  Lithium metal penetrations through the liquid-electrolyte-wetted porous
separator and solid electrolytes are a major safety concern of next-generation
rechargeable metal batteries. The penetrations were frequently discovered to
occur through only a few isolated channels, as revealed by "black spots" on
both sides of the separator or electrolyte, which manifest a highly localized
ionic flux or current density. Predictions of the penetration time have been
infeasible due to the hidden and unclear dynamics in these penetration
channels. Here, using the glass capillary cells, we investigate for the first
time the unexpectedly sensitive influence of channel geometry on the
concentration polarization and dendrite initiation processes. The
characteristic time for the complete depletion of salt concentration on the
surface of the advancing electrode, i.e. Sand's time, exhibits a nonlinear
dependence on the curvature of the channel walls along the axial direction.
While a positively deviated Sand's time scaling exponent can be used to infer a
converging penetration area through the electrolyte, a negatively deviated
scaling exponent suggests that diffusion limitation can be avoided in expanding
channels, such that the fast-advancing tip-growing dendrites will not be
initiated. The safety design of rechargeable metal batteries will benefit from
considering the true local current densities and the conduction structures.
