Many-particle mobility and diffusion tensors for objects in viscous sheets

TL;DR

This paper derives a positive-definite mobility tensor for multiple cylindrical objects in viscous sheets, enabling accurate hydrodynamic interaction modeling in systems like biomembranes and liquid films.

Contribution

The authors introduce a new mobility tensor for cylindrical particles in viscous sheets that ensures positive dissipation, extending the Rotne-Prager-Yamakawa tensor to two-dimensional systems.

Findings

Tensor guarantees positive dissipation for all configurations

Validated with a ring of radially driven particles

Applicable in Brownian Dynamics simulations of biological systems

Abstract

We derive a mobility tensor for many cylindrical objects embedded in a viscous sheet. This tensor guarantees a positive dissipation rate for any configuration of particles and forces, analogously to the Rotne-Prager-Yamakawa tensor for spherical particles in a three-dimensional viscous fluid. We test our result for a ring of radially driven particles, demonstrating the positive-definite property at all particle densities. The derived tensor can be utilized in Brownian Dynamics simulations with hydrodynamic interactions for such systems as proteins in biomembranes and inclusions in free-standing liquid films.