Impact of interaction potential lengthscale and surface heterogeneity on phoretic and autophoretic mobilities: Moving beyond the slip velocity approach

The motion of phoretic and self-phoretic particles is typically estimated by assuming a slip velocity at the surface. However, this approach is only valid when the lengthscale of the interaction potential is much smaller than the particle size. Further, this approach relies on a lumped phoretic mobility coefficient and overlooks the physics of the phoretic interaction between the particle and the fluid. In this study, we employ reciprocal theorem to derive compact expressions for translational and rotational velocities for a phoretically driven particle without imposing restrictions on interaction lengthscales and surface heterogeneities. Our approach does not rely on the slip velocity approximation and can recover well-known mobility expressions for diffusiophoretic, electrophoretic, and self-phoretic systems in literature. To demonstrate the utility of our results, we study the effect of interaction lengthscale in catalytically coated spherical particles. We analyze the effect of catalytic cap size, surface potential, and activity on particle translation. Our analysis reveals that when compared to slip velocity calculations, translational velocities are significantly smaller due to corrections arising out of finite concentration gradients and interaction lengthscales.