Abstract
We analyze the problem of phase coexistence, surface tension and the interface patterns between liquid and vapour for the nonlocal free energy functional derived by Lebowitz, Mazel, and Presutti from a system of particles interacting through Kac potentials in the continuum. We study the sharp interface limit in d dimensions and characterize the shape of the interface profiles in the temperature region where a monotonicity property is valid. We further extend our analysis beyond this domain by performing numerical simulations.
Similar content being viewed by others
REFERENCES
G. Alberti and G. Bellettini, A non-local anisotropic model for phase transition: Asymptotic behavior of rescaled energies, Eur. J. Appl. Math. 9:261–284 (1998).
G. Alberti and G. Bellettini, A non-local anisotropic model for phase transition: The optimal profile problem, Math. Ann. 310:527–560 (1998).
G. Alberti, G. Bellettini, M. Cassandro, and E. Presutti, Surface tension in Ising systems with Kac potentials, J. Stat. Phys. 82:743–796 (1996).
G. Bellettini, M. Cassandro, and E. Presutti, Constrained minima of nonlocal free energy functionals, J. Stat. Phys. 84:1337–1349 (1996).
O. Benois, T. Bodineau, P. Buttà, and E. Presutti, On the validity of the van der Waals theory of surface tension, Markov Process. Related fields 3:175–198 (1997).
T. Bodineau, The Wulff construction in three and more dimensions, Comm. Math. Phys. 207:197–229 (1999).
T. Bodineau, D. Ioffe, and Y. Velenik, Rigorous probabilistic analysis of equilibrium crystal shapes, J. Math. Phys. 41:1033–1098 (2000).
R. Cerf, Large deviations for three dimensional supercritical percolation, Astérisque 267 (2000).
R. Cerf and A. Pisztora, On the Wulff crystal in the Ising model, Ann. Probab. 28: 947–1017 (2000).
R. Cerf and A. Pisztora, Phase coexistence in Ising, Potts and percolation models, Ann. Inst. H. Poincaré Probab. Statist. 37:643–724 (2001).
G. Dal Maso, An Introduction to Γ Convergence (Birkhäuser, 1993).
A. De Masi, E. Orlandi, E. Presutti, and L. Triolo, Uniqueness of the instanton profile and global stability in non-local evolution equations, Rend. Mat. Appl. (7) 14:693–723 (1994).
A. De Masi, T. Gobron, and E. Presutti, Travelling fronts in non-local evolution equations, Arch. Rational Mech. 132:143–205 (1995).
A. De Masi, E. Olivieri, and E. Presutti, Spectral properties of integral operators in problems of interface dynamics and metastability, Markov Process. Related Fields 4: 27–112 (1998).
R. L. Dobrushin, R. Kotecký, and S. Shlosman, Wulff Construction: A Global Shape from Local Interaction, AMS Translations Series, Vol. 104 (AMS, Providence, R.I., 1992).
L. C. Evans and R. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Math. (CRC Press, Boca Raton, 1992).
V. Gayrard, E. Presutti, and L. Triolo, Density oscillations at the interface between liquid and vapor, J. Stat. Phys. 108:863–884 (2002).
D. Ioffe, Large deviations for the 2D Ising model: A lower bound without cluster expansions, J. Stat. Phys. 74:411–432 (1994).
D. Ioffe, Exact deviation bounds up to Tc for the Ising model in two dimensions, Probab. Theory Related Fields 102:313–330 (1995).
D. Ioffe and R. Schonmann, Dobrushin-Kotecký-Shlosman theory up to the critical temperature, Comm. Math. Phys. 199:117–167 (1998).
J. L. Lebowitz, A. Mazel, and E. Presutti, Liquid-vapor phase transitions for systems with finite-range interactions, J. Stat. Phys. 94:955–1025 (1999).
A. Messager, S. Miracle-Sole, and J. Ruiz, Convexity properties of the surface tension and equilibrium crystals, J. Stat. Phys. 67:449–470 (1992).
C. E. Pfister, Large deviations and phase separation in the two dimensional Ising model, Helv. Phys. Acta 64:953–1054 (1991).
C. E. Pfister and Y. Velenik, Large deviations and continuum limit in the 2D Ising model, Probab. Theory Related Fields 109:435–506 (1997).
E. Presutti, From statistical mechanics towards continuum mechanics, in preparation.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Masi, A., Gobron, T. Liquid-Vapor Interfaces and Surface Tension in a Mesoscopic Model of Fluid with Nonlocal Interactions. Journal of Statistical Physics 115, 643–679 (2004). https://doi.org/10.1023/B:JOSS.0000019834.85465.a2
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000019834.85465.a2