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Effect of interfacial viscosities on droplet migration at low surfactant concentrations

Published online by Cambridge University Press:  03 September 2020

Rajat Dandekar  and
Arezoo M. Ardekani Open the ORCID record for Arezoo M. Ardekani [Opens in a new window]
Rajat Dandekar
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN49707, USA
Arezoo M. Ardekani*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN49707, USA
*
†Email address for correspondence: ardekani@purdue.edu
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Abstract

In this paper, we theoretically investigate the migration of a surfactant covered droplet in a Poiseuille flow by including the surface viscosities of the droplet. We employ a regular perturbation expansion for low surface Péclet numbers and solve the problem up to a second-order approximation. We represent the drop surface as a two-dimensional homogeneous fluid using the Bousinessq–Scriven law and employ Lamb's general solution to represent the velocity fields inside and outside the droplet. We obtain an expression for the cross-stream migration velocity of the droplet, where the surface viscosities are captured by the Bousinessq numbers for surface shear and surface dilatation. We elucidate the influence of the surface viscosities on the migration characteristics of the droplet and the surfactant redistribution on the droplet surface. Our study sheds light on the importance of including the droplet surface viscosities to accurately predict the migration characteristics of the droplet.

JFM classification

Drops and Bubbles: Drops Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A2
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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