Asymmetric collapse by dissolution or melting in a uniform flow.

ABSTRACT: An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-analytic function is examined for three different test case

SUBMITTER: Rycroft CH 

PROVIDER: S-EPMC4786035 | biostudies-literature | 2016 Jan

REPOSITORIES: biostudies-literature