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Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models

Published online by Cambridge University Press:  11 February 2014

P. J. Zuk ,
E. Wajnryb ,
K. A. Mizerski  and
P. Szymczak
P. J. Zuk
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
E. 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
K. A. Mizerski
Affiliation:
Department of Magnetism, Institute of Geophysics, Polish Academy of Sciences, ul. Ksiecia Janusza 64, 01-452 Warsaw, Poland
P. Szymczak*
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00-681 Warsaw, Poland
*
†Email address for correspondence: piotrek@fuw.edu.pl
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Abstract

The Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equal-sized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, different-sized beads, which we illustrate with an example.

JFM classification

Complex Fluids: Complex Fluids Mathematical Foundations: Computational methods Low-Reynolds-number flows: Low-Reynolds-number flows Mathematical Foundations: Mathematical Foundations Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , R5
Copyright
© 2014 Cambridge University Press 

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