Hydrochemical interactions of phoretic particles: a regularized multipole framework

Chemically-active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and gradients that trajectories other particles. As a result, dynamics reactive suspensions is fundamentally governed by hydro-chemical interactions. A full solution detailed problem with many particles challenging computationally expensive. Most current methods rely on Green's functions Laplace Stokes operators approximate particle signatures far-field, which only valid very dilute limit simple geometries. To overcome these limitations, we propose regularized mutipole framework, directly inspired Force Coupling Method (FCM), model phoretic suspensions. Our approach, called Diffusio-phoretic FCM (DFCM), relies grid-based volume averages field compute surface moments. These moments define multipoles diffusion (Laplace) provide swimming forcing equations. Unlike far-field models based singularity superposition, DFCM accounts for mutually-induced dipoles. The accuracy method evaluated against exact accurate numerical solutions few canonical cases. We also quantify its improvements over approximations wide range inter-particle distances. resulting framework can readily be implemented into efficient CFD solvers, allowing large scale simulations semi-dilute diffusio-phoretic