Abstract.
In this paper we propose a phase-field model for analyzing the influence of evaporation on Marangoni convection in liquid-vapor systems. The theoretical description is based on the Navier-Stokes equation with extra terms responsible for describing the Marangoni effect, the heat equation with a supplementary term responsible for describing evaporation phenomena, and the continuity equation. We report on 2D simulations for both Marangoni instabilities in linear approximation and we compare the results with the literature.
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References
J.S. Langer, in Directions in Condensed Matter, edited by G. Grinstein, G. Mazenko (World Scinetific, Singapore, 1986), p. 165
D.M. Anderson, G.B. McFadden, A.A. Wheeler, Annu. Rev. Fluid Mech. 30, 139 (1998)
D.M. Anderson, G.B. McFadden, A.A. Wheeler, Physica D 135, 175 (2000)
B. Nestler, A.A. Wheeler, L. Ratke, C. Stöcker, Physics D 141, 133 (2000)
L. Ratke, Metallurgical and Material Transactions A 34, 449 (2003)
R.J. Braun, B.T. Murray, J. Cryst. Growth 174, 41 (1997)
X. Tong, C. Beckermann, A. Karma, Q. Li, Phys. Rev. E 63, 061601 (2001)
L. Gránásy, T. Pusztai, J.A. Warren, J.F. Douglas, T. Börzsönyi, V. Ferreiro, Nature Materials 2, 82 (2003)
A. Karma, D.A. Kessler, H. Levine, Phys. Rev. Lett. 87, 045501 (2001)
R. Borcia, M. Bestehorn, Phys. Rev. E 67, 066307 (2003)
R. Borcia, M. Bestehorn, in Proceedings of the Fifth General Conference of the Balkan Physical Union BPU-5, Vrnjačka Banja, Serbia and Montenegro, August 25-29, 2003, edited by S. Jokić, I. Milošević, A. Balaž, Z. Nikolić, p. 1219
R. Borcia, D. Merkt, M. Bestehorn, Int. J. Bifurcat. Chaos 14, 4105 (2004)
L.M. Pismen, Y. Pomeau, Phys. Rev. E 62, 2480 (2000)
D. Jasnow, J. Viñals, Phys. Fluids 8, 660 (1996)
J.S. Rowlinson, B. Widom, Molecular Theory of Capillarity (Clarendon Press, Oxford, 1982) p. 56
P. Colinet, J.C. Legros, M.G. Velarde, Nonlinear Dynamics of Surface-Tension-Driven Instabilities (Wiley-V. C. H., Berlin, 2001)
C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 1 (John Wiley, New York, 1988), p. 201
J.P. Burelbach, S.G. Bankoff, S.H. Davis, J. Fluid Mech. 195, 463 (1998)
A. Engel, J.B. Swift, Phys. Rev. E 62, 6540 (2000)
M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)
D. Merkt, M. Bestehorn, Physica D 185, 196 (2003)
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Borcia, R., Bestehorn, M. Phase-field simulations for evaporation with convection in liquid-vapor systems. Eur. Phys. J. B 44, 101–108 (2005). https://doi.org/10.1140/epjb/e2005-00104-9
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DOI: https://doi.org/10.1140/epjb/e2005-00104-9