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

TL;DR

This paper extends the Rotne-Prager-Yamakawa approximation to include both translational and rotational hydrodynamic interactions, providing regularized corrections for overlapping particles and generalizations for various geometries and boundary conditions.

Contribution

It introduces a comprehensive extension of the RPY method, incorporating rotational degrees of freedom and boundary condition generalizations, with regularization for overlapping particles.

Findings

Extended RPY includes rotational interactions.

Derived regularizing corrections for overlaps.

Generalized RPY for different geometries.

Abstract

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 is 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.