Self-Diffusiophoresis and Symmetry-Breaking of a Janus Dimer: Analytic Solution

Abstract

A self-diffusiophoretic problem is considered for a chemically active dimer consisting of two equal touching spherical colloids that are exposed to different fixed-flux and fixed-rate surface reactions. A new analytic solution for the autophoretic mobility of such a catalytic Janus dimer is presented in the limit of a small Péclet number and linearization of the resulting Robin-type boundary value problem for the harmonic solute concentration. Explicit solutions in terms of the physical parameters are first obtained for the uncoupled electrostatic and hydrodynamic problems. The dimer mobility is then found by employing the reciprocal theorem depending on the surface slip velocity and on the normal component of the shear stress acting on the inert dimer. Special attention is given to the limiting case of a Janus dimer composed of an inert sphere and a chemically active sphere where the fixed-rate reaction (Damköhler number) is infinitely large. Examples are given, comparing the numerical and approximate analytic solutions of the newly developed theory. Singular points arising in the model are discussed for a dimer with a fixed-rate reaction, and the flow field around the dimer is also analysed. The new developed theory introduces a fast way to compute the mobility of a freely suspended dimer and the induced flow field around it, and thus can also serve as a sub grid scale model for a multi-scale flow simulation.