Dynamics of a self-diffusiophoretic particle in shear flow

Colloidal particles can achieve autonomous motion by a number of physicochemical mechanisms. For instance, if a spherical particle acts as a catalyst with an asymmetric surface reactivity, a molecular solute concentration gradient will develop in the surrounding fluid that can propel the particle via self-diffusiophoresis. Theoretical analyses of self-diffusiophoresis have mostly been considered in quiescent fluid, where the solute concentration is usually assumed to evolve solely via diffusion. In practical applications, however, self-propelled colloidal particles can be expected to reside in flowing fluids. Here, we examine the role of ambient flow on self-diffusiophoresis by quantifying the dynamics of a model Janus particle in a simple shear flow. The imposed flow can distort the self-generated solute concentration gradient. The extent of this distortion is quantified by a Peclet number, Pe, associated with the shear flow. Utilizing matched asymptotic analysis, we determine the concentration gradient surrounding a Janus particle in shear flow at a small, but finite, Peclet number and the resulting particle motion. For example, when the symmetry axis of the particle is aligned with the imposed flow, the Janus particle experiences an O(Pe) cross-streamline drift and an O(Pe(3/2)) reduction in translational velocity along the flow direction. We then analyze the in-plane trajectory of the Janus particle in shear. We find that the particle performs elliptical orbits around its initial position in the flow, which decrease in size with increasing Pe.