent microscale (λ ) (V3/ w)1/4). For droplets larger than λ, droplet disruption occurs due to the inertia force. The turbulent inertia stress (τt) acting on a droplet can be described as the total energy associated with the pressure fluctuations as follows:14
τt ) C1Fe(wd)2/3
(24)
For droplets smaller than λ, the breakage occurs by the turbulent viscous stress inside the eddy, and at low elongational force,
386
Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006
Table 2. Coefficients in Correlations for the Sauter Mean Diameter (d32), Obtained for the Wet-Type Jet Mill Partial Regression Coefficients (× 106 ) ranges of applicable data
a0
a1
a2
a3
a4
a5
a6
MRCa (%)
1.0 mPa s e ηc e 15 mPa s, 0.96 mPa s e ηd e 21.8 mPa s, 0.02 e φ e 0.6, w e 2000, 1 e n e 10, 50 MPa e P e 250 MPa 15 mPa s < ηc e 71 mPa s, 0.96 mPa s e ηd e 21.8 mPa s, 0.02 e φ e 0.6, w e 2000, 1 e n e 10, 50 MPa e P e 250 MPa 1.0 mPa s e ηc e 6.31 mPa s, 21.8 mPa s < ηd e 61.0 mPa s, 0.02 e φ e 0.6, w e 2000, 1 e n e 10, 50 MPa e P e 250 MPa 15 mPa s < ηc e 71 mPa s, 21.8 mPa s < ηd e 61.0 mPa s, 0.02 e φ e 0.6, w e 2000, 1 e n e 10, 50 MPa e P e 250 MPa
0.520
-0.599
0.300
0.398
0.055
-0.596
-0.603
99.8
0.330
-0.401
0.300
0.402
0.011
-0.595
-0.601
99.8
0.573
-0.597
0.301
0.276
0.007
-0.594
-0.606
99.8
0.332
-0.403
0.300
0.279
0.002
-0.595
-0.010
99.7
a
Multiple regression coefficient.
Table 3. Coefficients in Correlations for the Sauter Mean Diameter (d32), Obtained for the Ramond Supermixer (RSM) Partial Regression Coefficients (× 106 ) ranges of applicable data
a0
a1
a2
a3
a4
a5
a6
a7
MRCa (%)
1.0 mPa s e ηc e 15 mPa s, 0.96 mPa s e ηd e 21.8 mPa s, 0.02 e φ e 0.6, w e 2000, 2 e N e 10, 0.37 m/s e VL e 1.24 m/s, 1 e n e 15 15 mPa s < ηc e 71 mPa s, 0.96 mPa s e ηd e 21.8 mPa s, 0.02 e φ e 0.6, w e 2000, 2 e N e 10, 0.37 m/s e VL e 1.24 m/s, 1 e n e 15 1.0 mPa s e ηc e 6.31 mPa s, 21.8 mPa s < ηd e 61.0 mPa s, 0.02 e φ e 0.6, w e 2000, 2 e N e 10, 0.37 m/s e VL e 1.24 m/s, 1 e n e 15
1.040
-0.595
0.305
0.397
0.057
-0.500
-1.24
-0.600
99.8
0.712
-0.390
0.302
0.400
0.006
-0.501
-1.26
-0.602
99.8
1.280
-0.597
0.301
0.277
0.005
-0.506
-1.25
-0.604
99.8
a
Multiple regression coefficient.
the turbulent viscous stress is given as the product of shear rate and the emulsion viscosity, which is further simplified as follows:34
τt ) C2ηe
() w V
1/2
(25)
The effect of φ, which results in attenuation of the turbulent intensity and coalescence frequency, is incorporated into the term ηe. Hinze35 proposed that the continuous-phase flow fluctuations should induce internal phase flows within the droplet in the order τt of . The internal viscous stress (τv) which opposes the Fd droplet disruption, can be defined for inertial sub-range (λ < di) and viscous sub-range (λ > di), separately as follows:
x
( )( )
τ V ) C3
ηd τ t d Fd
()
1/2
) C4
()()
ηe τ V ) C5 Fd
1/2
w V
Fe Fd
d
d
()( ) ]
[
d32 Fe 0.5 d32 0.33 0.6 ) C7We-0.6f-0.4 1 + C8Caf0.33 d0 Fc d0 (for the inertial sub-range) (30)
( )( ) [
d32 Fe V/V ) C9We-1 d0 ηe f
0.5
( )( ) ]
ηeFd 0.5 V/V -0.25 ηdFe f (for the viscous sub-range) (31)
1 + C10Ca
Here, the generalized Weber number (We), the generalized Capillary number (Ca, which is the ratio of internal viscous stress to surface cohesive stress), and the friction factor (f) are defined as follows:
1/2
ηdw1/3d-2/3
We )
(for the inertial sub-range) (26)
1/4η
form is obtained, for the inertial sub-range and viscous subrange, respectively, where dmax is replaced by d32, taken from eqs 16 and 17.
f)
(for the viscous sub-range) (27) Ca )
The interfacial tension results in the surface cohesive stress (τs), which counteracts the droplet deformation. It can be defined as35
σ τs ) C6 d
()
(28)
At the balance between the turbulence disruptive stress, which has a tendency to disrupt the droplets, and internal viscous and surface cohesive stress, which holds the droplet, the droplet diameter reached its maximum value, dmax. Therefore, under dynamic equilibrium conditions, the following equation can be given:
τt,d)dmax ) τs,d)dmax + τv,d)dmax
(29)
Add terms from eqs 24-28 to eq 29, and the following final
Fe(V/)2do σ w d0 2(V/)3
()
ηdV/ Fe σ Fd
(32) (33)
0.5
(34)
V/ is taken to be Vor for the wet-type jet mill and VL for the RSM. The values of the coefficients were determined by linear regression analysis. Coefficient values of C1 ) 1, C4 ) 0.29, C6 ) 0.29, C7 )0.29, and C8 ) 1.25 were determined for droplets obtained in the inertia sub-range by the wet-type jet mill. For droplets in the viscous sub-range, the following values were obtained for coefficients C2, C5, C6, C9, and C10, with respect to the emulsifier used; 1, 0.08, 0.08, 1.76 × 10-3, and 6.687 for the wet-type jet mill, and 1, 0.15, 0.15, 3.3 × 10-3, and 6.687 for the RSM. It was observed that C1 and C2 are always unity and the coefficient in internal viscous stress term (C4 or C5) is equal to the coefficient in the surface cohesive
Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 387
Figure 15. Relationship between d32 and Wecr at different ηc values for n ) 1: (a) wet-type jet mill, ion-exchanged water and aqueous solutions of sucrose; (b) wet-type jet mill, aqueous solutions of PEG 6000; (c) RSM, ion-exchanged water and aqueous solutions of sucrose; and (d) RSM, aqueous solutions of PEG 6000.
term (C10) at any sub-range. The coefficient that was accompanied by the effect of the Ca and f terms (C8) is the same, regardless of the emulsifier. For the model proposed in eq 31, only the value of C9 differs, with respect to the emulsifier. The energy dissipation sub-range is clearly distinguished, with respect to the emulsifier. In the wet-type jet mill, the energy dissipation occurred in the viscous sub-range for low K (ca. K < 30). At large K (in other words, at high ηd and low ηc), the inertia sub-range became predominant. In the RSM, it was difficult to obtain submicrometer emulsions at very large K. At any K, where submicrometer emulsions can be produced by the RSM, the energy dissipation was determined to occur completely in the viscous sub-range. Models given in eqs 30 and 31 predicted the measured values of d32 with an error of
