Microhydrodynamics of an autophoretic particle

We study the autophoretic motion of an active particle interacting chemically and hydrodynamically with its thermally fluctuating environment. For a spherical active particle in an unbounded domain, we have shown that the boundary integral formulation of Stokes equation can be solved exactly in a basis of tensor spherical harmonics [1]. Here, by simultaneously solving the boundary integral equations of Laplace and Stokes, we extend this to the full chemo-hydrodynamics of an autophoretic swimmer. In an unbounded domain, we again find an exact solution. While in more complex environments the rigid body motion of a passive particle in a fluctuating fluid can be defined in terms of mobilities alone, activity gives rise to extra contributions from so-called propulsion tensors. Using an iterative method, we can obtain these tensors to arbitrary accuracy numerically. To leading order, we provide ready solutions for various experimentally relevant settings. Similarly, we obtain analytical expressions for an autophoretic particle’s elastance and linear response to a background concentration field. We then apply this to the dynamics of a bottom-heavy Brownian Janus swimmer near a plane interface characterised by an arbitrary ratio of viscosities and diffusivities. The resulting dynamical system, containing both the chemical and fluctuating hydrodynamic interactions between the particle and the interface, is explored in numerical simulations.



[1] Turk G, Singh R and Adhikari R. Phys Rev E 106. 014601 (2022)