Roughness-induced filling

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 6, 2002, Pages

  Rejmer, K ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ADSORPTION; APPROXIMATION THEORY; FREE ENERGY; FUNCTIONS; HAMILTONIANS; PHASE DIAGRAMS; WETTING;

LANDAU THEORY; LONG RANGE INTERACTIONS; MEAN-FIELD VERSIONS; PLANAR SUBSTRATES;

SURFACE ROUGHNESS;

ARTICLE;

EID: 41349093093     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.061606     Document Type: Article

References (69)

1. P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).
2. D. Sullivan and M. M. Telo da Gama, in Fluid Interfacial Phenomena, edited by C. A. Croxton (Wiley, New York, 1985).
3. S. Dietrich, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebovitz (Academic, London, 1988), Vol. 12, p. 1.
4. M. Schick, in Proceedings of the Liquids at Interfaces, Les Houches, Session XLVIII, edited by J. Chavrolin, J. F. Joanny, and J. Zinn-Justin (Elsevier, New York, 1990), p. 415.
5. R. Evans, in Proceedings of the Liquids at Interfaces, Les Houches, Session XLVIII, (Ref. 4), p. 1.
6. G. Forgacs, R. Lipowsky, and T. M. Nieuwenhuizen, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebovitz (Academic, London, 1991), Vol. 14, p. 136.
7. E. M. Blokhuis and B. Widom, Colloid Interface Sci. 1, 424 (1996).
8. R. Lipowsky and M. E. Fisher, Phys. Rev. B 36, 2126 (1987).
9. H. Nakanishi and M. E. Fisher, Phys. Rev. Lett. 49, 1565 (1982).
10. E. Brezin, B. I. Halperin, and S. Leibler, Phys. Rev. Lett. 50, 1387 (1983).
11. A. J. Jin and M. E. Fisher, Phys. Rev. B 48, 2642 (1993).
12. K. Binder, D. P. Landau, and S. Wansleben, Phys. Rev. B 40, 6971 (1989).
13. K. Binder, D. P. Landau, and A. M. Ferrenberg, Phys. Rev. E 51, 2823 (1995).
14. R. N. Wenzel, J. Phys. Colloid Chem. 53, 11 466 (1949);
15. R. N. WenzelInd. Eng. Chem. 28, 988 (1936).
16. D. Andelman, J. F. Joanny, and M. O. Robbins, Europhys. Lett. 7, 731 (1988);
17. M. O. Robbins, D. Andelman, and J. F. Joanny, Phys. Rev. A 43, 4344 (1991).
18. P. Pfeifer, Y. J. Wu, M. W. Cole, and J. Krim, Phys. Rev. Lett. 62, 1997 (1989);
19. Phys. Rev. Lett.P. Pfeifer, M. W. Cole, and J. Krim, 65, 663 (1990).
20. M. Kardar and J. O. Indekeu, Phys. Rev. Lett. 65, 662 (1990);
21. M. KardarJ. O. IndekeuEurophys. Lett. 12, 161 (1990);
22. H. Li and M. Kardar, Phys. Rev. B 42, 6546 (1990);
23. J. Krim and J. O. Indekeu, Phys. Rev. E 48, 1576 (1993).
24. E. Cheng, M. W. Cole, and A. L. Stella, Europhys. Lett. 8, 537 (1989);
25. E. Cheng, M. W. Cole, and P. Pfeifer, Phys. Rev. B 39, 12 962 (1989).
26. G. Giugliarelli and A. L. Stella, Phys. Scr. T35, 34 (1991);
27. G. GiugliarelliA. L. StellaPhys. Rev. E 53, 5035 (1996);
28. G. GiugliarelliA. L. StellaPhysica A 239, 467 (1997);
29. G. Sartori, A. L. Stella, G. Ggiugliarelli, and M. R. D’Orsogna, Europhys. Lett. 39, 6333 (1997).
30. M. Napiórkowski, W. Koch, and S. Dietrich, Phys. Rev. A 45, 5760 (1992).
31. G. Palasantzas, Phys. Rev. B 48, 14 472 (1993);
32. Phys. Rev. BG. Palasantzas51, 14 612 (1995).
33. J. Z. Tang and J. G. Harris, J. Chem. Phys. 103, 8201 (1995).
34. Y. Pomeau, J. Colloid Interface Sci. 113, 5 (1985).
35. E. H. Hauge, Phys. Rev. A 46, 4994 (1992).
36. A. Marmur, Langmuir 12, 5704 (1996).
37. C. Borgs, J. De Connick, R. Kotecký, and M. Zinque, Phys. Rev. Lett. 74, 2292 (1995);
38. K. Topolski, D. Urban, S. Brandon, and J. DeConnick, Phys. Rev. E 56, 3353 (1997).
39. A. O. Parry, P. S. Swain, and J. A. Fox, J. Phys.: Condens. Matter 8, L659 (1996).
40. P. S. Swain and A. O. Parry, J. Phys. A 30, 4597 (1997).
41. R. R. Netz and D. Andelmann, Phys. Rev. E 55, 687 (1997).
42. K. Rejmer and M. Napiórkowski, Z. Phys. B: Condens. Matter 102, 101 (1997).
43. P. S. Swain and A. O. Parry, Eur. Phys. J. B 4, 459 (1998).
44. S. Dietrich, in New Approaches to Old and New Problems in Liquid State Theory—Inhomogeneities and Phase Separation in Simple, Complex and Quantum Fluids, Vol. 529 of NATO Advanced Study Institute, Series C: Mathematics, edited by C. Caccamo (Kluwer, Dordrecht, 1999), p. 197.
45. K. Rejmer, S. Dietrich, and M. Napiórkowski, Phys. Rev. E 60, 4027 (1999).
46. K. Rejmer and M. Napiórkowski, Phys. Rev. E 62, 588 (2000).
47. C. Rascón and A. O. Parry, J. Phys.: Condens. Matter 12, A369 (2000).
48. C. Rascón, A. O. Parry, and A. Sartori, Phys. Rev. E 59, 5697 (1999);
49. C. Rascón and A. O. Parry, Nature (London) 407, 986 (2000).
50. G. P. Kubalski, M. Napiórkowski, and K. Rejmer, J. Phys.: Condens. Matter 13, 4727 (2001).
51. P. S. Swain and R. Lipowsky, Langmuir 14, 6772 (1998).
52. P. Lenz and R. Lipowsky, Phys. Rev. Lett. 80, 1920 (1998).
53. H. Gau, S. Herminghaus, S. Lenz, and R. Lipowsky, Science 238, 46 (1999).
54. C. Bauer, S. Dietrich, and A. O. Parry, Europhys. Lett. 47, 474 (1999).
55. P. Lenz and R. Lipowsky, Eur. Phys. J. E 1, 249 (2000).
56. A. O. Parry, C. Rascón, and A. J. Wood, Phys. Rev. Lett. 83, 5535 (1999);
57. Phys. Rev. Lett.A. O. ParryC. RascónA. J. Wood85, 345 (2000).
58. A. O. Parry, A. J. Wood, and C. Rascón, J. Phys.: Condens. Matter 12, 7671 (2000).
59. C. Rascón and A. O. Parry, J. Phys. A 112, 5175 (2000).
60. A. O. Parry, E. D. Mcdonald, and C. Rascón, J. Phys.: Condens. Matter 13, 383 (2000).
61. M. J. Wood and A. O. Parry, J. Chem. Phys. 112, 5175 (2000).
62. The expression given in Eq. (3.1), (Formula presented)can be rewritten in an equivalent form (Formula presented)where (Formula presented)(Formula presented) are arbitrary numbers. This transformation does not change (Formula presented) and resembles the gauge transformation in electrodynamics. (Formula presented) (Formula presented) can be chosen in such a (unique) way that the sinus functions do not appear in the expansion (3.1). The linearization breaks this gauge symmetry; it is an additional argument against the linearization procedure.
63. (Formula presented) is an even function of s, as follows from Eq. (4.4). The expression given in Eq. (4.5) has to be an even function as well. It is a simple consequence of the following identity: (Formula presented)
64. Instead of integrating step by step function (Formula presented) we can transform its integral into the Bessel integral (Formula presented)This is a very particular case concerning short-range, purely exponential effective interaction potential. In a general case there is no other way leading to the Hamiltonian (Formula presented) than integrating step by step the potential (Formula presented)
65. N. Shahizadeh, D. Bonn, K. Ragil, D. Brosetta, and J. Meunier, Phys. Rev. Lett. 80, 3992 (1998);
66. J. O. Indekeu, K. Ragil, D. Bonn, D. Brosetta, and J. Meunier, J. Stat. Phys. 95, 109 (1995);
67. D. Ross, D. Bonn, and J. Meunier, Nature (London) 400, 737 (1999);
68. J. O. Indekeu, Phys. Rev. Lett. 85, 4188 (2000);
69. Phys. Rev. Lett.E. Bertrand, D. Bonn, and J. Meunier, 85, 4189 (2000).