Mass Transfer at Topologically Singular Points

We study the convective deposition of mass onto the leading edge of a substrate, a problem analogous to the transport of momentum onto the leading edge of an airfoil. Mass deposition at the leading edge region has a significant influence on the morphology of the deposit, at a region many times ignored in classical electrodeposition morphological stability analysis. The deposition leading edge region spatially precedes the Leveque-type concentration boundary layer downstream, and encompasses a topological transition between an inert wall and a reactive electrode.



We consider two representative leading edge transition geometries: a flat transition between an inert wall and an active electrode; and step transition between the inert wall and the electrode, representing a corner leading edge geometry.

In both geometries, the rate of mass deposition is inversely proportional to the length scale of the leading edge region, controlled by the Peclet number and the inert wall to reactive electrode topological transition length. Larger Peclet numbers and shorter transition lengths demonstrate less morphological stability. The ion flux obtains a local maximum at the leading edge of the electrode and decays in magnitude further downstream to match the Leveque concentration boundary layer.