Interfacial dynamics in transport-limited dissolution

Various model problems of “transport-limited dissolution” in two dimensions are analyzed using time-dependent conformal maps. For diffusion-limited dissolution (reverse Laplacian growth), several exact solutions are discussed for the smoothing of corrugated surfaces, including the continuous analogs of “internal diffusion-limited aggregation” and “diffusion-limited erosion.” A class of non-Laplacian, transport-limited dissolution processes is also considered, which raises the general question of when and where a finite solid will disappear. In a case of dissolution by advection-diffusion, a tilted ellipse maintains its shape during collapse, as its center of mass drifts obliquely away from the background fluid flow, but other initial shapes have more complicated dynamics.