  We theoretically and numerically investigate the instabilities driven by
diffusiophoretic flow, caused by a solutal concentration gradient along a
reacting surface. The important control parameter is the Peclet number Pe,
which quantifies the ratio of the solutal advection rate to the diffusion rate.
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
8pi, mass transport by convection overtakes that by diffusion, and a
symmetry-breaking mode arises, which is consistent with numerical results. For
even larger Pe, non-linear terms become important. For Pe larger than 16pi,
multiple concentration plumes are emitted from the catalytic plane, which
eventually merges into a single larger one. When Pe is even larger, there are
continuous emissions and merging events of the concentration plumes. This
newly-found flow state reflects the non-linear saturation of the system. The
critical Peclet number for the transition to this state depends on Schmidt
number Sc. 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
chaotic motion of the phoretic particle. Our results thus help to understand
the experimentally observed chaotic motion of catalytic particles in the high
Pe regime.
