Two-dimensional solidification and melting in potential flows

LINDA M. CUMMINGS; YURI E. HOHLOV; SAM D. HOWISON; KONSTANTIN KORNEV

doi:10.1017/S0022112098003188

Abstract

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The problem of solidification or melting under the action of a forced hydrodynamic flow is considered. In the appropriate parameter régime, the problem admits a formulation in terms of analytic functions. It is shown that a crystal with a parabolic tip propagates without change of shape at a steady velocity. Some novel explicit solutions are presented.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Cummings, L.J. and Kornev, K. 1999. Evolution of flat crystallisation front in forced hydrodynamic flow – some explicit solutions. Physica D: Nonlinear Phenomena, Vol. 127, Issue. 1-2, p. 33.

Yortsos, Yanis C. and Stubos, Athanassios K. 2001. Phase change in porous media. Current Opinion in Colloid & Interface Science, Vol. 6, Issue. 3, p. 208.

Hwang, W. and Redner, S. 2001. Dissolution in a field. Physical Review E, Vol. 64, Issue. 4,

Vasil’ev, Alexander 2001. Univalent Functions in the Dynamics of Viscous Flows. Computational Methods and Function Theory, Vol. 1, Issue. 2, p. 311.

Vasil'ev, Alexander 2003. Univalent Functions in Two-Dimensional Free Boundary Problems. Acta Applicandae Mathematica, Vol. 79, Issue. 3, p. 249.

Bazant, Martin Z. Choi, Jaehyuk and Davidovitch, Benny 2003. Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena. Physical Review Letters, Vol. 91, Issue. 4,

Bazant, Martin Z. 2004. Conformal mapping of some non-harmonic functions in transport theory. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 460, Issue. 2045, p. 1433.

Medvedev, Dmitry and Kassner, Klaus 2005. Lattice Boltzmann scheme for crystal growth in external flows. Physical Review E, Vol. 72, Issue. 5,

Bazant, Martin Z. and Crowdy, Darren 2005. Handbook of Materials Modeling. p. 1417.

Taponecco, F. 2005. Using potential theory and dense texture-based visualization for external motion applications. Vol. 2, Issue. , p. 426.

Alimov, M.M. 2006. A general solution of the Hele–Shaw problem for flows in a channel. Journal of Applied Mathematics and Mechanics, Vol. 70, Issue. 3, p. 346.

Rogosin, Sergei and Vaitekhovich, Tatsyana 2007. Hele-Shaw Model for Melting/Freezing with Two Dendrits. Materials Science Forum, Vol. 553, Issue. , p. 143.

McDONALD, N. R. 2011. Generalised Hele-Shaw flow: A Schwarz function approach. European Journal of Applied Mathematics, Vol. 22, Issue. 6, p. 517.

Braff, William A. Buie, Cullen R. and Bazant, Martin Z. 2013. Boundary Layer Analysis of Membraneless Electrochemical Cells. Journal of The Electrochemical Society, Vol. 160, Issue. 11, p. A2056.

Mohaghegh, Fazlolah Mousel, John A. and Kumar, Uday 2013. Effect of Interface Thickness on Smoothed Profile Modeling of Flow Over a Stationary Sphere in 1<Re<300.

von Kurnatowski, Martin Grillenbeck, Thomas and Kassner, Klaus 2013. Selection theory of free dendritic growth in a potential flow. Physical Review E, Vol. 87, Issue. 4,

Alimov, M. M. 2013. Evolution of the boundary of a viscous fluid occupying a half-space type domain in a Hele-Shaw slot. Fluid Dynamics, Vol. 48, Issue. 6, p. 800.

Kondratiuk, Paweł and Szymczak, Piotr 2015. Steadily Translating Parabolic Dissolution Fingers. SIAM Journal on Applied Mathematics, Vol. 75, Issue. 5, p. 2193.

Rycroft, Chris H. and Bazant, Martin Z. 2016. Asymmetric collapse by dissolution or melting in a uniform flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 472, Issue. 2185, p. 20150531.

Alimov, M. M. 2016. Unsteady motion of a bubble in a Hele-Shaw cell. Fluid Dynamics, Vol. 51, Issue. 2, p. 253.

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Two-dimensional solidification and melting in potential flows

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Two-dimensional solidification and melting in potential flows

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