Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 70, Issue 9, Pages 1810-1831Publisher
WILEY
DOI: 10.1002/cpa.21689
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- FSU First-Year Assistant Professor (FYAP) award [036209, 551]
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The classical Stefan problem involves the motion of boundaries during phase transition, but this process can be greatly complicated by the presence of a fluid flow. Here we consider a body undergoing material loss due to either dissolution (from molecular diffusion), melting (from thermodynamic phase change), or erosion (from fluid-mechanical stresses) in a fast-flowing fluid. In each case, the task of finding the shape formed by the shrinking body can be posed as a singular Riemann-Hilbert problem. A class of exact solutions captures the rounded surfaces formed during dissolution/melting, as well as the angular features formed during erosion, thus unifying these different physical processes under a common framework. This study, which merges boundary-layer theory, separated-flow theory, and Riemann-Hilbert analysis, represents a rare instance of an exactly solvable model for high-speed fluid flows with free boundaries. (C) 2017 Wiley Periodicals, Inc.
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