Abstract
Basic assumptions of the capillary wave theory of fluid interfaces are examined critically as a function of space dimensionalityd. When the predictions of capillary wave theory are compared with those of the nonclassical Maxwell-van der Waals theory, agreement is found ind=3 and 4, but strong disagreement occurs ind=2. It is shown that the total effective mass density obtained from the Hamiltonian describing the collective capillary wave excitations has a logarithmic divergence ind=2. This result suggests the possibility of anomalous behavior for fluid interfaces ind=2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F. P. Buff, R. A. Lovett, and F. H. Stillinger,Phys. Rev. Lett. 15:621 (1965).
M. Robert, in Proceedings of the 13th Annual Conference on Statistical Physics, Oaxtepec (Mexico), January 3–6, 1984,Kinam 6A:19 (1984);Phys. Rev. Lett. 54:444 (1985).
J. C. Maxwell,Scientific Papers, Vol. 2 (Dover, New York, 1965), p. 561.
J. D. van der Waals,Z. Phys. Chem. 13:657 (1894).
F. H. Stillinger and F. P. Buff,J. Chem. Phys. 37:1 (1962); J. L. Lebowitz and J. K. Percus,J. Math. Phys. 4:116 (1963).
H. W. Diehl, D. M. Kroll, and H. Wagner,Z. Phys. B36:329 (1980).
R. A. Lovett, Ph.D. thesis, University of Rochester (1965), p. 78.
M. Robert,Phys. Rev. A 30:2785 (1984).
F. P. Buff, 38th National Colloid Symposium, Austin (Texas), July 11–13, 1964, Proceedings of the International Conference on Colloids and Surfaces; F. P. Buff, R. A. Lovett, and F. H. Stillinger,Phys. Rev. Lett. 15:621 (1965), footnotes 5 and 7; B. Widom,J. Chem. Phys. 43:3892 (1965).
P. W. Anderson and D. J. Thouless,Phys. Lett. 1:155 (1962).
J. D. van der Waals,Z. Phys. Chem. 13:657 (1894); L. S. Ornstein and F. Zernike,Proc. Akad. Sci. (Amsterdam) 17:793 (1914).
L. D. Landau and E. M. Lifshitz,Fluid Mechanics (Addison-Wesley, Reading, Massachusetts, 1959).
R. A. Lovett, Ph.D. thesis, University of Rochester (1965), p. 125.
H. Minkowski, Kapillarität, inEnc. der Math. Wiss. (A. Sommerfeld, ed.), Vol. 5, Part 1 (Teubner Verlag, Leipzig, 1906), pp. 589.
J. Lighthill,Waves in Fluids (Cambridge University Press, Cambridge, 1978), Chap. 3, Section 3.2.
J. Lighthill,Waves in Fluids (Cambridge University Press, Cambridge, 1978), p. 213.
D. B. Abraham and P. Reed,Phys. Rev. Lett. 33:377 (1974);Commun. Math. Phys. 49:35 (1976); see also D. B. Abraham and M. Issigoni,J. Phys. A12:L125 (1979).
J. Bricmont, J. L. Lebowitz, and C.-E. Pfister,J. Stat. Phys. 26:313 (1981).
F. P. Buff, inHandbuch der Physik, Vol. X, S. Flugge, ed. (Springer, Berlin, 1960), p. 295.
R. A. Lovett, Ph.D. thesis, University of Rochester (1965), Appendix VI, pp. 167–177.
F. P. Buff and R. A. Lovett, inSimple Dense Fluids, H. L. Frisch and Z. W. Salsburg, eds. (Academic Press, New York (1968); D. G. Triezenberg and R. Zwanzig,Phys. Rev. Lett. 28:1183 (1972); R. A. Lovett, P. W. DeHaven, J. J. Vieceli, and F. P. Buff,J. Chem. Phys. 58:1880 (1973).
D. B. Abraham and A. Martin-Löf,Commun. Math. Phys. 32:245 (1973).
B. Kaufman and L. Onsager (1948), unpublished; C. N. Yang,Phys. Rev. 85:808 (1952); G. Benettin, G. Gallavotti, G. Jona-Lasinio, and A. L. Stella,Commun. Math. Phys. 30:45 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Buff, F.P., Robert, M.A. Some considerations of fluid interfaces in two dimensions. J Stat Phys 41, 1037–1044 (1985). https://doi.org/10.1007/BF01010014
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01010014