Effect of Nonionic Surfactant on the Deformation and Breakup of a Drop in an Electric Field

Propulsion of zwitterionic surfactant-stabilized water-in-oil droplets by low electric fields

We show directional and controllable propulsion of zwitterionic surfactant-stabilized water-in-oil droplets driven by low electric fields. Our results suggest that the propulsion mechanism is based on stimulus-responsive on-demand interfacial phenomena.

Influence of surface viscosities on the electrodeformation of a prolate viscous drop

Contaminants and other agents are often present at the interface between two fluids, giving rise to rheological properties such as surface shear and dilatational viscosities. The dynamics of viscous drops with interfacial viscosities has attracted greater interest in recent years, due to the influence of surface rheology on deformation and the surrounding flows. We investigate the effects of shear and dilatational viscosities on the electro-deformation of a viscous drop using the Taylor-Melcher leaky dielectric model. We use a large deformation analysis to derive an ordinary differential equation for the drop shape. Our model elucidates the contributions of each force to the overall deformation of the drop and reveals a rich range of dynamic behaviors that show the effects of surface viscosities and their dependence on rheological and electrical properties of the system. We also examine the physical mechanisms underlying the observed behaviors by analyzing the surface dilatation and surface deformation.

Surfactant and dilatational viscosity effects on the deformation of liquid droplets in an electric field

HYPOTHESIS

A conducting droplet suspended in an insulating continuous phase, e.g. an aqueous electrolyte in an oil, is deformed by an applied electric field to nonspherical equilibrium shapes, and can even break-up under strong fields. Many technologies use electro-deformation to manipulate fluid dispersions, with surfactants present on the droplet interfaces forming stabilizing monolayers. While surfactants lower the interface tension which facilitates electro-deformation, the monolayer elasticity resists deformation. High molecular weight surfactants, with large dilatational viscosities, can potentially retard the deformation dynamics.

NUMERICS

A boundary integral method simulates the dynamic interfacial deformation of a perfectly conducting droplet in a dielectric in a uniform field. The interface contains an insoluble monolayer which is a Newtonian fluid with constant dilatational viscosity obeying a Langmuir state equation. A range of initial surfactant surface concentrations are studied, with elasticity proportional to concentration.

FINDINGS

Equilibrium drop deformations, unaffected by surface viscosity, are strongly resisted by elasticity at high surface concentrations, and field strengths necessary for break-up increase with elasticity. Dilatational viscosity scales with the ratio, κ^∗, the surface viscosity (divided by the droplet radius) to the bulk viscosity, and can extend the deformation time. Extended times are described by a time rescaling proportional to κ^∗.

Electro-Hydrodynamics of Emulsion Droplets: Physical Insights to Applications

The field of droplet electrohydrodynamics (EHD) emerged with a seminal work of G.I. Taylor in 1966, who presented the so-called leaky dielectric model (LDM) to predict the droplet shapes undergoing distortions under an electric field. Since then, the droplet EHD has evolved in many ways over the next 55 years with numerous intriguing phenomena reported, such as tip and equatorial streaming, Quincke rotation, double droplet breakup modes, particle assemblies at the emulsion interface, and many more. These phenomena have a potential of vast applications in different areas of science and technology. This paper presents a review of prominent droplet EHD studies pertaining to the essential physical insight of various EHD phenomena. Here, we discuss the dynamics of a single-phase emulsion droplet under weak and strong electric fields. Moreover, the effect of the presence of particles and surfactants at the emulsion interface is covered in detail. Furthermore, the EHD of multi-phase double emulsion droplet is included. We focus on features such as deformation, instabilities, and breakups under varying electrical and physical properties. At the end of the review, we also discuss the potential applications of droplet EHD and various challenges with their future perspectives.

Breakups of an encapsulated surfactant-laden aqueous droplet under a DC electric field

We investigate the breakups of an encapsulated conducting aqueous droplet under a direct-current electric field via extensive experiments and theoretical analysis. The encapsulating shell phase and the ambient phase consist of leaky dielectric liquids. We change the surface tension by using an aqueous core with different surfactant (Tween 80) concentrations. Moreover, we vary the core size under different electric-field conditions and observe the core dynamics. We present three different breakup modes of the encapsulated droplet. In the first mode, the encapsulated core forms asymmetric Janus shapes after breakup. In the second and third breakup modes, stable and unstable ternary droplets are formed, respectively. We show that the surfactant molecules significantly alter the dynamics of core stretching. According to the theoretical analysis, we identify the critical conditions of instability leading to breakup. We plot the breakup modes in the form of a phase diagram in the electric capillary number (Ca₂₃ = ε₃r_sE_o²/γ₂₃; ratio of interfacial electric to capillary stresses) vs. radius ratio of the core to the shell (β = r_c/r_s) parametric space at different nondimensional surfactant concentrations (C* = C_Tween 80/C_CMC, where C_CMC represents the critical micellar concentration). The study provides essential physical insight into encapsulated emulsions and is useful for their application in various areas of science and technology.

Electric fields enable tunable surfactant transport to microscale fluid interfaces

The transport dynamics of oil-soluble surfactants to oil-water interfaces are quantified using a custom-built electrified capillary microtensiometer platform. Dynamic interfacial tension measurements reveal that surfactant transport is enhanced under a dc electric field, due to electro-migration of charge carriers in the oil toward the interface. Notably, this enhancement can be precisely tuned by altering the field strength and temporal scheduling. We demonstrate electric fields as a new parameter to manipulate surfactant transport to microscale fluid-fluid interfaces.

Effects of surfactant transport on electrodeformation of a viscous drop

In this work we quantify the effects of surfactant transport on the deformation of a viscous drop under a DC electric field. We study how convective and diffusive transport of surfactants at drop surfaces influence the equilibrium and dynamic deformation of a leaky dielectric drop and a conducting drop. Focusing on the prolate drop shape (elongates along the electric field), we show the differences in equilibrium deformation and flow circulation between a leaky dielectric drop and a conducting drop. We quantify the drop electrodeformation via its dependence on the interior flow circulation and the dominant surfactant transport regime (characterized by the surface Péclet number Pe_{s}). For a leaky dielectric drop with dominant surfactant diffusion (Pe_{s}≪1), equator-to-pole (pole-to-equator) circulation yields smaller (larger) equilibrium deformation with increasing surfactant coverage, compared to a clean drop. However, when convection dominates (Pe_{s}≫1), the equilibrium drop deformation increases (decreases) with larger surfactant coverage for equator-to-pole (pole-to-equator) circulation. Larger equilibrium drop deformation is found for a leaky dielectric drop than a conducting drop when the interior flow is from equator to pole. For an interior flow from pole to equator, we identify cases where larger deformation is found for a conducting interior fluid. Finally, we study the effect of the surfactant transport on the dynamic evolution of drop shape. We found the drop undergoes an overshoot in the early deformation phase, before settling to its equilibrium shape-similar to the overshoot observed for unsteady Stokes flow.

Methodology to calculate interfacial tension under electric field using pendent drop profile analysis

In this paper, we present a methodology to calculate interfacial tension of a water-oil interface under an electric field. The Young-Laplace equation, conventionally used to estimate surface/interfacial tension in axisymmetric drop shape analysis (ADSA), is modified to include electrostatic effects. The solution needs normal component of the Maxwell stress at the interface which is calculated separately by solving the Laplace equation for electric potential. The optimized fitting between the resulting theoretical profile and the experimentally obtained profile results into Bond number which is used to calculate the apparent value of interfacial tension. The algorithm can process a large number of drop profiles in one go. The methodology can be applied in the ADSA studies for adsorption dynamics where a drop is held for a long time while surface active molecules are allowed to adsorb. The method discussed in this paper will help the future studies in adsorption dynamics at fluid interfaces under electric field and the resulting interfacial property evolution.

Colloidal stability dictates drop breakup under electric fields

Electric fields can deform drops of fluid from their equilibrium shape, and induce breakup at sufficiently large field strengths. In this work, the electric field induced breakup of a squalane drop containing a colloidal suspension of carbon black particles with polyisobutylene succinimide (OLOA 11000) surfactant is studied. The drop is suspended in silicone oil. The breakup mode of a drop containing carbon black depends strongly on the suspension stability. It is observed that a drop of a stable suspension of carbon black has the same breakup mode as a drop with surfactant alone, i.e., without added carbon black. At lower electric fields, these drops break by the formation of lobes at the two ends of the drop; and at higher fields the homogeneous lobes break in a non-axisymmetric manner. However, a drop of an unstable suspension shows a drastically different breakup mode, and undergoes breakup much faster compared to a drop with surfactant alone. These drops elongate and form asymmetric lobes that develop into fingers and eventually disintegrate in an inhomogeneous, three-dimensional fashion. As a basis for comparison, the breakup of a pure squalane drop, and a squalane drop with equivalent surfactant concentrations but no carbon black particles is examined. Axisymmetric boundary integral computations are used to elucidate the mechanism of breakup. Our work demonstrates the impact of colloidal stability on the breakup of drops under an electric field. Colloidal stability on the time scale of drop deformation leads to rich and unexplored breakup phenomena.

Electrohydrodynamics of a viscous drop with inertia

Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number Oh, and the electric field is characterized by an electric capillary number Ca_{E}. Below the critical Ca_{E}, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed Ca_{E}, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical Ca_{E}, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

Electric-field-assisted formation of nonspherical microcapsules

A new method for studying the effect of pH on the polysiloxane network formation using electric fields is presented. The kinetic data obtained using these experiments indicates that the two-step interfacial polycondensation of silanes is strongly dependent on the pH, and the mechanism is essentially different at low and neutral to high values of pH. Very rapid hydrolysis followed by moderate rates of condensation are observed at neutral and high pH. The rate of hydrolysis is drastically reduced, while that of condensation is slightly lowered at low pH as compared to that at high values of pH. The slow hydrolysis reaction at low pH is then exploited to synthesize nonspherical microcapsules. Nonspherical polysiloxane microcapsules with varying aspect ratios from 1.05to 1.97 are synthesized by controlling the applied electric field.

Catastrophic drop breakup in electric field

We report novel observations revealing the catastrophic breakup of water drops containing surfactant molecules, which are suspended in oil and subjected to an electric field of strength approximately 10(5) V/m. The observed breakup was distinctly different from the gradual end pinch-off or tip-streaming modes reported earlier in the literature. There was no observable characteristic deformation of the drop prior to breakup. The time scales involved in the breakup and the resultant droplet sizes were much smaller in the phenomenon observed by us. We hypothesize that this mode of drop breakup is obtained by the combined effect of an external electric field that imposes tensile stresses on the surface of the drop, and characteristic stress-strain behavior for tensile deformation exhibited by the liquid drop in the presence of a suitable surfactant, which not only lowers the interfacial tension (and hence the cohesive strength) of the drop but also simultaneously renders the interface nonductile or brittle at high enough concentration. We have identified the relevant thermodynamic parameter, viz., the sum of interfacial tension, sigma, and the Gibbs elasticity, epsilon, which plays a decisive role in determining the mode of drop breakup. The parameter (epsilon + sigma) represents the internal restoration stress of a liquid drop opposing rapid, short-time-scale perturbations or local deformations in the drop shape under the influence of external impulses or stresses. A thermodynamic "state" diagram of (epsilon + sigma) versus interfacial area per surfactant molecule adsorbed at the drop interface shows a "maximum" at a critical transition concentration (ctc). Below this concentration of the surfactant, the drop undergoes tip streaming or pinch off. Above this concentration, the drop may undergo catastrophic disintegration if the external stress is high enough to overcome the ultimate cohesive strength of the drop's interface.

Deformation of water droplets on solid surface in electric field

The purpose of this paper is to analyze the deformation of water droplets on a solid surface under electric stress. A mathematical model making it possible to simulate the axisymmetric as well as non-axisymmetric deformations of droplets is developed. According to this model, the droplet deformation depends on several parameters such as the volume and the number of droplets, the conductivity and the permittivity of droplets, their proximity to one another, the surface of the solid material, and the location of each droplet on the dielectric surface. The results of the simulation show the disturbance of the background field through the presence of a single or multiple droplets. An experimental study is also achieved by considering one to three droplets aligned simultaneously on a dielectric smooth surface between two electrodes subjected to AC voltages. The influence of the background field and the droplet location regarding the electrodes on the deformation of water droplets are evidenced.

Hydrodynamic Interaction between Spheres Coated with Deformable Thin Liquid Films

In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.

Breakup of a Multiple Emulsion Drop in a Uniform Electric Field

The steady deformation and breakup of emulsion drops in a uniform electric field are considered experimentally. Due to the low volume fraction of inner drops, the emulsions can be effectively assumed as Newtonian fluids with spatial nonuniformity. The measurements of the electrical properties show that the oil-in-water (o/w) emulsion drop behaves like a conducting drop. On the other hand, the water-in-oil (w/o) emulsion drops can be regarded as inhomogeneous leaky dielectric drops. It is found that the viscosity ratio is not an important parameter within the small deformation limit and breakup mode of the o/w emulsion drops. In the case of w/o emulsion drops, however, the breakup mode depends on the viscosity ratio. Inherent nonuniformity of the emulsion drops makes drop more deformable and unstable. The tip-streaming is the dominant breakup mode of o/w emulsion drops when the nonuniformity of drop phase is appreciable. Copyright 1999 Academic Press.