Drop deformation and emulsion rheology under the combined influence of uniform electric field and linear flow

Electrohydrodynamics of a leaky dielectric suspended drop subjected to the combined influence of a uniform electric field and linear velocity field is analysed analytically and numerically. In the limit of small charge convection and small shape deformation, an analytical solution is obtained for the deformed drop shape when the imposed linear flow is of uniaxial extensional type with the extensional component aligned in the direction of the electric field. This perturbation approach is then applied towards obtaining the effect of a uniform electric field on the effective extensional rheology of a dilute emulsion. Key results indicate that the magnitude and sense of drop deformation not only depends on the material properties of the drop and medium but is also governed by the strength of the applied electric field relative to the applied flow field. The interfacial charge convection is found to increase or decrease the drop deformation depending on the direction of electrohydrodynamic flow and relative strength of electric field. The electrohydrodynamic flow and drop deformation modulates the effective extensional viscosity of the emulsion. Importantly, the presence of the electric field leads to strain-rate-dependent effective extensional viscosity of the emulsion. The emulsion is found to exhibit strain-rate thinning/thickening behaviour depending on the drop to medium charge relaxation time scale. The analytically obtained drop shape and deformation are in excellent agreement with numerical simulations for the small deformation ranges.

Download Full-text

The elongated shape of a dielectric drop deformed by a strong electric field

Journal of Fluid Mechanics ◽

10.1017/s0022112010004581 ◽

2010 ◽

Vol 664 ◽

pp. 286-296 ◽

Cited By ~ 5

Author(s):

DOV RHODES ◽

EHUD YARIV

Keyword(s):

Electric Field ◽

Electric Fields ◽

Strong Electric Field ◽

Outer Region ◽

Spherical Shape ◽

Problem Formulation ◽

Boundary Integral ◽

Uniform Electric Field ◽

Cross Sectional ◽

Drop Shape

A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood (J. Fluid Mech., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood (J. Phys. A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.

Download Full-text

Transient Electrohydrodynamic Manipulation of Particles on the Surface of a Drop

Volume 2: Heat Transfer in Multiphase Systems; Gas Turbine Heat Transfer; Manufacturing and Materials Processing; Heat Transfer in Electronic Equipment; Heat and Mass Transfer in Biotechnology; Heat Transfer Under Extreme Conditions; Computational Heat Transfer; Heat Transfer Visualization Gallery; General Papers on Heat Transfer; Multiphase Flow and Heat Transfer; Transport Phenomena in Manufacturing and Materials Processing ◽

10.1115/ht2016-1051 ◽

2016 ◽

Cited By ~ 1

Author(s):

Edison C. Amah ◽

Ian S. Fischer ◽

Pushpendra Singh

Keyword(s):

Electric Field ◽

Applied Electric Field ◽

Control Parameter ◽

Transient Behavior ◽

Uniform Electric Field ◽

Electrohydrodynamic Flow ◽

Dielectric Model ◽

Leaky Dielectric Model ◽

Leaky Dielectric

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens even when the applied electric field is uniform; the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this study, we use leaky dielectric model to model the transient behavior of particles at low electric field frequencies. We show that the frequency of the electric field is an important control parameter that under certain conditions can be used to collect particles at the poles or the equator, and to move them from the poles to the equator. The speed with which particles move on the surface depends on the strength of the electrohydrodynamic flow which diminishes with increasing frequency.

Download Full-text

Effect of uniform electric field on the drop deformation in simple shear flow and emulsion shear rheology

Physics of Fluids ◽

10.1063/1.4995473 ◽

2017 ◽

Vol 29 (7) ◽

pp. 072109 ◽

Cited By ~ 15

Author(s):

Shubhadeep Mandal ◽

Suman Chakraborty

Keyword(s):

Shear Flow ◽

Electric Field ◽

Simple Shear ◽

Uniform Electric Field ◽

Drop Deformation ◽

Simple Shear Flow ◽

Shear Rheology

Download Full-text

Electrohydrodynamic settling of drop in uniform electric field: beyond Stokes flow regime

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.744 ◽

2019 ◽

Vol 881 ◽

pp. 498-523 ◽

Cited By ~ 3

Author(s):

Nalinikanta Behera ◽

Shubhadeep Mandal ◽

Suman Chakraborty

Keyword(s):

Electric Field ◽

Flow Regime ◽

Stokes Flow ◽

Capillary Number ◽

Uniform Electric Field ◽

Fluid Inertia ◽

Drop Shape ◽

Wide Range ◽

Settling Speed ◽

Leaky Dielectric

The electrohydrodynamics of a weakly conducting buoyant drop under the combined influence of gravity and a uniform electric field is studied computationally, focusing on the inertia-dominated regime. Numerical simulations are performed for both perfectly dielectric and leaky dielectric drops over a wide range of dimensionless parameters to explore the interplay of fluid inertia and electrical stress to govern the drop shape and charge convection. For perfectly dielectric drops, the fluid inertia alters the drop shape and the deformation behaviour of the drop follows a non-monotonic path. The drop shape at steady state exhibits the transition from oblate to prolate shape on increasing the electric field strength, in sharp contrast to the cases concerning the Stokes flow regime. Similar behaviour is also obtained for leaky dielectric drops for certain fluid properties. For leaky dielectric drops, the fluid inertia also affects the convective transport of charges at the drop surface and thereby alters the drop dynamics. Unlike the Stokes flow regime, where surface charge convection has little effect on the settling speed, the same modifies the drop settling speed quite significantly in the finite inertial regime depending on the combination of electrical conductivity ratio and permittivity ratio. For oblate drops at low capillary number, charge convection alters drop shape, while keeping the nature of deformation unaltered. However, for relatively large capillary number, the oblate drop transforms into a dimpled shape due to charge convection. For all cases, an interesting fact is noticed that under the combined action of electric and inertial forces, the resultant deformation is less than the summation of the deformations caused by individual effects, when inertial effects are strong. These results are likely to provide deep insights into the interplay of various nonlinearities towards altering electrohydrodynamic settling of drops and bubbles.

Download Full-text

The role of field-enhanced dissociation in electrohydrodynamic flow formation in a highly non-uniform electric field

Journal of Electrostatics ◽

10.1016/j.elstat.2018.04.008 ◽

2018 ◽

Vol 93 ◽

pp. 104-109 ◽

Cited By ~ 3

Author(s):

V.A. Chirkov ◽

S.A. Vasilkov ◽

Yu.K. Stishkov

Keyword(s):

Electric Field ◽

Uniform Electric Field ◽

Electrohydrodynamic Flow ◽

Flow Formation

Download Full-text

Removal of Particles From the Surface of a Droplet

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2008-55247 ◽

2008 ◽

Author(s):

N. Aubry ◽

P. Singh ◽

S. Nudurupati ◽

M. Janjua

Keyword(s):

Dielectric Constant ◽

Electric Field ◽

Strong Electric Field ◽

Dielectric Constants ◽

The Other ◽

Uniform Electric Field ◽

Drop Deformation ◽

Ambient Fluid ◽

Dielectrophoretic Force ◽

Different Types

We present a technique to concentrate particles on the surface of a drop, separate different types of particles, and remove them from the drop by subjecting the drop to a uniform electric field. The particles are moved under the action of the dielectrophoretic force which arises due to the non-uniformity of the electric field on the surface of the drop. Experiments show that depending on the dielectric constants of the fluids and the particles, particles aggregate either near the poles or near the equator of the drop. When particles aggregate near the poles and the dielectric constant of the drop is greater than that of the ambient fluid, the drop deformation is larger than that of a clean drop. In this case, under a sufficiently strong electric field the drop develops conical ends and particles concentrated at the poles eject out by a tip streaming mechanism, thus leaving the drop free of particles. On the other hand, when particles aggregate near the equator, it is shown that the drop can be broken into three major droplets, with the middle droplet carrying all particles and the two larger sized droplets on the sides being free of particles. The method also allows us to separate particles for which the sign of the Clausius-Mossotti factor is different, making particles of one type aggregate at the poles and of the second type aggregate at the equator. The former are removed from the drop by increasing the electric field strength, leaving only the latter inside the drop.

Download Full-text

On the rheology of a dilute emulsion in a uniform electric field

Journal of Fluid Mechanics ◽

10.1017/s0022112010005379 ◽

2011 ◽

Vol 670 ◽

pp. 481-503 ◽

Cited By ~ 35

Author(s):

PETIA M. VLAHOVSKA

Keyword(s):

Electric Field ◽

Stokes Equations ◽

Fluid Motion ◽

Shear Thickening ◽

Small Deformation ◽

Uniform Electric Field ◽

Drop Deformation ◽

Normal Stresses ◽

Shape Distortion ◽

The One

A small-deformation perturbation analysis is developed to describe the effect of a uniform electric field on drop deformation and orientation in linear flows and emulsion shear rheology. All media are treated as leaky dielectrics, and fluid motion is described by the Stokes equations. The one-particle contribution to the effective stress of a dilute emulsion is obtained from the drop stresslet. Analytical solutions are derived as regular perturbations in the limits of small capillary number and large viscosity ratio. The results show that both shape distortion and charge convection modify emulsion rheology. Drop deformation due to application of an electric field in a direction perpendicular to the shear flow gives rise to normal stresses and may lead to shear thickening or shear thinning, depending on the electric properties of the fluids. Charge convection due to the imposed shear affects both the shear viscosity and normal stresses.

Download Full-text