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Mobility of an axisymmetric particle near an elastic interface

Published online by Cambridge University Press:  07 December 2016

Abdallah Daddi-Moussa-Ider ,
Maciej Lisicki Open the ORCID record for Maciej Lisicki [Opens in a new window]  and
Stephan Gekle
Abdallah Daddi-Moussa-Ider*
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany
Maciej Lisicki
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, UK Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
Stephan Gekle
Affiliation:
Biofluid Simulation and Modeling, Fachbereich Physik, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany
*
†Email address for correspondence: abdallah.daddi-moussa-ider@uni-bayreuth.de
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Abstract

Using a fully analytical theory, we compute the leading-order corrections to the translational, rotational and translation–rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle’s shape-dependent bulk mobility and the shape-independent parameters such as the membrane–particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle’s eccentricity. We find that the corrections to the translation–rotation coupling mobility are primarily determined by bending, whereas shearing manifests itself in a more pronounced way in the rotational mobility. We demonstrate the validity of the analytical approximations by a detailed comparison with boundary integral simulations of a truly extended spheroidal particle. They are found to be in a good agreement over the whole range of applied frequencies.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Blood flow Biological Fluid Dynamics: Capsule/cell dynamics Biological Fluid Dynamics: Membranes

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Papers
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Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 210 - 233
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© 2016 Cambridge University Press 

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Footnotes

‡

These authors contributed equally to this work.

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