Motion of hydrodynamically interacting active particles

TL;DR

This paper presents a comprehensive hydrodynamic theory for interacting active particles of arbitrary shape in viscous fluids, incorporating slip velocities and hydrodynamic interactions, with applications to chemically active particles and diffusiophoresis.

Contribution

It introduces a general framework for modeling hydrodynamic interactions of active particles with arbitrary shapes using slip velocities and applies it to chemically active particles and their autonomous motion.

Findings

Developed a hydrodynamic theory for active particles of arbitrary shape.

Extended the theory to include hydrodynamic interactions up to force quadrupoles.

Applied the theory to chemically active particles moving by diffusiophoresis.

Abstract

We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on the otherwise rigid particle surfaces. We introduce the general framework for particle rotations and translations by applying the Lorentz reciprocal theorem for a collection of mobile particles with arbitrary surface slip. We then develop an approximate theory applicable to widely separated spheres, including hydrodynamic interactions up to the level of force quadrupoles. We apply our theory to a general example involving a prescribed slip velocity, and a specific case concerning the autonomous motion of chemically active particles moving by diffusiophoresis due to self-generated chemical gradients.