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Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors

Published online by Cambridge University Press:  28 August 2013

Eligiusz Wajnryb ,
Krzysztof A. Mizerski ,
Pawel J. Zuk  and
Piotr Szymczak
Eligiusz Wajnryb
Affiliation:
Department of Mechanics and Physics of Fluids, Institute of Fundamental and Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106, Warsaw, Poland
Krzysztof A. Mizerski*
Affiliation:
Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, ul. Ksiecia Janusza 64, 01-452 Warsaw, Poland
Pawel J. Zuk
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681, Warsaw, Poland
Piotr Szymczak
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681, Warsaw, Poland
*
†Email address for correspondence: krzysztof.mizerski@gmail.com
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Abstract

The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all long-range terms (i.e. decaying as ${R}^{- 3} $ or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions.

JFM classification

Mathematical Foundations: Computational methods Low-Reynolds-number flows: Low-Reynolds-number flows Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , R3
Copyright
©2013 Cambridge University Press 

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