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

Published online by Cambridge University Press:  03 March 2016

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

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.

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 792 , 10 April 2016 , pp. 553 - 589
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© 2016 Cambridge University Press 

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