Jiang, Yunshan; McDonald, NR; (2022) Dissolution of plane surfaces by sources in potential flow. Physica D: Nonlinear Phenomena , 442 , Article 133549. 10.1016/j.physd.2022.133549.

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Abstract

The two-dimensional free boundary problem for a surface dissolving in potential flow owing to concentrated sources of dissolving agent c is formulated and solved. The surface boundary evolves quasi-steadily, and the resulting steady advection–diffusion equation for c, and Laplace’s equation for the velocity potential form a coupled pair of conformally invariant PDEs. The dynamics of the coupled fluid flow and evolving surface depends on the Péclet number: Pe = UL/D, where U and L are typical velocity and lengthscales respectively, and D is the diffusivity of c. The conformally invariant property is exploited in finding an equation of the Polubarinova–Galin class for the conformal map from the unit ζ -disk to the evolving domain in physical space. The equation is solved numerically and the timeevolution of the dissolving surface determined. For a single concentrated source with flow initially parallel to a flat surface, a Pe-dependent scallop-like surface shape typically develops. The problem involving a periodic array of concentrated sources aligned parallel to an initially flat surface is also solved.

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