Instabilities driven by diffusiophoretic flow on catalytic surfaces

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 Peclet number Pe, which quantifies the ratio of the solutal advection rate to the diffusion rate, and the Schmidt number Sc, 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 Pe larger than 8p mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger Pe, nonlinear terms become important. For Pe > 16 pi, multiple concentration plumes are emitted from the catalytic plane, which eventually merge into a single larger one. When Pe is even larger (Pe greater than or similar to 603 for Schmidt number Sc = 1), there are continuous emissions and merging events of the concentration plumes. The newly found flow states have different flow structures for different Sc: for Sc >= 1, 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 Sc < 1, chaotic flow motion occurs also in the bulk. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Peclet number again find continuous plume emission and plume merging, now leading to a chaotic motion of the phoretic particle. Our results thus help us to understand the experimentally observed chaotic motion of catalytic particles in the high Pe regime.