Surrounded by a spherically symmetric solute cloud, chemically active homogeneous spheres do not undergo conventional autophoresis when suspended in an unbounded liquid domain. When exposed to external flows, solute advection deforms that cloud, resulting in a generally asymmetric distribution of diffusio-osmotic slip which, in turn, modifies particle motion. Inspired by classical forced-convection analyses [Acrivos and Taylor, Phys. Fluids 5, 387 (1962); Frankel and Acrivos, Phys. Fluids 11, 1913 (1968)] we illustrate this phoretic phenomenon using two prototypic configurations, one where the particle sediments under a uniform force field and one where it is subject to a simple shear flow. In addition to the Péclet number $\mathrm{Pe}$ associated with the imposed flow, the governing nonlinear problem also depends upon $\alpha$, the intrinsic Péclet number associated with the chemical activity of the particle. As in the forced-convection problems, the small-Péclet-number limit is nonuniform, breaking down at large distances away from the particle. Calculation of the leading-order autophoretic effects thus requires use of matched asymptotic expansions, the outer region being at distances that scale inversely with $\mathrm{Pe}$ and ${\mathrm{Pe}}^{1/2}$ in the respective sedimentation and shear problems. In the sedimentation problem we find an effective drag reduction of fractional amount $\alpha /8$; in the shear problem we find that the magnitude of the stresslet is decreased by a fractional amount $\alpha /4$. For a dilute particle suspension the latter result is manifested by a reduction of the effective viscosity.

• Received 12 December 2016

DOI:https://doi.org/10.1103/PhysRevFluids.2.012201