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

Published online by Cambridge University Press:  15 November 2016

Shubhadeep Mandal ,
Aditya Bandopadhyay  and
Suman Chakraborty
Shubhadeep Mandal
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Aditya Bandopadhyay
Affiliation:
Advanced Technology Development Center, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Suman Chakraborty*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India Advanced Technology Development Center, Indian Institute of Technology Kharagpur, West Bengal 721302, India
*
†Email address for correspondence: suman@mech.iitkgp.ernet.in
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Abstract

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.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles
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Papers
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Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 726 - 774
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© 2016 Cambridge University Press 

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