pubs.acs.org/Langmuir © 2009 American Chemical Society
Electrocoalescence: Effects of DC Electric Fields on Coalescence of Drops at Planar Interfaces Hamarz Aryafar and H. Pirouz Kavehpour* Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, California 90095 Received July 28, 2008. Revised Manuscript Received September 28, 2009 The current work attempts to explore the role of DC electric fields on neutrally charged coalescing conductive droplets. The droplet is isolated inside of silicone oil and allowed to coalesce into a planar bulk of its own fluid under the influence of the electric field. The effect of this additional field in conjunction with the effects of other physical properties of the liquids including viscosity and interfacial tension are studied with the use of a digital high-speed camera. By scaling the electric field appropriately, distinct regions of behavior are defined in which electrically induced partial coalescence occurs within a viscous environment. Furthermore, it is shown that droplet size and field strength will determine if the processes of coalescence leads to either jet formation or Taylor cone formation on the planar interface for sufficiently strong electric fields.
Introduction The effect of an electric field on droplet interactions has been a subject of study for over 100 years. In the late 19th century, Lord Rayleigh examined the behavior of droplet sprays under the influence of an electric field using a primitive strobing technique.1 With the arrival of more advanced technologies in the 20th century, researchers such as Charles and Mason were able to resolve the behavior of individual droplets coalescing under the influence of electric fields.2 It was not until digital technologies were sufficiently developed in the 1990s, however, that the field fully blossomed and the term “electrocoalescence” gained widespread use. Simply defined, electrocoalescence is the manipulation of coalescing bodies with the introduction of electric forces. In most instances, it is used to enhance or accelerate the process of interfacial film thinning and rupture. Additionally, electrocoalescence techniques are gaining popularity in microscale fluidics for the manipulation, mixing, and separation of small fluid quantities in applications such as “lab-on-chip”.3 Although electrocoalescence has been utilized for a number of years in demulsifiers, detailed knowledge of the physics involved is limited. Many studies on this subject deal with demulsifier systems and not on the underlying mechanisms.4-10 For a single droplet coalescing into a fluid bulk of its own material, it has the possibility of pinching off a secondary drop that will not enter the bulk. A well established parameter for secondary drop formation is the Ohnesorge number, Oh = μ/(RFσ12)1/2,11 where μ is viscosity, R is the radius of the drop, F is density, σ is interfacial surface tension, and the indices 1 and 2 indicate the *Corresponding author. E-mail:
[email protected].
(1) Rayleigh, L. Proc. R. Soc. London, Ser. A 1879, 28, 406–409. (2) Charles, G. E.; Mason, S. G. J. Colloid Sci. 1960, 15, 236–267. (3) Priest, C.; Herminghaus, S.; Seemann, R. Appl. Phys. Lett. 2006, 89(13), 134101. (4) Bailes, P. J.; Larkai, S. K. L. Trans. Inst. Chem. Eng. 1981, 59(4), 229–237. (5) Frising, T.; Noik, C.; Dalmazzone, C. J. Dispersion Sci. Technol. 2006, 27(7), 1035–1057. (6) Bailes, P. J.; Larkai, S. K. L. Chem. Eng. Res. Des. 1987, 65(5), 445–447. (7) Eow, J. S.; Ghadiri, M. Sep. Purif. Technol. 2002, 29(1), 63–77. (8) Eow, J. S.; Ghadiri, M. Colloid Surf., A 2003, 219(1-3), 253–279. (9) Eow, J. S.; Ghadiri, M.; Sharif, A. O. J. Pet. Sci. Eng. 2007, 55(1-2), 146– 155. (10) Schotland, R. M. Discuss. Faraday Soc. 1960, 30, 72–77. (11) Aryafar, H.; Kavehpour, H. P. Phys. Fluids 2006, 18, 072105.
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medium and drop properties, respectively. The Ohnesorge number is the ratio of the viscous to inertial capillary time scales. At an Ohnesorge number greater than or equal to unity (when the fluid system is brought into the Stokes regime), secondary drop formation is suppressed. Other researchers have shown much lower Ohnesorge number limiting values as well as weak Bond number, Bo=ΔFgL2/σ12, dependencies in the absence of an electric field,12-14 where g is gravitational acceleration and L is the length scale of the fluid body. Allan and Mason studied the effect of electrified droplets as well as externally applied DC fields on this process,15 and described a suppression of secondary drop formation with an increase in electric field strength, although their data is arguably insufficient to make any definitive conclusions. The focus of the current study is to explore the effect of electric fields on coalescence, specifically in the high Ohnesorge number domain, where partial coalescence is suppressed. Before coalescence is initiated, the system consists of a droplet and a large fluid reservoir; see Figure 1. During coalescence, a fluid column exists that consists of the union of the droplet and the fluid bulk that behaves similar to a laminar jet.11 In the following section, the critical electric field strengths associated with droplet breakup, planar fluid/fluid interface destabilization, and laminar jet stability will be examined. It is the intention of the current work to establish distinct regions of electrocoalescence behavior using the critical electric fields defined within this section. If an isolated fluid droplet is subject to a low electric field, it will assume either a prolate or oblate spheroid shape.16,17 The transverse electric stress exerted at the interface can cause a flow to form inside and outside of the droplet, resulting in the change in geometry.18,19 If the field strength is further increased, the droplet will form Taylor cones at its ends which will be aligned with the (12) Blanchette, F.; Bigioni, T. P. Nat. Phys. 2006, 2(4), 254–257. (13) Chen, X. P.; Mandre, S.; Feng, J. J. Phys. Fluids 2006, 18(5), 051705. (14) Yue, P. T.; Zhou, C. F.; Feng, J. J. Phys. Fluids 2006, 18(10), 102102. (15) Allan, R. S.; Mason, S. G. J. Chem. Soc., Faraday Trans. 1961, 57(11), 2027. (16) Torza, S.; Cox, R. G.; Mason, S. G. Philos. Trans. R. Soc., A 1971, 269 (1198), 295. (17) Lac, E.; Homsy, G. M. J. Fluid Mech. 2007, 590, 239–264. (18) Melcher, J. R.; Taylor, G. I. Annu. Rev. Fluid Mech. 1969, 1, 111. (19) Taylor, G. I. Philos. Trans. R. Soc., A 1964, 280(138), 383. (20) Stone, H. A.; Lister, J. R.; Brenner, M. P. Philos. Trans. R. Soc., A 1999, 455(1981), 329–347.
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in the gap between the fluid interface and an upper electrode providing the electric field. Solving with numerical methods, they were able to determine the critical electric field strength beyond which the interface would become unstable: 12 1 2 ðF2 - F1 Þgσ12 4 ð2Þ Ecrit;plane ≈ ε1
Figure 1. Configuration of fluids for electrocoalescence research.
electric field lines and will eventually break apart.16,20-22 The electric field applies stress through electric charge transfer to interfaces that have permittivity and conductivity discontinuities. When this electric stress is balanced by surface tension, the interface is considered to be in a state of equilibrium. By considering energy balance between the field and the interface, O’Konski and Thacher23 calculated the equilibrium shapes for drops in a uniform electric field. Many researchers have since approached and solved this problem using a variety of techniques to include high levels of deformity as well as compressibility.19,24-28 Dubash and Mestel29 explored the role of viscosity on droplet breakup due to an electric field by employing a boundary integral numerical scheme. Their results generally agree with those of experimentation in that they show the dependence of breakup on the viscosity ratio. Noting that the characteristic surface charge density may be written as (ε1σ12/R)1/2, most results, both numerical and experimental, point to a critical electric field strength beyond which a conducting drop should break up as: rffiffiffiffiffiffiffiffiffiffi Cσ 12 ð1Þ Ecrit;drop ¼ ε1 R where C is a constant and ε is permittivity. The exact value of C varies slightly in the literature and is approximately 0.204.19,24,26,29 Stone et al.20 numerically simulated highly elongated droplets showing a relationship between the aspect ratio and the electric field strength and derived a minimum electric field to aspect ratio power law that defines the transition boundary to conical tip formation, Ecrit,cone ∼ [(ε2/ε1) - 1]-11/12R, where R is the aspect ratio of the major to minor radius of the deformed droplet. If a flat fluid/fluid interface is considered, having mismatched permittivity and subject to gravity, a localized electric field applied across the interface will cause a corresponding localized pressure difference. If the electric field does not encompass the entire interface, a small bulge can form such that the gravitational forces equalize the induced pressure difference. However, the electric field can be of sufficient strength such that the interface becomes locally unstable. Taylor and McEwan30 explored such a scenario by assuming a nonlinear profile for the electric potential (21) (22) 730. (23) (24) (25) (26) 211. (27) (28) (29) (30)
Saville, D. A. Annu. Rev. Fluid Mech. 1997, 29, 27–64. Wilson, C. T. R.; Taylor, G. I. Proc. Cambridge Philos. Soc. 1925, 22, 728– O’Konski, C. T.; Thacher, H. C. J. Phys. Chem. 1953, 57(9), 955–958. Basaran, O. A.; Scriven, L. E. Phys. Fluids 1989, 1(5), 799–809. Eow, J. S.; Ghadiri, M. Chem. Eng. Process. 2003, 42(4), 259–272. Garton, C. G.; Krasucki, Z. Proc. R. Soc. London, Ser. A 1964, 280(138), A. I.; Zharov A. N.; Shiryaeva, S. O. Tech. Phys. 1999, 44(8), 908–912. Sample, S. B.; Raghupat, B.; Hendrick, C. D. Int. J. Eng. Sci. 1970, 8(1), 97. Dubash, N.; Mestel, A. J. Phys. Fluids 2007, 19(7), 072101. Taylor, G. I.; McEwan, A. D. J. Fluid Mech. 1965, 22.
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This result was later confirmed by Terasawa et al.31 Finally, the effect of an electric field applied parallel to a fluid jet in an immiscible medium is considered. For low electric field strengths as well as in the absence of an electric field, the tendency of this configuration is for Rayleigh instabilities to grow along the surface of the jet, resulting in its eventual breakup into droplets. The electric stress serves to dampen the Rayleigh modes. If the field is increased beyond a critical value, the Rayleigh instability will be completely suppressed and the onset of unstable modes will be shifted to nonlinear domain.32 This critical field strength is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πσ 12 ð3Þ Ecrit;jet ≈ ðε2 - ε1 ÞR Note that this expression relies on the jet fluid having a finite conductivity, while the two previous scenarios were for a perfectly conducting component. It has been shown that a perfect conductor is not essential for both drop breakup and the occurrence of Taylor cone formation as long as the permittivity of the conducting fluid is much larger than that of the surrounding fluid.19 For this reason, water can have a finite permittivity and still be used as the working fluid in most experiments. If the jet fluid were a perfect conductor, this expression would point to a critical electric field of zero required to dampen the Rayleigh modes. However, this is not realistic, as it would require an infinitely large potential difference across the jet to sustain any sort of electric field. Using eqs 1-3, a set of dimensionless state variables can be formed. The current work intends to explain and predict the behavior of viscous coalescing droplets in high electric fields using these state variables along with the Ohnesorge number. The difference between the current study and prior studies is that effort has been taken to isolate individual droplets under the influence of electric fields instead of dealing with the analysis of bulk coalescence processes.7,9,33-35 Because the initial droplet velocity and release height above the interface are minimized in the current study, the energy in the system consists of the surface energy of the droplet and the energy provided by the electric field. Therefore, the current study is unique in that it isolates the interactions between the droplet, the interface, and the electric field.
Setup The fluids were housed in a 125 in.3 transparent Plexiglas walled cube that allowed any processes within to be recorded (31) Terasawa, H.; Mori, Y. H.; Komotori, K. Chem. Eng. Sci. 1983, 38(4), 567– 573. (32) Hohman, M. M.; Shin, M.; Rutledge, G.; Brenner, M. P. Phys. Fluids 2001, 13(8), 2201–2220. (33) Eow, J. S.; Ghadiri, M.; Sharif, A. O.; Williams, T. J. Chem. Eng. J. 2001, 84 (3), 173–192. (34) Eow, J. S.; Ghadiri, M.; Sharif, A. O. Chem. Eng. Process. 2002, 41(8), 649– 657. (35) Shin, W. T.; Yiacoumi, S.; Tsouris, C. Curr. Opin. Colloid Interface Sci. 2004, 9(3-4), 249–255.
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Aryafar and Kavehpour Table 1. Properties of Fluids Used during Experimentationa interfacial tension (N/m) fluid
3
density (kg/m ) absolute viscosity (kg/m s) dielectric constant -3
78 water 1000 1.00 10 glycerol 1260 7.74 10-1 60 ethylene glycol 1113.2 1.64 10-2 37 silicone oil 1000 cSt 971 9.71 10-1 2.5 silicone oil 5000 cSt 973 5.36 2.5 silicone oil 10 000 cSt 974 9.74 2.5 a Viscosities were verified using an Advanced rheometer from TA Instruments, while instrument from Thermo.
with high-speed photography (Phantom v4, v5, and v7, Vision Research, Inc.). The tank was first filled with two immiscible fluids and then degassed for 30 min to 1 h. Afterward, the lid containing the top electrode was positioned on the box. Brass electrodes were attached to the top and bottom of the container, as shown in Figure 1. Droplets were introduced through a small hole cut into the lid. Droplets were released 1 cm above the fluid interface with the use of glass pipets. They were allowed to settle onto the interface for 1-15 min depending on the viscosity of the silicone oil before a DC electric potential was applied. The potential was supplied by way of a high voltage power supply (Trek Inc., 610A). With a fixed distance between the interface and the top electrode, voltage was varied to produce electric fields of varying strengths. Video was taken using Phantom high-speed cameras having frame rates of 100-4000 frames per second with a maximum and minimum resolution of 800 600 and 256 256 pixels, respectively. The top insulating fluid was Gelest conventional silicone fluid of varying viscosities. The conducting/droplet fluids used for these experiments were chosen based on their dielectric constants, densities relative to silicone oil, viscosity, volatility, and surface energy. Because of the numerous prerequisites that the fluids had to meet, only three fluids were determined to be appropriate: water, glycerol, and ethylene glycol. These fluids have dielectric constants of 78, 60, and 37, respectively; see Table 1 for fluid properties. Due to the relatively high dielectric constants of the bulk fluids into which the droplet coalesces, the charge relaxation time of the interface was approximated to be negligible at the launch of the electric potential on the electrodes. This results in bringing the potential of the lower electrode to the interface such that the electric field in the nonconductive fluid medium can be approximated as E¥=ΔV/d1, where ΔV is the potential difference between the electrodes and d1 is the thickness of the insulating layer. This thickness is always kept large compared to the size of the droplet (10-100 times) to keep the electric field lines approximately straight. The process was recorded using the high-speed camera, with the first frame showing the bridging between the interface and the droplet designated to be the onset of coalescence. The offset between the electric field being initialized and the onset of bridging was always less than one frame. The total time of coalescence was taken to be the time from the onset of bridging to the time of secondary drop pinch off. In the scenario where secondary drops are not formed, the time of coalescence was taken to be from the onset of coalescence to the time when the interface height is no higher than 10% of the original drop radius measured from the interface’s original equilibrium position. This limit accounts for the approximate amount of displacement the planar interface has undergone due to the electric field.
Results and Discussion 1. Defining Geometries. Because coalescence in general involves complex geometries that are often hard to analyze, an attempt will be made to first characterize concrete parameters which describe coalescing droplets. To describe the geometry of a coalescing droplet, two lengths are defined: the distance from the 12462 DOI: 10.1021/la902758u
air
water
glycerol
ethylene glycol
-2
7.20 10 5.82 10-2 1.49 10-2 2.12 10-2 3.76 10-2 2.89 10-2 1.49 10-2 2.14 10-2 4.15 10-1 2.15 10-2 4.35 10-2 interfacial tensions were measured using the DCA-315
undeformed planar interface to the highest point of the coalescing droplet, l, and the radius of the coalescing fluid column at a distance l/2 above the undeformed interface, a (see Figure 2d). If these quantities are considered to be the height and width of the coalescing droplet, then an aspect ratio can be defined, χ = l/a. This will be utilized analogously to the aspect ratio employed by Stone et al.20 By this definition, the aspect ratio of a droplet before coalescing should be a value of 2. The aspect ratio should eventually progress with time to 0 through the process of coalescence. A possible issue that needs to be addressed in this definition of aspect ratio is in cases where secondary drops are formed. Near the point of pinch off, the droplet often has a very narrow region that would be measured as “a” in the aspect ratio. This causes an artificially high aspect ratio, which is not truly representative of the height and width ratio of the geometry. This shows the difficulty and complexity in trying to define the geometry of coalescence. To avoid these arbitrarily large values, only the aspect ratio defined for times not near pinch off are considered. These values will only be used to represent the occurrence of secondary drop formation and do not represent the maximum aspect ratio reached by the coalescing droplet. For cases where no secondary drop forms, the value of the aspect ratio is always finite and is expected to reasonably represent the geometry. Since the transition to secondary drop formation is of primary concern, the maximum aspect ratio, χmax, is considered a primary variable, as this is the geometry that is most vulnerable to break up. In order to analyze the effects of the electric field, the geometry of coalescence in the absence of an electric field must first be examined. This will be used to establish the behavior of the aspect ratio in the mid range Ohnesorge number regime (∼1) as well as high Ohensorge numbers. Figure 3 shows the maximum aspect ratio from experimentation for a variety of fluid combinations that do not produce secondary droplets plotted versus their Ohnesorge numbers. Trend lines follow families of similar viscosity ratios, γ = μ1/μ2. The maximum aspect ratio in the low Ohnesorge number regime would be expected to be large (more than a critical cutoff value determined by the radius of the fluid column and the optimum wavelength for Rayleigh-Taylor breakup) such that it produces secondary droplets. If an Ohnesorge number of unity is approached and secondary drop formation is suppressed, there is a trend toward lower aspect ratios as the effects of viscosity become more dominant.12 At high Ohnesorge numbers, as shown in Figure 3, the aspect ratio appears to reach a maximum value of 2.3. Lower viscosity ratios appear to delay this trend, but aspect ratios still reach the same plateau with a high enough Ohnesorge number. For high viscosity ratios, there is a transition period which ends at approximately an Ohnesorge number of 3, after which the maximum aspect ratio remains constant. If this figure is to be used to determine distinct areas of consistent behavior in terms of aspect ratio, then it is evident that, for high viscosity ratios, our electrocoalescence experiments Langmuir 2009, 25(21), 12460–12465
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Figure 2. Droplets coalescing at a planar interface under the influence of various electric fields. The black reference bars are 1 mm long. Images are taken at approximately 25% of the total time of coalescence apart. (a) A 4 mm initial diameter water droplet in 10 000 cSt viscosity silicone oil under 327 kV/m lasting 1.57 s. (b) A 3.2 mm initial diameter ethylene glycol droplet in 1000 cSt viscosity silicone oil under 395 kV/m lasting 0.385 s. (c) A 2.5 mm initial diameter glycerol droplet in 1000 cSt viscosity silicone oil under 415 kV/m lasting 0.743 s. (d) A 5 mm initial diameter water droplet in 1000 cSt viscosity silicone oil under no electric field lasting 0.193 s. Dashed lines represent the interface and center line. l is the height of the coalescing droplet, and a is the radius at l/2.
should have an Ohnesorge number greater than 3 in order to be completely in the Stokes regime. These results can be explained by considering the characteristics of the droplet midway through coalescence. Its geometry is best described as a fluid column (see Figure 2d). The curvature of the interface at the droplet apex produces a pressure imbalance by way of Laplace pressure, which then drives the fluid into the bulk. If the outer fluid were replaced by a solid and the Laplace pressure by an inlet of equivalent pressure, this would represent Poiseuille flow in a circular pipe. The experimental system can be modeled as such if γ > 1 and Oh . 1. In other words, the outer fluid is highly viscous yet the drop fluid is sufficiently inviscid to not exhibit plug flow. With these conditions met, it can be expected that an inner column of drop fluid will move into the reservoir at a faster rate than the fluid lining the walls, resulting in the fluid column radius reducing at a faster rate than the overall column height. As the viscosity ratio is increased, this phenomenon becomes more pronounced at smaller Ohnesorge numbers. If the viscosity of the outer fluid is not sufficiently large or the viscosity ratio is near unity, then the drop will drain in a uniform fashion. The maximum aspect ratio would then be expected to equal the initial value, χ ∼ 2, if the Bond number is sufficiently small. It is tempting to contribute the trend lines in Figure 3 entirely to Bond number contributions; however, this is not the case as the initial aspect ratios for the majority of our experiments were approximately equal to 2. This indicates a nearly spherical initial droplet. The exact origin of the limiting aspect ratio of 2.3 is left for a more indepth study of Stokes regime coalescence. 2. Electrocoalescence. Figure 2a-c shows the three different conductive droplet fluids in the process of electrocoalescence. Series (a) and (b) show droplets of water and ethylene glycol, Langmuir 2009, 25(21), 12460–12465
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Figure 3. In the absence of an electric field but within an Ohnesorge number range that does not normally produce secondary drops, there exists a relationship between the maximum aspect ratio to which the droplet will deform and the viscosity ratio, γ. The observation seems to agree with the concept of different rates of fluid drainage at the center of the coalescing droplet than at its boundaries. At a sufficiently large Ohnesorge number, both the higher and lower viscosity ratios reach a plateau aspect ratio of approximately 2.3. Trend lines are provided as purely qualitative.
Figure 4. Normalized times of coalescence for high Ohnesorge number coalescence experiments (Oh > 3) under the influence of a range of dimensionless electric field strengths do not show significant change. The magnitude of the dimensionless time is expected to vary with viscosity ratio. The data shown is for a viscosity ratio greater than 1000. Values averaging around 15 were seen for the viscosity ratio of approximately unity but still showed no variation with changes in electric field. T is the total time of coalescence, and Tc is the coalescence time scale.
respectively, in silicone oil forming secondary fluid lobes that in most experiments would break up into different sized secondary droplets. Glycerol droplets in silicone oil, series (c), show the formation of a semistable jet structure protruding from the top of the droplet which in this case moved side to side in wiping motions. With a large increase in electric field strength, all cases experienced the formation of stable fluid jet of comparable diameter to the original droplet that would protrude through the nonconductive medium and eventually short the electrodes. Time of coalescence is often a good indicator of the dominating force behind coalescence. If the time can be scaled properly, the results indicate that the scaling factors are determining the rate at which the droplet is coalescing. If the time of coalescence is normalized with the viscous capillary time scale, Tc=μ2R/σ12, which one would suspect is the correct time scale for the Stokes regime, it can be plotted versus an appropriately scaled electric field strength; see Figure 4. It is apparent that the DOI: 10.1021/la902758u
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Figure 5. Aspect ratio of coalescing droplets plotted versus dimensionless time, T*=t/T for water droplets in silicone oil for various electric field strengths, where t is time. The aspect ratio follows a baseline trend in the absence of an electric field, which is then amplified with increasing electric field strength. Once a critical aspect ratio and electric field strength are reached, the aspect ratio grows and either drop breakup or jet formation will occur at its apex.
normalized time of coalescence is unchanged with large increases in the dimensionless electric field strength defined as E* = E¥/ Ecrit,jet. Under large electric fields, droplets in the Stokes regime coalesce at the same rate they would with no electric field present. This held true for the full range of Ohnesorge numbers in this experiment, 3-30. This can only mean that the underlying mechanism driving coalescence is essentially unchanged by the electric field; that is, the process is still driven by capillarity and retarded by viscous forces. This might be attributed to the fact that the electric field is oriented orthogonally to the interfacial film. It does not affect the rate of expansion of the rupture of the interfacial film once the process has started. With the time of coalescence being unaffected by the electric field, the geometry of the droplet would also be expected to be unaffected by the electric field. This, however, is not the case. The aspect ratio of coalescing droplets in a viscous medium versus percentage of the total coalescence time is shown in Figure 5. As expected, without an electric field, the high Ohnesorge number case did not produce a secondary drop and, moreover, did not go through large aspect ratios as it coalesced. With an increase in the dimensionless electric field strength, the apex of the aspect ratio curve also increased. After reaching a critical electric field strength and a critical aspect ratio (approximately 0.65 and 2.9 for a water droplet in silicone oil, respectively), the coalescence behavior changed entirely. The aspect ratio steadily increased, and there was secondary drop fluid ejected into the ambient fluid. This marked the end of complete coalescence and the transition to electrically induced partial coalescence. If the field was then increased again beyond a second critical E* value (approximately the same value mentioned previously for the inertia dominated coalescence of a water droplet in silicone oil), the coalescing droplet acted as a perturbation to the now unstable fluid interface. The droplet formed the base of a fluid column, jetting out of the planar interface to reach the upper electrode. This was expected as the limit was reached at which a flat fluid interface will become unstable under the influence of an electric field.30 With the variation of the droplet fluid, the role of the dielectric constants in partial coalescence can be explored, as shown in Figure 6. The first data set shows water droplets in silicone oil with viscosities of 1000, 5000, and 10 000 cSt. With Ohnesorge numbers of 3-30, the critical electric field strength at which partial coalescence occurs remained the same. This shows that, once in 12464 DOI: 10.1021/la902758u
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Figure 6. Maximum aspect ratio plotted for various drop fluids versus the dimensionless electric field strength for the high Ohnesorge number regime. The dielectric constants are given for the fluids where ε0 is the permittivity of a vacuum. Open symbols represent experiments that resulted in secondary fluid being left behind in the medium after the completion of coalescence. A decrease in the dielectric constant results in a shift to the right of the critical dimensionless electric field strength at which secondary fluid is created. Also, there is a tendency of the aspect ratio to be smaller for a lower dielectric constant. Table 2. Relevant Parameters for Various Drop Fluids Tabulated for Oh > 1a drop fluid
Ecrit,jet/ Ecrit,drop
Ecrit,jet/Ecrit,plane, R = 1 mm
E* = E¥/Ecrit,jet = drop f jet
water 1.01 0.92 0.65 0.70 glycerol 1.16 0.66 0.75 0.82 ethylene glycol 1.48 0.86 0.87 1.01 a The ratio Ecrit,jet/Ecrit,drop shows that, for values greater than unity, one will reach the point of droplet breakup due to the electric field before the formation of fluid jets. Ecrit,jet/Ecrit,plane is evaluated with a drop radius of 1 mm and shows that jet formation occurs before the planar fluid interface becomes unstable. Below a lower limit of drop size, the opposite becomes true. The final column shows the critical values of E* for the onset of drop breakup and jet formation experimentally determined by the current work.
the Stokes regime, the increases in viscosity will not effect the electric field’s ability or inability to produce partial coalescence. This is significant, as it shows that the secondary droplets formed are the result of the electric field competing with some other retarding force besides viscosity, most likely inertial-capillary forces The next two data sets have the droplet fluid changed to glycerol and ethylene glycol while the medium is restricted to silicone oil of 1000 cSt viscosity. A decrease in the dielectric constant of the drop results in the decrease in the maximum aspect ratio reached during coalescence, similar to what is reported by Stone et al.20 It also delays the critical dimensionless electric field strength at which partial coalescence begins. For glycerol and ethylene glycol, the critical dimensionless electric field strength for the onset of partial coalescence was 0.75 and 0.87, respectively. Figure 6 does not include cases where stable fluid jets formed. To better illustrate what is occurring, the critical electric field strengths for various fluid combinations are tabulated in Table 2. If a water droplet in silicone oil is considered, increasing the electric field beyond the point where droplet breakup will occur results in jet formation as well since the critical values of electric fields are very close to one another, Ecrit,jet/Ecrit,drop = 1.01. This means that there should only be a small band of electric field strengths that cause partial coalescence before transitioning to stable fluid jet formation. This is in fact reflected in the experimental data. Partial coalescence for water droplets occurs only for E* values from 0.65 to 0.70. Beyond 0.70, only fluid jet would form. Because the band between complete coalescence and jet formation is so small for water droplets, Langmuir 2009, 25(21), 12460–12465
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they often form jet with small increases in the electric field. Glycerol and ethylene glycol displayed similar behavior; however, they had correspondingly larger bands of E* in which partial coalescence occurs for larger ratios of Ecrit,jet/Ecrit,drop. This meant that the transition for those two fluids from complete coalescence to jet formation was more distinct and easier to control. Referring again to Table 2, the ratio of critical electric field strength for jet formation to plane interface destabilization, Ecrit,jet/Ecrit,plane, is less than 1 for all three fluids if a 1 mm droplet is considered. This would suggest that jet formation should supersede interface destabilization. This is only true if the droplet is of sufficient size. For water and silicone oil, there exists a critical drop radius of 854μm, below which the planar interface will become unstable and form Taylor cones. In this circumstance, the droplet will not form the jet that causes an electrical short between electrodes. Glycerol and ethylene glycol have their own critical drop radius below which interface destabilization supersedes jet formation. This once again depends on the ratio, Ecrit,jet/Ecrit,plane. In most cases, the current work conducted experiments with droplets larger than the critical size and confirmed the formation of jets. A limited number of experiments with very small droplets exhibited the formation of Taylor cones, but the exact cut-off radius was not explored further.
Conclusion For droplets of high Ohnesorge number, the phenomenon known as partial coalescence is suppressed in the absence of an electric field. With the introduction of a DC electric field of sufficient strength, the conducting coalescing droplet can be made to partially coalescence in an insulating fluid. The
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Letter
critical field strength at which this occurs depends on surface tension, drop radius, and permittivity. If the field is instead increased past the threshold for droplet breakup, a second process will begin to occur as the droplet will cease to coalescence and will instead form into a semistable fluid jet. Eventually, at E* ≈ 1, the fluid jets will become fully stable, although in practice this stability is not long-lived due to shorting between electrodes. These outcomes hold true only if the droplet is of sufficient size such that the limit for Taylor cone formation on the surface of a planar interface is not reached first. For the design of electrocoalescence demulsifiers, it is preferable to stay below the threshold for partial coalescence, as these secondary droplets can be very difficult to eliminate. Because the initial composition of the emulsion will most likely not be uniform, this would best be achieved by a multistep demulsifier which eliminates the largest droplets in the first step and then proceeds to the smaller and smaller droplets by incremental increases in the field strength. A similar effect could be achieved through the use of an AC field. Care must always be taken to not to be in the band of E* which causes partial coalescence for a given dielectric constant. For other devices that may need to produce stable fluid jets at particular locations on the fluid interface, one could seed the interface with droplets of sufficient size to satisfy Ecrit,jet/Ecrit,plane being less than 1 and then introduce an E* of greater than 1. If the goal is to produce Taylor cones, the size of the droplets should be small enough for Ecrit,jet/Ecrit,plane to be greater than 1. By breaking this complex process into its individual parts, there is now a simple set of parameters which determine the state of the electrocoalescence system.
DOI: 10.1021/la902758u
12465
