Instabilities driven by diffusiophoretic flow on catalytic surfaces

Abstract

We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameters are the Péclet number, which quantifies the ratio of the solutal advection rate to the diffusion rate, and the Schmidt number, which is the ratio of viscosity and diffusivity. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for larger than mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger, nonlinear terms become important. For 16{\rm \pi}$]]>, multiple concentration plumes are emitted from the catalytic plane, which eventually merge into a single larger one. When is even larger (for Schmidt number), there are continuous emissions and merging events of the concentration plumes. The newly found flow states have different flow structures for different: for, we observe the chaotic emission of plumes, but the fluctuations of concentration are only present in the region near the catalytic plane. In contrast, for