Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic of the velocity of a dilute suspension of droplets with interfacial tension

Authors: Eric Bonnetier, David Manceau and Faouzi Triki
Journal: Quart. Appl. Math. 71 (2013), 89-117
MSC (2010): Primary 35R30
DOI: https://doi.org/10.1090/S0033-569X-2012-01275-7
Published electronically: October 12, 2012
MathSciNet review: 3075537
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we derive the asymptotic expansion of the velocity field of a small deformable droplet immersed in an incompressible Newtonian fluid. Using an appropriate physical scaling of the surface tension with respect to the droplet volume, we show that the first order of the asymptotic can be expressed in terms of the velocity field in the absence of the droplet and a new kind of moment tensor, called the curvature moment tensor. Our asymptotic formula extends those already derived for rigid droplets and aimed to obtain simplified macroscale properties of a dilute suspension composed of identical droplets dispersed in an incompressible Newtonian fluid from knowledge of its microscopic properties. We finally determine explicitly the curvature moment tensor for ellipses and ellipsoids.

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Additional Information

Eric Bonnetier
Affiliation: Laboratoire Jean Kuntzmann, Université de Joseph Fourier & CNRS, 38041 Grenoble Cedex 9, France
Email: eric.bonnetier@imag.fr

David Manceau
Affiliation: Laboratoire de Mathématiques appliquées du Havre, Université du Havre, 25 rue Philippe Lebon, BP 540, 76058 Le Havre cedex, France
Email: david.manceau@univ-lehavre.fr

Faouzi Triki
Affiliation: Laboratoire Jean Kuntzmann, Université de Joseph Fourier & CNRS, 38041 Grenoble Cedex 9, France
Email: faouzi.triki@imag.fr

DOI: https://doi.org/10.1090/S0033-569X-2012-01275-7
Keywords: Stokes system, asymptotic expansion, surface tension, viscous moment tensor, droplets
Received by editor(s): March 30, 2011
Published electronically: October 12, 2012
Article copyright: © Copyright 2012 Brown University

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