Ind. Eng. Chem. Res. 1994,33, 1858-1866
1858
Experimental Study on the Breakup of Model Viscoelastic Drops in Uniform Shear Flow Padma Prabodh Varanasi Physical Sciences Department, S.C. Johnson & Son, Inc., Racine, Wisconsin 53403
Michael
E. Ryan
Department of Chemical Engineering, State University of New York at Buffalo,Buffalo,New York 14260
Pieter Stroeve' Department of Chemical Engineering and Materials Science, University of California at Davis, Davis, California 95616
The characteristics of deformation and breakup of model viscoelastic drops suspended in immiscible purely viscous Newtonian fluids undergoing simple shear flow were investigated. In this study the simple shear flow was generated by a counterrotating cone-and-plate device. The results were compared with data obtained on purely viscous Newtonian drops under similar conditions. The ratio of viscous forces to interfacial tension forces a t breakup (Eb) was found to depend on the ratio of the viscosity of the dispersed phase to that of the continuous phase @), the shear stress prevailing in the continuous phase a t breakup, and the primary normal stress difference. At any given value of p, Eb was observed to increase with increasing shear rate, ye,and with increasing weight fraction of the polymer in the droplet phase, i.e., with increasing degree of elasticity of the drop. Depending upon the value of p, a certain shear rate (y*)was found to exist below which model viscoelastic drops were easier to break up than purely viscous Newtonian drops. Similarly, at any fixed shear rate, a characteristic viscosity ratio @*) was observed above which model viscoelastic drops were easier to break up than purely viscous Newtonian drops. The magnitudes of both y* and p* were found to depend upon the degree of elasticity of the dispersed drops. Introduction The dispersion of one liquid into a second immiscible liquid is an important characteristic associated with a variety of industrial processes. In the area of polymer processing, the blending of two immiscible polymers is employed to obtain a resulting morphology of the blend possessing advantageous transport or mechanical properties. Color concentrates, stabilizers, processing aids, antistatic agents, and a variety of other additives are commonly dispersed in the bulk polymer in order to modify its properties.lg In the manufacturing of pharmaceuticals, cosmeticsand paints, the emulsification of one immiscible liquid into another is often a key step in the overall process. In all of the above-mentioned situations, a knowledge of the mean droplet size and size distribution of the dispersed phase as a function of the process conditions is essential to control the properties (physical, rheological, optical, etc.) of the finished product. Such knowledge regarding the size distribution of the dispersed phase as a function of the mixing conditions is also important in applications involving extraction with double emulsions.P6 The accurate prediction of the mean droplet size and size distribution for a particular set of process conditions is exceedingly ~hallenging.~a However, valuable information regarding the size distribution and breakup characteristics of the dispersed phase can be obtained from a fundamental understanding of the mechanism of deformation and breakup of isolated drops and viscous threads in welldefined flow fields (e.g., simple shear, uniaxial extensional flow, etc.). Flow-induced drop deformation and breakup, as well as coalescence, are the primary mechanisms which determine the drop size distribution. Much of the previous work that has been reported in the literature on the subject of drop deformation and
breakup has been focused mainly on purely viscous Newtonian systems (Le., the dispersed-phase and the continuous-phaseliquids are Newtonian and do not exhibit any measurable degree of elasticity). An extensive literature exists, and some excellent reviews of the subject have been given by Han? Acrivos? Rallison,lo Van de Ven," Utracki and Shi,12and Janssen.13 Relatively few experimental of theoretical studies have dealt with nonNewtonian viscoelastic systems. Taylor14 appears to be the first investigator to have systematically studied the deformation and breakup of Newtonian drops suspended in another immiscible Newtonian fluid undergoing either a simple shear flow or a two-dimensional elongational (plane hyperbolic) flow. He found that in these purely viscous Newtonian systemsthe deformation and breakup of drops, in the absence of inertial forces, is governed by two dimensionless parameters: 1. The first is the capillary number or dimensionless shear rate, e, which represents the ratio of the viscous stresses exerted on the drop by the external flow field to the interfacial tension forces that tend to restore the drop to a spherical shape. The capillary number is defined as E
= v,ya/u
(1)
where tcis the viscosity of the continuous phase, y is the shear rate, a is the radius of the drop prior to undergoing deformation, and u is the interfacial tension between the droplet phase and the continuous phase. The capillary number corresponding to the critical shear rate in the continuous phase ( y e ) at which the droplet becomes unstable and breaks is called the critical capillary number and is denoted by Cb.
* Author to whom correspondence should be addressed. 0 1994 American Chemical Society 08S8-5885/94/2633-185~~~4.50/0
Ind. Eng. Chem. Res., Vol. 33, No. 7,1994 1859 2. The second dimensionless parameter is ratio of the viscosity of the dispersed phase to that of the continuous phase, P. Experimental data obtained by various investigators on the breakup of drops in purely viscous Newtonian systems in the case of simple shear flow indicates that (1) there exists a minimum in the value of Cb, (2) the minimum value of t b occurs for values of p between 0.1 and 1.0, (3) for values of p greater than 4,drops cannot be broken, and (4) for values of p less than 0.1,1Og(tb) varies linearly with 10g@).l5J6 It has also been observed that there is a lower limit of p below which no breakup occurs. In simple shear this lower limit occurs at approximately p = 0.005.17 For plane hyperbolic flow no asymptotic limits, above or below which drops cannot be broken, have been observed.18 For the range of viscosity ratios studied @ = 1.3 X 10-4 to p = 29), the value of Cb in the case of plane hyperbolicflow is always smaller than it is for simple shear flow at any given value of p, indicating that extensional flow fields are more effective than shear for droplet deformation and breakup. For plane hyperbolicflow, the minimum in the value of Cb was found to be about 0.3. Severaltheoretical treatrnents8Jsm are available in the literature which are capable of predicting the deformation and breakup characteristics of purely viscous Newtonian systems. The stability of liquid jets and extended threads has been analyzed by Rayleigh,SoWeber,3l and Tomotika,32 among others. For small deformations or viscosity ratios, the deformation and breakup of droplets in Newtonian systems has been extensivelystudied and can be described analyti~ally.1~~25 The results are found to be in reasonably good agreement with experimental data. Unfortunately, this is not the case for non-Newtonian systems. Gauthier et al.33 studiedthe breakup of Newtonian drops suspended in a shear-thinning, non-Newtonian liquid in Poiseuille flow. However, little quantitative information was given regarding drop breakup. Gauthier et al.33have also reported briefly on the breakup of Newtonian drops suspended in viscoelastic liquids. A more extensive experimental study was provided by Flumerfelt.34 He found that the mode of breakup and the pattern after breakup in these systems were similar to those in purely viscous Newtonian systems. Representing the rheological constitutive equation of the non-Newtonian viscoelastic continuous phase by a Bird-Carrea~~~ model, Flumerfelt suggested that the breakup of Newtonian drops in these fluids can be completely expressed in terms of the following dimensionless groups:
where qc is the zero shear rate viscosity of the continuous phase, q d is the Newtonian viscosity of the dispersed phase, A1 and A2 are time constants, and a1 and a2 are dimensionless empirical parameters associated with the constitutive equation. For the fluids Flumerfelt studied, the ratios X1/A2 and al/a2 were constant. In view of this, the above expression reduces to
(4) For all of the fluid systems studied, Flumerfelt observed the following linear relationship between the value of Cb and the dimensionless group hly. (5)
where $1 and $2 are functions of the viscosity ratio qd/qc. The minimum droplet size that is achievable in these
systems can be obtained by (1)decreasing the interfacial tension between the two liquid phases, (2) decreasing the elasticity of the continuous phase, and (3) increasing the viscosity of the continuous phase. As the elasticity of the continuous phase approaches zero (i.e., h1-y 0), Cb becomes a function of the viscosity ratio only, as in the case of purely viscous Newtonian systems. Gauthier et al.33 also studied the deformation and breakup of non-Newtonian (shear thinning) and viscoelastic drops suspended in a purely viscous Newtonian liquid in Poiseuille flow. They observed that in the case of shear-thinning drops, the modes of deformation and breakup were identicalto those observed for purely viscous Newtonian drops. The critical capillary number (Cb) at any given viscosity ratio was found to be more or less identical to that for purely viscous Newtonian drops. However, viscoelastic drops exhibited deformation and breakup patterns similar to those found in the case of purely viscous Newtonian drops only at low viscosity ratios. At high viscosity ratios, the drops were pulled into threads which broke up under quiescent conditions once shearing was stopped. The values of t b were observed to be considerably higher for viscoelasticdrops as compared to purely Newtonian systems. Unfortunately, insufficient data were available to construct plots of Eb versus viscosity ratio for comparison with the data of Grace15 and Torza et al.'6 In a study of the breakup of viscoelastic drops suspended in another viscoelasticfluid undergoing simple shear flow, T a ~ g a observed c~~ that the elasticity of the continuous phase stabilizes drops at low viscosity ratios and destabilizes drops at high viscosity ratios. Han and Funatsu2 experimentally studied the breakup of viscoelasticdrops in pressure-driven flows. However, their data were insufficient to arrive at any conclusionsregarding the role of elasticity on the breakup behavior. Lee and Flumerfelt3' theoreticallyanalyzedthe breakup of viscoelastic threads suspended in another viscoelastic fluid. They obsemd that, below a zero shear rate viscosity ratio of 1.0,increasing the elasticityof the continuousphase (or decreasing the elasticity of the dispersed phase) increased the sizes of the drops that resulted from threadlike breakup. Above a zero shear rate viscosity ratio of 1.0, the conversewas found to be true. The theoretical results were in reasonable agreement with their experimental data. Chin and Han38339performed a similar theoretical study of the breakup of viscoelastic threads when the continuous viscoelastic phase was undergoing Poiseuille flow. They found that increasing the elasticity of the continuous phase, for a given elasticity ratio, produced smaller drops after breakup. Recently, various researchers have published experimental results on the deformation and breakup of polymer drops undergoing extensional deformations. Bentley and Lealu2 have employed a computer-controlled, four-roll mill for investigating particle and drop dynamics in plane hyperbolic flow. Elmendorp,4 Palierne and Lequeux,44 and Janssen13 experimentally studied the breakup of viscoelasticthreads in a quiescent Newtonian fluid. They observed that upon cessation of the extensional flow the elongated thread deformed nonuniformly into a series of dumbbell shapes in contrast to the sinusoidaldisturbances (capillary waves) observed for Newtonian threads. Milliken and Leal&*&studied viscoelastic drops in linear two-dimensional flows over a broad range of viscosity ratio, p. For p > 1,no differences were found from the behavior of Newtonian drops. For p < 1,smaller values of t b were observed in comparison to Newtonian systems. By
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1860 Ind. Eng. Chem. Res., Vol. 33, No. 7, 1994 Table 1. Purely Viscous Newtonian Drops Dispersed in Purely Viscous Newtonian Liquids drop phase
viscosity (Pes) 6.59 12.6 12.6 12.6 12.6 0.41 0.41 12.6
continuous phase corn syrup corn eyrup corn syrup corn syrup corn syrup silicone oil* silicone oila silicone oilb
Viscosity (Pas) 0.96 10.6 14.1 31.8 55.8 12.6 6.59 12.6
interfacial tension (N/m X 109) 28.6 27.5 28.5 31.0 28.7 3.3 2.1 3.6
1. silicone oila 2. silicone oilb 3. silicone oilb 4. silicone oilb 5. silicone oilb poly(propy1ene glycol)c(MW = 2000) 6. poly(propy1ene glyco1)c (MW = 2000) 7. poly(propy1ene glyco1)C (MW = 4OOO) 8. a Silicone oil (S2000),Cannon Instrument Co. Silicone oil (Fluid 12,500),Brookfield Engineering Laboratory. Poly(propy1ene glycol), Aldrich Chemical Co.
contrast, de Bruijn47 reported a slight increase in tb in simple shear flow for viscoelastic drops. Due to the advent of constant viscosity elastic fluids (Boger fluids4*),it is possible to experimentally separate the contributions due to elasticity and shear-thinning behavior on drop deformationand breakup in simple shear flow. In the present study, the role played by the elasticity of dispersed drops of model viscoelastic fluids, suspended in a Newtonian fluid, on their deformation and breakup is investigated for simple shear flow. Specifically, the breakup conditions (critical capillary number) for these fluids, for varying degrees of drop elasticity, are determined.
Experimental Section Apparatus. In this study, a transparent cone-and-plate device with a cone angle of 2 O was used to generate a simple shear flow. This device is similar to the one used by Schmid-Schonbein et al.49 and has been described elsewhere by Stroeve and Varanasiq6Due to the small cone angle used, the shear rate was essentially independent of the spatial position within the device. The cone and plate were 2.5 cm in diameter and were rotated at equal and opposite speeds by friction of a rotatingrubber cone whose axis was connected through a gear wheel to a speedcontrolled servomotor. The speed of the servomotor could be varied by means of an electronic control circuit. The whole device was placed on the stage of an inverted microscope. The beam splitter in the microscope directed the transmitted light either to the oculars or to a video camera of an image analyzer. Appropriate care was taken that the cone and plate were aligned with each other and that the apex of the conejust made contact with the center of the plate. Materials. The densities of all liquids used in the breakup studies were determined by gravimetric analysis. The viscosities of the Newtonian liquids were determined using Cannon-Fenske capillary viscometers. The viscosities and the elasticities (expressedin terms of their primary normal stress differences) of the model viscoelastic fluids were measured with a model R20 Weissenberg rheogoniometer. When working with corn syrup solutions, small traces of silicone oil were applied to the samples (in the rheogoniometer) at the rim of the cone and plate in order to prevent the sample from drying at the edges. The interfacial tensions of all liquid/liquid systems used in this study were determined using the sessile drop technique. In this study, Dorsey's profile fitting method, as described by Padday,M,was adopted. The accuracy of this technique was h2.0 X 10-4 N/m. To obtain a record of the profile of a sessile drop, an optical arrangement similar to that of Kingery and Hammerick's was used.W Since the new surface of the drop is exposed to the continuous phase during drop deformation and breakup,
the dynamic as opposed to the equilibrium interfacial tension should be used in computing the value of the breakup parameter or critical capillary number, eb. In this study, the dynamic interfacial tension was obtained by extrapolating the interfacial tension versus time data to zero time. The dynamic interfacial tensions were only 1 X 103 to 3 X 103 N/m higher than the equilibrium interfacial tension. Procedure. At a given shear rate, the observational field in the vicinity of the periphery of the cone-and-plate device was examined to locate the largest drop. In this region of the cone-and-plate fixtures the drop size is less than 10% of the gap distance between the cone and plate surfaces. Once the largest drop was identified, the shearing of the suspension was stopped. Subsequently, the shear rate was gradually increased to its original level and the deformation of the drop was monitored. A very slight further increase in the applied shear rate caused the drop to break up into a series of smaller droplets, thereby confirming that the maximum droplet diameter at any given shear rate had been determined.
Results and Discussion Newtonian Drops. Prior to conducting experiments on the breakup of model viscoelastic drops, the cone-andplate device was tested by studying the breakup of purely viscous Newtonian drops suspendedin another immiscible purely viscous Newtonian medium. Table 1describes all the purely viscous Newtonian systems used in this study and their physical properties. The breakup data obtained from the present experiments were correlated in terms of the dimensionlessgroups €b and p. For every system, the viscosity ratio was fixed and approximately 10 data points on breakup were obtained for each system. Figure 1 shows a comparison of the data with the breakup data of Grace's and Torza et al.16 Accounting for the differences in the types of apparatus used for generating the simple shear flow, there is reasonable quantitative agreement between the results obtained in the present study and those obtained by Gracels and Torza et al.16 The quantitative discrepancy between the present results and the data reported by Gracel6and Torza et al.16may be due in part to boundary effects associated with the cone-and-plate device. According to these results, Qb exhibits a minimum when p is in the range of 0.1-1.0 and the value of this minimum is around 0.7. This is reasonably close to the value of 0.5 observed by Grace.15 For values of p greater than 1.0, €b increases with p up to a value of p equal to about 4.0. For higher values of p, the drops could not be ruptured by shear. Similar to the studies of Grace15and Torza et al.,16 a continuous increase in the value of Qb was observed with decreasing p for values of p ranging from 0.1 to 0.01. Breakup of Model Viscoelastic Drops. The model viscoelastic fluids (Boger fluids) were prepared by dis-
Ind. Eng. Chem. Res., Vol. 33, No. 7,1994 1861 100
z2
lo
$
1
i3
I
GRACE ( 1 982)
€6
.I
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: .
-
D2 D3
SHEAR R A T E ( I / sac )
Figure 2. Primary normal stress difference as a function of shear rate for model viscoelastic fluids D1, D2, D3, D4, and D5. Table 2. Viscosity of Model Viscoelastic Fluids sample description ( w t % of designation Separan AP30 in corn syrup) viscosity (Pass) D1 0.0100 3.0 D2 0.0200 3.6 D3 0.0275 2.7 D4 0.0400 4.0 D5 0.0600 4.0
solving different amounts of Separan Ap30 in a series of concentrated corn syrup (Karo) solutions of different viscosities. Separan AP30 is a high molecular weight anionic polyacrylamide produced by Dow Chemical Co. Because of the difficulty encountered in dissolving this polyacrylamidein high-viscosity,concentrated corn syrup solutions, a given amount of polymer was first dissolved in a small amount of water which was then mixed with a concentrated corn syrup solution. Table 2 lists the viscosities, the compositions,and the designations of the various model viscoelastic fluids used in this study. Figure 2 gives the variation of the elastic properties, expressed in terms of the primary normal stress difference,with shear rate for these model viscoelastic fluids. The magnitude of elasticity of these model viscoelasticfluids, at any given shear rate, was found to increase with increasing weight
Table 3. Physical Properties of Various Continuous-Phase Newtonian Fluids Used in the Breakup Studies of Model Viscoelastic Fluids sample designation description viscosity (Paes) density (g/mL) c1 silicone oil 90.0 0.9630 C!2 silicone oil 60.0 0.9624 c3 silicone oil 26.0 0.9611 c4 silicone oil 12.0 0.9616 c5 Silicone oil 6.2 0.8741 C6 silicone oil 3.7 0.9602 c7 silicone oil 1.7 0.9565 0.860 C8 Indopol H25 2.3 Table 4. Interfacial Tension between Dispersed Phase and Continuous Phase interfacial tension continuous phasea dispersed phasea (N/m X 108) c1 Dl-D5 31.6 c2 Dl-D5 31.8 c3 Dl-D5 31.7 c4 Dl-D5 35.8 c5 Dl-D5 34.2 C6 Dl-D5 32.6 c7 Dl-D5 35.5 C8 D1-D5 33.3 a For definitions of C14X and D1-D5 in this table, see Tables 2 and 3.
fraction of polymer. Even the solution containing the lowest fraction of polymer (0.01 wt %) was observed to possess a measurable amount of elasticity. The rheological behavior of these systems has been shown to be a logical consequence of dissolvinga small amount of high molecular weight polymer in a highly viscous Newtonian liquid.61 The slopes of the lines representing the variation of the logarithm of the primary normal stress difference with the logarithm of the shear rate were close to 1.0 and increased somewhatwith increasingweight fraction of the polymer. Breakup experiments were performed by dispersing a small amount (0.5 vol % ) of the model viscoelastic fluid in a series of Newtonian liquids (continuous phase). In general, the dispersed phase was introduced through a micropipet as a single large drop. However, in several instances, the dispersed phase was introduced as several distinct small drops. No apparent differencesin the results could be observed between these two cases. At concentrations of 0.5% by volume of the dispersed phase, no evidence of appreciable collision and coalescence could be observed and the droplets behaved essentially independently of one another. At higher concentrations (>0.5% by volume) there was some evidence of coalescence and droplet interaction at high shear rates (>250 8-9. However, at high shear rates, the interaction time during the deformation process is short and the potential for coalescence becomes limited by the drainage of the liquid film between the drops. The Newtonian fluids were siliconeoils (BrookfieldEngineeringand Sigma Chemical) and IndopolH25 (Amoco). Tables 3 and 4 list, respectively, the physical properties of the continuous-phasefluids and the interfacial tension between the continuous and dispersed phases. For any given continuous phase, no measurable variation in the interfacial tension was found with increasing weight fraction of the polymer in the dispersed phase. Therefore, for any given continuous phase, only a singlevalue of the interfacialtension between that continuous phase and the dispersed phase is required and is listed in Table 4. Before systematically obtaining quantitative data regarding the breakup of model viscoelastic drops, the
1862 Ind. Eng. Chem. Res., Vol. 33, No. 7,1994
B
b
..
?In
10
0
.
I
I
I
0
20
40
60
80
100
SEAR RATE (1 / 9 C )
Figure 4. Cb as a function of y for model viscoelastic fluids D1,D3, and D 4 and for purely viscous Newtonian drops for a viscosity ratio p of approximately 0.045.
reproducibility of drop breakup data was determined by conducting replicate runs at a fixed shear rate for various systems. The maximum diameter (D,,) of a drop that can exist at any shear rate was found to be reproducible to within f7 % . The shear rate was increased very gradually to the set value in order to enable the droplets to deform from one steady-state configuration to another. If the shear rate is increased too rapidly, the droplets may wobble and be subjected to tip streaming. If the shear rate is decreased too suddenly, the droplets may become unstable and breakup. The mode of deformation and breakup of the model viscoelastic drops was observed to depend on the magnitude of the shear rate applied to the system. In general, the mode of breakup was due to extension of the drops into long threadlike filaments which became unstable as the critical shear rate yc was approached. The filament then ruptured into many smaller drops. This mode of breakup corresponds to the B2 mode of the classification schemedefined by Torza et al.16 Drops rarely fragmented into only two smaller drops but usually several droplets. The phenomenon of tip streaming was not observed. At low shear rates (
