Saffman-Taylor fingers with kinetic undercooling

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Bennett P J GardinerTimothy J Moroney

Abstract

The mathematical model of a steadily propagating Saffman-Taylor finger in a Hele-Shaw channel has applications to two-dimensional interacting streamer discharges which are aligned in a periodic array. In the streamer context, the relevant regularization on the interface is not provided by surface tension but instead has been postulated to involve a mechanism equivalent to kinetic undercooling, which acts to penalize high velocities and prevent blow-up of the unregularized solution. Previous asymptotic results for the Hele-Shaw finger problem with kinetic undercooling suggest that for a given value of the kinetic undercooling parameter, there is a discrete set of possible finger shapes, each analytic at the nose and occupying a different fraction of the channel width. In the limit in which the kinetic undercooling parameter vanishes, the fraction for each family approaches 1/2, suggesting that this "selection" of 1/2 by kinetic undercooling is qualitatively similar to the well-known analog with surface tension. We treat the numerical problem of computing these Saffman-Taylor fingers with kinetic undercooling, which turns out to be more subtle than the analog with surface tension, since kinetic undercooling permits finger shapes ...Continue Reading

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Citations

Mar 22, 2016·Proceedings. Mathematical, Physical, and Engineering Sciences·Michael C Dallaston, Scott W McCue
Nov 14, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pedro H A AnjosJosé A Miranda
Jun 8, 2017·Proceedings. Mathematical, Physical, and Engineering Sciences·Christopher C GreenScott W McCue

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