PyStokes: phoresis and Stokesian hydrodynamics in Python

Abstract

We present a modular Python library for computing many-body hydrodynamic and phoretic interactions between spherical active particles in suspension, when these are given by solutions of the Stokes and Laplace equations. Underpinning the library is a grid-free methodology that combines dimensionality reduction, spectral expansion, and Ritz-Galerkin discretization, thereby reducing the computation to the solution of a linear system. The system can be solved analytically as a series expansion or numerically at a cost quadratic in the number of particles. Suspension-scale quantities like fluid flow, entropy production, and rheological response are obtained at a small additional cost. The library is agnostic to boundary conditions and includes, amongst others, confinement by plane walls or liquid-liquid interfaces. The use of the library is demonstrated with six fully coded examples simulating active phenomena of current experimental interest.