Uniform electric-field-induced lateral migration of a sedimenting drop

We investigate the motion of a sedimenting drop in the presence of an electric field in an arbitrary direction, otherwise uniform, in the limit of small interface deformation and low-surface-charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the correction in drop velocity due to shape deformation and surface-charge convection considering small capillary number and small electric Reynolds number which signifies the importance of charge convection at the drop surface. We show that tilt angle, which quantifies the angle of inclination of the applied electric field with respect to the direction of gravity, has a significant effect on the magnitude and direction of the drop velocity. When the electric field is tilted with respect to the direction of gravity, we obtain a non-intuitive lateral motion of the drop in addition to the buoyancy-driven sedimentation. Both the charge convection and shape deformation yield this lateral migration of the drop. Our analysis indicates that depending on the magnitude of the tilt angle, conductivity and permittivity ratios, the direction of the sedimenting drop can be controlled effectively. Our experimental investigation further confirms the presence of lateral migration of the drop in the presence of a tilted electric field, which is in support of the essential findings from the analytical formalism.

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Electrorheology of a dilute emulsion of surfactant-covered drops

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.745 ◽

2019 ◽

Vol 881 ◽

pp. 524-550 ◽

Cited By ~ 1

Author(s):

Antarip Poddar ◽

Shubhadeep Mandal ◽

Aditya Bandopadhyay ◽

Suman Chakraborty

Keyword(s):

Electric Field ◽

Applied Electric Field ◽

Surface Deformation ◽

Three Dimensional ◽

Shear Thickening ◽

Field Configuration ◽

Uniform Electric Field ◽

Surface Tension Gradient ◽

Drop Surface ◽

Flow Perturbation

We investigate the effects of surfactant coating on a deformable viscous drop under the combined action of shear flow and a uniform electric field. Employing a comprehensive three-dimensional approach, we analyse the non-Newtonian shearing response of the bulk emulsion in the dilute suspension regime. Our results reveal that the location of the peak surfactant accumulation on the drop surface may get shifted from the plane of shear to a plane orthogonal to it, depending on the tilt angle of the applied electric field and strength of the electrical stresses relative to their hydrodynamic counterparts. The surfactant non-uniformity creates significant alterations in the flow perturbation around the drop, triggering modulations in the bulk shear viscosity. Overall, the shear-thinning or shear-thickening behaviour of the emulsion appears to be greatly influenced by the interplay of surface charge convection and Marangoni stresses. We show that the balance between electrical and hydrodynamic stresses renders a vanishing surface tension gradient on the drop surface for some specific shear rates, rendering negligible alterations in the bulk viscosity. This critical condition largely depends on the electrical permittivity and conductivity ratios of the two fluids and orientation of the applied electric field. Also, the physical mechanisms of charge convection and surface deformation play their roles in determining this critical shear rate. As a consequence, we obtain new discriminating factors, involving electrical property ratios and the electric field configuration, which govern the same. Consequently, the surfactant-induced enhancement or attenuation of the bulk emulsion viscosity depends on the electrical conductivity and permittivity ratios. The concerned description of the drop-level flow physics and its connection to the bulk rheology of a dilute emulsion may provide a fundamental understanding of a more complex emulsion system encountered in industrial practice.

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Particle-Particle Interactions on the Surface of a Drop Subjected to a Uniform Electric Field

Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C ◽

10.1115/imece2008-67796 ◽

2008 ◽

Author(s):

S. Nudurupati ◽

M. Janjua ◽

P. Singh ◽

N. Aubry

Keyword(s):

Electric Field ◽

Immiscible Liquid ◽

The Other ◽

Uniform Electric Field ◽

Particle Interactions ◽

Drop Surface ◽

Dielectrophoretic Force ◽

Dipole Interactions ◽

Electric Field Direction ◽

Local Direction

We recently proposed a technique in which an externally applied uniform electric field was used to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Particles move along the drop surface to form a ring near the drop equator or collect at the poles depending on their dielectric constant relative to that of the two liquid involved. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is non-uniform, despite the fact that the applied electric field is uniform. This technique could be useful to concentrate particles at a drop surface within well-defined regions (poles and equator), and separate two types of particles at the surface of a drop. In this paper we show that in addition to the dielectrophoretic force the particles also interact with each other via the dipole-dipole interactions to form chains or move away from each other depending the local direction of the electric field. The regions in which the local electric field is normal to the drop surface, i.e., the poles, the particles move away from each other. On the other hand, near the equator, where the local direction of electric field is tangential to the drops surface, they form chains that are aligned parallel to the electric field direction.

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The effect of uniform electric field on the cross-stream migration of a drop in plane Poiseuille flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.677 ◽

2016 ◽

Vol 809 ◽

pp. 726-774 ◽

Cited By ~ 24

Author(s):

Shubhadeep Mandal ◽

Aditya Bandopadhyay ◽

Suman Chakraborty

Keyword(s):

Steady State ◽

Electric Field ◽

Numerical Simulations ◽

Poiseuille Flow ◽

Shape Deformation ◽

Uniform Electric Field ◽

Plane Poiseuille Flow ◽

Stream Migration ◽

The Cross ◽

Transverse Position

The effect of a uniform electric field on the motion of a drop in an unbounded plane Poiseuille flow is studied analytically. The drop and suspending media are considered to be Newtonian and leaky dielectric. We solve for the two-way coupled electric and flow fields analytically by using a double asymptotic expansion for small charge convection and small shape deformation. We obtain two important mechanisms of cross-stream migration of the drop: (i) shape deformation and (ii) charge convection. The second one is a new source of cross-stream migration of the drop in plane Poiseuille flow which is due to an asymmetric charge distribution on the drop surface. Our study reveals that charge convection can cause a spherical non-deformable drop to migrate in the cross-stream direction. The combined effect of charge convection and shape deformation significantly alters the drop velocity, drop trajectory and steady state transverse position of the drop. We predict that, depending on the orientation of the applied uniform electric field and the relevant drop/medium electrohydrodynamic parameters, the drop may migrate either towards the centreline of the flow or away from it. We obtain that the final steady state transverse position of the drop is independent of its initial transverse position in the flow field. Most interestingly, we show that the drop can settle in an off-centreline steady state transverse position. Two-dimensional numerical simulations are also performed to study the drop motion in the combined presence of plane Poiseuille flow and a tilted electric field. The drop trajectory and steady state transverse position of the drop obtained from numerical simulations are in qualitative agreement with the analytical results.

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The effect of surface-charge convection on the settling velocity of spherical drops in a uniform electric field

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.286 ◽

2016 ◽

Vol 797 ◽

pp. 536-548 ◽

Cited By ~ 13

Author(s):

Ehud Yariv ◽

Yaniv Almog

Keyword(s):

Difference Equation ◽

Electric Field ◽

Surface Charge ◽

Settling Velocity ◽

Numerical Solutions ◽

Weak Field ◽

Uniform Electric Field ◽

Electrostatic Problem ◽

Settling Speed ◽

The Difference

The mechanism of surface-charge convection, quantified by the electric Reynolds number $Re$, renders the Melcher–Taylor electrohydrodynamic model inherently nonlinear, with the electrostatic problem coupled to the flow. Because of this nonlinear coupling, the settling speed of a drop under a uniform electric field differs from that in its absence. This difference was calculated by Xu & Homsy (J. Fluid Mech., vol. 564, 2006, pp. 395–414) assuming small $Re$. We here address the same problem using a different route, considering the case where the applied electric field is weak in the sense that the magnitude of the associated electrohydrodynamic velocity is small compared with the settling velocity. As convection is determined at leading order by the well-known flow associated with pure settling, the electrostatic problem becomes linear for arbitrary value of $Re$. The electrohydrodynamic correction to the settling speed is then provided as a linear functional of the electric-stress distribution associated with that problem. Calculation of the settling speed eventually amounts to the solution of a difference equation governing the respective coefficients in a spherical harmonics expansion of the electric potential. It is shown that, despite the present weak-field assumption, our model reproduces the small-$Re$ approximation of Xu and Homsy as a particular case. For finite $Re$, inspection of the difference equation reveals a singularity at the critical $Re$-value $4S(1+R)(1+M)/(1+S)M$, wherein $R$, $S$ and $M$ respectively denote the ratios of resistivity, permittivity and viscosity values in the suspending and drop phases, as defined by Melcher & Taylor (Annu. Rev. Fluid Mech., vol. 1, 1969, pp. 111–146). Straightforward numerical solutions of this equation for electric Reynolds numbers smaller than the critical value reveal a non-monotonic dependence of the settling speed upon the electric field magnitude, including a transition from velocity enhancement to velocity decrement.

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