Abstract
The shape of a meniscus of one phase between two others is studied in two dimensions using random walk models. An interface with a meniscus is approximated by two random walks forming microscopic droplets of the intruding phase before and after a macroscopic lens. Within this class of models, we establish a Wulff construction and prove the Herring relations between contact angles. We give explicit formulas for the contact angles as functions of temperature, both at low temperatures and near the wetting transition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. De Coninck, Ph. de Gottal, and F. Menu,J. Stat. Phys. 56:23 (1989).
W. Selke and W. Pesch,Z. Phys. B 47:335 (1982).
M. E. Fisher,J. Stat. Phys. 34:667 (1984).
D. B. Abraham and P. M. Duxbury,J. Phys. A 19:385 (1986).
F. Dunlop and J. Ruiz,Ann. Inst. H. Poincaré 48:229 (1988).
C. Herring, inStructure and Properties of Solid Surfaces, R. Gomer and C. S. Smith, eds. (University of Chicago Press, Chicago, Illinois, 1953).
J. De Coninck, F. Dunlop, and V. Rivasseau,Commun. Math. Phys. 121:401 (1989).
J. De Coninck and F. Dunlop,J. Stat. Phys. 47:827 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
De Coninck, J., Dunlop, F. & Menu, F. Exact results for a meniscus in a three-phase system within an SOS-type approximation. J Stat Phys 61, 1121–1139 (1990). https://doi.org/10.1007/BF01014368
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01014368