A scalable method to model large suspensions of colloidal phoretic particles with arbitrary shapes

TL;DR

This paper introduces a scalable computational framework for simulating large suspensions of arbitrarily shaped phoretic particles, capturing chemical and hydrodynamic interactions efficiently and accurately, enabling exploration of new physical phenomena.

Contribution

The authors develop a versatile, efficient boundary element-based method that models interactions in large suspensions of complex-shaped phoretic particles, including thermal fluctuations.

Findings

Enables large-scale simulations of suspensions with arbitrary particle shapes.

Captures chemical and hydrodynamic interactions with reduced computational cost.

Facilitates exploration of previously inaccessible physical phenomena.

Abstract

Phoretic colloids self-propel thanks to surface flows generated in response to surface gradients (thermal, electrical, or chemical), that are self-induced and/or generated by other particles. Here we present a scalable and versatile framework to model chemical and hydrodynamic interactions in large suspensions of arbitrarily shaped phoretic particles, accounting for thermal fluctuations at all Damkholer numbers. Our approach, inspired by the Boundary Element Method (BEM), employs second-layer formulations, regularised kernels and a grid optimisation strategy to solve the coupled Laplace-Stokes equations with reasonable accuracy at a fraction of the computational cost associated with BEM. As demonstrated by our large-scale simulations, the capabilities of our method enable the exploration of new physical phenomena that, to our knowledge, have not been previously addressed by numerical simulations.