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Drag and diffusion coefficients of a spherical particle attached to a fluid–fluid interface

Published online by Cambridge University Press:  10 February 2016

Aaron Dörr ,
Steffen Hardt ,
Hassan Masoud  and
Howard A. Stone
Aaron Dörr*
Affiliation:
Institute for Nano- and Microfluidics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
Steffen Hardt
Affiliation:
Institute for Nano- and Microfluidics, Center of Smart Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany
Hassan Masoud
Affiliation:
Department of Mechanical Engineering, University of Nevada, Reno, NV 89557, USA Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the flat interface between two immiscible fluids are constructed for the case of a vanishing viscosity ratio between the fluid phases. The model is designed to account explicitly for the dependence on the contact angle between the two fluids and the solid surface. The Lorentz reciprocal theorem is applied in the context of geometric perturbations from the limiting cases of $90^{\circ }$ and $180^{\circ }$ contact angles. The model agrees well with the experimental and numerical data from the literature. Also, an advantage of the method utilized is that the drag and diffusion coefficients can be calculated up to one order higher in the perturbation parameter than the known velocity and pressure fields. Extensions to other particle shapes with known velocity and pressure fields are straightforward.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Particle/fluid flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 607 - 618
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Copyright
© 2016 Cambridge University Press 

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