Convective mitigation of dendrite growth

The growth of metallic dendrites during the electrodeposition and solidification of metal films is a formidable scientific and industrial problem. It is mostly known for hindering the use of high energy-density solid metal electrodes in rechargeable batteries. Over a century ago, it was experimentally shown that metallic dendrites may be mitigated under the action of mass advection in the liquid adjacent to a solid metal surface which grows out of a melt. Similar observations were reported for electrochemical deposition four decades ago and very recently. However, these insights proved inconclusive; dendrites appear to grow to different extents in many advection-based deposition systems, such as flow batteries, augmented finger batteries, and convective solidification. Here, we scrutinize the contribution of high Peclet metal ion convection in a dilute solution to the growth rate of metal dendrites, emphasizing convective effects near the metal surface. We employ an ideal model system for the isothermal flow of an ion solution along a duct where ions desorb from one solid surface of the duct, transport through the solution, and adsorb (undergo deposition) onto the other side. To account for the limit where metal-ion transport through the solution is the bottleneck for the rate of metal deposition (contributions to dendrite mitigation from near equilibrium surface phenomena are assumed small), we employ the perspective of kinetic stability to elucidate the contribution of ion convection to the mitigation of dendrite growth. We show that while the convection of metal ions appears to enhance dendrite growth --- an intuitive insight --- it also enhances the growth of the bulk solid metal on which the dendrites grow --- a well-known phenomenon. We demonstrate that for a fixed growth rate of the bulk solid metal, the rate of growth of dendrites is smaller in the presence of convective flow compared to the case where ion transport is solely by diffusion. The difference in the relative rate of growth in the presence and absence of convective flow may span orders of magnitude, which explains the absence of significant dendrites in corresponding experiments.