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Viscous Marangoni migration of a drop in a Poiseuille flow at low surface Péclet numbers

Published online by Cambridge University Press:  28 July 2014

On Shun Pak ,
Jie Feng  and
Howard A. Stone
On Shun Pak
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA
Jie Feng
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08544, USA
*
†Email address for correspondence: hastone@princeton.edu
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Abstract

The motion of a spherical drop with a bulk-insoluble surfactant immersed in a background flow in the limits of low surface Péclet number and low Reynolds number is investigated. We develop a reciprocal theorem that applies to any prescribed background flow and provide a specific example of an unbounded Poiseuille flow. Analytical formulas for the migration velocity of the drop are obtained perturbatively in powers of the surface Péclet number. We show that the redistribution of surfactant due to the background flow acts to retard the motion of the drop, with the magnitude of this slip velocity being independent of the drop’s position in the Poiseuille flow. Moreover, a surfactant-induced cross-streamline migration of the drop occurs towards the centre of the Poiseuille flow, with its magnitude depending linearly on the distance of the drop from the centre of the Poiseuille flow.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles Low-Reynolds-number flows: Low-Reynolds-number flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 753 , 25 August 2014 , pp. 535 - 552
Copyright
© 2014 Cambridge University Press 

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Footnotes

‡

These authors contributed equally to this work.

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