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

Bandopadhyay, Aditya; Mandal, Sumantra; Kishore, Nanda; Chakraborty, Suman

doi:10.1017/jfm.2016.84

Cited by 70 publications

(56 citation statements)

References 55 publications

(57 reference statements)

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“…Studies on the droplet motion in the presence of external effects such as electric (Ahn et al 2006;Link et al 2006;Bandopadhyay et al 2016;Mandal et al 2016), magnetic (Seemann et al 2012), temperature (Karbalaei et al 2016) and acoustic fields (Seemann et al 2012) are gaining much importance nowadays due to the ease with which these fields can be applied in respective applications. The presence of these fields induces an imbalance in stresses at the droplet interface and modifies the net force acting on the droplet which in turn alters the droplet velocity and associated flow field.…”

Section: Introductionmentioning

confidence: 99%

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017

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The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactantladen droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface diffusion dominated surfactant transport considering small surface Péclet number, and (ii) surface convection governed surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, strength of which relative to viscous stress is represented by thermal Marangoni number, has strong influence on the distribution of surfactant on the droplet surface. Temperature field not only affects the axial velocity of the droplet but also has significant effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of Poiseuille flow, the droplet migrates towards the flow centerline. The magnitude of both axial and crossstream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centerline or away from it. Present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centerline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow for which droplet always moves towards the flow centerline.

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Section: Introductionmentioning

confidence: 99%

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017

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“…On the theoretical side, Shutov (2002) and Shkadov & Shutov (2002) attempted to include it in a small-deformation theory; however, these authors neglected convection at first order and only included it at second order, which as we will show below is incorrect. Very recently, Bandopadhyay et al (2016) studied the dynamics of a drop sedimenting under gravity while subject to an electric field using double asymptotic expansions in electric capillary number Ca E and electric Reynolds number Re E , which compares electric to viscous stresses. Their theory included linearized charge convection but was limited to small Re E , even though small deviations from drop sphericity only necessitate Ca E to be small as we show in this work.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Das¹,

Saintillan²

2016

J. Fluid Mech.

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The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the MelcherTaylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of Taylor (1966), there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theory accurate to second order in electric capillary number O(Ca 2 E ) for the complete Melcher-Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary-element formulation and with existing experimental data in the small-deformation regime.

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“…Based on the above perturbation scheme the linearized hydrodynamic equations are solved using the generalized Lamb solution technique (Happel & Brenner, 1981;Bandopadhyay et al, 2016). Accordingly the velocity and pressure field inside (u d , p d ) and outside (u c , p c ) the drop can be expressed a series of solid spherical harmonics given as (Haber & Hetsroni, 1971, 1972…”

Section: Asymptotic Solutionmentioning

confidence: 99%

“…The various arbitrary constants (A n , B n , C n , A −n−1 , B −n−1 , C −n−1 , A n ,B n ,Ĉ n ,Â −n−1 ,B −n−1 andĈ −n−1 ) are to be determined by simultaneously solving the surfactant transport equation and the appropriate form of the hydrodynamic boundary conditions. The detailed procedure regarding the treatment of these boundary conditions is tedious and can be found in earlier studies (Haber & Hetsroni, 1972;Bandopadhyay et al, 2016). The governing equations electrical potential (equation (4)) in both the drop and continuous phase are solved by expanding the potential in the form…”

Section: Asymptotic Solutionmentioning

confidence: 99%

“…The electrohydrodynamic flow and drop deformation get further affected by the presence of finite charge convection at the interface (Feng, 1999;Xu & Homsy, 2006;Yariv & Almog, 2016;Das & Saintillan, 2016). The significance of a tilted electric field configuration in breaking the fore-aft symmetry of a sedimenting drop was experimentally shown by Bandopadhyay et al (2016). Later, they also observed that a similar phenomenon influences the migration characteristics of a drop in Poiseuille flow (Mandal et al, 2016b).…”

Section: Introductionmentioning

confidence: 96%

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Electrorheology of a dilute emulsion of surfactant-covered drops

et al. 2019

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The effects of surfactant coating on a deformable viscous drop under the combined action of a shear flow and a uniform electric field, are investigated by solving the coupled equations of electrostatics, fluid flow and surfactant transport. Employing a comprehensive three-dimensional solution technique, the non-Newtonian shearing response of the bulk emulsion is analyzed in the dilute suspension regime. The present results reveal that the surfactant non-uniformity creates significant alterations in the flow disturbance around the drop, thereby influencing the viscous dissipation from the flowing emulsion. This, in effect, triggers changes in the bulk shear viscosity. It is striking to observe that the balance between electrical and hydrodynamic stresses is affected in such a way that surface tension gradient on the drop surface vanishes for some specific shear rates and the corresponding effective change in the bulk viscosity becomes negligible too. This critical condition hugely 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 of surface deformation play their role in determining this critical shear rate. The charge convection instigated shear thinning or shear thickening behavior of the emulsion gets reversed due to a coupled interaction of the charge convection and Marangoni stress. In addition, the electrically created anisotropic normal stresses in the bulk rheology, get reduced due to the presence of surfactants, especially when the drop viscosity is much lesser than the continuous fluid. A thorough 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. *

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

Cited by 70 publications

References 55 publications

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

A nonlinear small-deformation theory for transient droplet electrohydrodynamics

Electrorheology of a dilute emulsion of surfactant-covered drops

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