A regularised singularity approach to phoretic problems

Abstract

An efficient, accurate, and flexible numerical method is proposed for the solution of the swimming problem of one or more autophoretic particles in the purely-diffusive limit. The method relies on successive boundary element solutions of the Laplacian and the Stokes flow equations using regularised Green's functions for swift, simple implementations, an extension of the well-known method of "regularised stokeslets" for Stokes flow problems. The boundary element method is particularly suitable for phoretic problems, since no quantities in the domain bulk are required to compute the swimming velocity. For time-dependent problems, the method requires no re-meshing and simple boundaries such as a plane wall may be added at no increase to the size of the linear system through the method of images. The method is validated against two classical examples for which an analytical or semi-analytical solution is known, a two-sphere system and a Janus particle, and provides a rigorous computational pipeline to address further problems with complex geometry and multiple bodies.

The matlab numerical code for the method described in this paper is freely available as the package RegBEM Phoretic from the matlab file exchange at http://uk.mathworks.com/matlabcentral/profile/authors/5102158-thomas-montenegro-johnson

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• Modeling chemo-hydrodynamic interactions of phoretic particles: a unified framework
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• Hydrochemical interactions of phoretic particles: a regularized multipole framework
• Microtransformers: controlled microscale navigation with flexible robots
• Local drag of a slender rod parallel to a plane wall in a viscous fluid
• The near and far of a pair of magnetic capillary disks
• A numerical method for suspensions of articulated bodies in viscous flows
• Passively parallel regularized stokeslets
• Clustering-induced self-propulsion of isotropic autophoretic particles
• A numerical framework for phoretic particles
• The autophoretic torus
• Method of regularised stokeslets: Flow analysis and improvement of convergence