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Solidification and separation in saline water
1. | Dipartimento di Matematica, Università di Bologna, Piazza di Porta S.Donato 5, 40127 Bologna, Italy |
2. | DICATAM, Università degli studi di Brescia, Via D.Valotti 9, 25133 Brescia |
3. | DIBRIS, Università di Genova, Via Opera Pia 13, 16145 Genova, Italy |
References:
[1] |
V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21.
doi: 10.1016/j.physd.2007.07.009. |
[2] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, Berlin, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[3] |
J. W. Cahn, On spinodal decomposition, Acta Metall., 9 (1961), 795-801. |
[4] |
J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267. |
[5] |
J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal., 88 (1985), 95-133.
doi: 10.1007/BF00250907. |
[6] |
M. Fabrizio, Ice-water and liquid-vapor phase transitions by a Ginzburg-Landau model, J. Math. Phys., 49 (2008), 102902, 13 pp.
doi: 10.1063/1.2992478. |
[7] |
M. Fabrizio, C. Giorgi and A. Morro, A thermodynamic approach to non-isothermal phase-field evolution in continuum physics, Physica D, 214 (2006), 144-156.
doi: 10.1016/j.physd.2006.01.002. |
[8] |
M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, Eur. J. Mech., 30 (2011), 281-287.
doi: 10.1016/j.euromechflu.2010.12.003. |
[9] |
E. Fried and M. E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Physica D, 68 (1993), 326-343.
doi: 10.1016/0167-2789(93)90128-N. |
[10] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[11] |
M. E. Gurtin, D. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Mod. Meth. Appl. Sci., 6 (1996), 815-831.
doi: 10.1142/S0218202596000341. |
[12] |
C. Himawan, R. J. C. Vaessen, H. J. M. Kramer, M. M. Seckler and G. J. Witkamp, Dynamic modeling and simulation of eutectic freeze crystallization, Journal of Crystal Growth, 237-239 (2002), 2257-2263.
doi: 10.1016/S0022-0248(01)02240-0. |
[13] |
B. Kutschan, K. Morawetz and S. Gemming, Modeling the morphogenesis of brine channels in sea ice, Phys. Rev. E, 81 (2010), 036106.
doi: 10.1103/PhysRevE.81.036106. |
[14] |
R. A. Lake and E. L. Lewis, Salt rejection by sea ice during growth, J. Geophys. Research, 75 (1970), 583-597.
doi: 10.1029/JC075i003p00583. |
[15] |
J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, Proc. R. Soc. Lond. A, 454 (1998), 2617-2654.
doi: 10.1098/rspa.1998.0273. |
show all references
References:
[1] |
V. Berti, M. Fabrizio and C. Giorgi, Well-posedness for solid-liquid phase transitions with a fourth-order nonlinearity, Physica D, 236 (2007), 13-21.
doi: 10.1016/j.physd.2007.07.009. |
[2] |
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer, Berlin, 1996.
doi: 10.1007/978-1-4612-4048-8. |
[3] |
J. W. Cahn, On spinodal decomposition, Acta Metall., 9 (1961), 795-801. |
[4] |
J. W. Cahn and J. E. Hilliard, Free energy of a non-uniform system. I. Interfacial free energy, J. Chem. Phys., 28 (1958), 258-267. |
[5] |
J. E. Dunn and J. Serrin, On the thermomechanics of interstitial working, Arch. Rational Mech. Anal., 88 (1985), 95-133.
doi: 10.1007/BF00250907. |
[6] |
M. Fabrizio, Ice-water and liquid-vapor phase transitions by a Ginzburg-Landau model, J. Math. Phys., 49 (2008), 102902, 13 pp.
doi: 10.1063/1.2992478. |
[7] |
M. Fabrizio, C. Giorgi and A. Morro, A thermodynamic approach to non-isothermal phase-field evolution in continuum physics, Physica D, 214 (2006), 144-156.
doi: 10.1016/j.physd.2006.01.002. |
[8] |
M. Fabrizio, C. Giorgi and A. Morro, Phase separation in quasi-incompressible Cahn-Hilliard fluids, Eur. J. Mech., 30 (2011), 281-287.
doi: 10.1016/j.euromechflu.2010.12.003. |
[9] |
E. Fried and M. E. Gurtin, Continuum theory of thermally induced phase transitions based on an order parameter, Physica D, 68 (1993), 326-343.
doi: 10.1016/0167-2789(93)90128-N. |
[10] |
M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D, 92 (1996), 178-192.
doi: 10.1016/0167-2789(95)00173-5. |
[11] |
M. E. Gurtin, D. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Mod. Meth. Appl. Sci., 6 (1996), 815-831.
doi: 10.1142/S0218202596000341. |
[12] |
C. Himawan, R. J. C. Vaessen, H. J. M. Kramer, M. M. Seckler and G. J. Witkamp, Dynamic modeling and simulation of eutectic freeze crystallization, Journal of Crystal Growth, 237-239 (2002), 2257-2263.
doi: 10.1016/S0022-0248(01)02240-0. |
[13] |
B. Kutschan, K. Morawetz and S. Gemming, Modeling the morphogenesis of brine channels in sea ice, Phys. Rev. E, 81 (2010), 036106.
doi: 10.1103/PhysRevE.81.036106. |
[14] |
R. A. Lake and E. L. Lewis, Salt rejection by sea ice during growth, J. Geophys. Research, 75 (1970), 583-597.
doi: 10.1029/JC075i003p00583. |
[15] |
J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn-Hilliard fluids and topological transitions, Proc. R. Soc. Lond. A, 454 (1998), 2617-2654.
doi: 10.1098/rspa.1998.0273. |
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