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 are also considered, which raise 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. 
Martin Z. Bazant (Mathematics, MIT)