Interfacial dynamics in transport-limited dissolution

TL;DR

This paper analyzes interfacial dynamics in transport-limited dissolution using conformal maps, providing exact solutions for diffusion-limited cases and exploring non-Laplacian processes, revealing complex shape evolution and dissolution conditions.

Contribution

It introduces a conformal map approach to model transport-limited dissolution, including exact solutions and analysis of non-Laplacian processes, advancing understanding of dissolution dynamics.

Findings

Exact solutions for smoothing of corrugated surfaces in diffusion-limited dissolution

Tilted ellipse maintains shape during advection-diffusion dissolution

Complex dynamics observed for non-elliptical initial shapes

Abstract

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.