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

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.