Interfacial dynamics of dissolving objects in fluid flow

An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow will be presented. By taking advantage of conformal invariance of the model, a numerical method will be introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of several dissolving objects will be shown, all of which show collapse to a single point in finite time. The simulations reveal a surprising connection between the position of the collapse point and the initial Laurent coefficients, which was subsequently derived analytically using residue calculus.