Contact lines over random topographical substrates. Part 1. Statics

Journal of Fluid Mechanics

Volumn 672, Issue , 2011, Pages 358-383

  Savva, Nikos ^a   Pavliotis, Grigorios A ^a   Kalliadasis, Serafim ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

contact lines; drops; thin films

Indexed keywords

DROPS; NORMAL DISTRIBUTION; RANDOM VARIABLES; THIN FILMS; WETTING;

CONTACT LINES; DISTRIBUTED RANDOM VARIABLES; FLAT SUBSTRATES; NUMERICAL EXPERIMENTS; PROBABILITY DENSITIES; STATIONARY RANDOMS; SUBSTRATE ROUGHNESS; WAVE NUMBERS;

SUBSTRATES;

EID: 79651475277     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112010005975     Document Type: Article

References (56)

1. Baker, G. A. & Graves-Morris, P. R. 1996 Padé Approximants. Cambridge University Press.
2. Barabási, A.-L. & Stanley, H. E. 1995 Fractal Concepts in Surface Growth. Cambridge University Press.
3. Berry, M. V. & Lewis, Z. V. 1980 On the Weierstrass-Mandelbrot fractal function. Proc. R. Soc. Lond. A 370 (1743), 459-484.
4. Bhushan, B. 2000 Surface roughness analysis and measurement techniques. In Modern Tribology Handbook (ed. B. Bhushan), vol. 1, chap. 2, pp. 49-119. CRC Press LLC.
5. Bhushan, B. & Majumdar, A. 1992 Elastic-plastic model for bifractal surfaces. Wear 153, 53-64.
6. Bico, J., Tordeux, C. & Quéré, D. 2001 Rough wetting. Europhys. Lett. 55 (2), 214-220.
7. Blake, T. D. 1993 Dynamic contact angles and wetting kinetics. In Wettability (ed. J. C. Berg), pp. 251-310. Marcel Dekker.
8. Blossey, R. 2003 Self-cleaning surfaces-virtual realities. Nature Mater. 2, 301-306.
9. Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739-805.
10. Borgs, C., De Coninck, J., Kotecký, R. & Zinque, M. 1995 Does the roughness of the substrate enhance wetting? Phys. Rev. Lett. 74 (12), 2292-2294.
11. Breiman, L. 1992 Probability. SIAM.
12. Callies, M. & Quéré, D. 2005 On water repellency. Soft Matt. 1, 55-61.
13. Chung, J. Y., Youngblood, J. P. & Stafford, C. M. 2007 Anisotropic wetting on tunable microwrinkled surfaces. Soft Matt. 3, 1163-1169.
14. Cox, R. G. 1983 The spreading of a liquid on a rough solid surface. J. Fluid Mech. 131, 1-26.
15. Dussan V., E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371-400.
16. Edwards, S. F. & Wilkinson, D. R. 1982 The surface statistics of a granular aggregate. Proc. R. Soc. Lond. A 381, 17-31.
17. Geary, R. C. 1930 The frequency distribution of the quotient of two normal variates. R. Stat. Soc. J. 93, 442-446.
18. de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57 (3), 827-863.
19. de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2003 Capillarity and Wetting Phenomena. Springer.
20. Good, R. J. 1952 A thermodynamic derivation of Wenzel's modification of Young's equation for contact angles; together with a theory of hysteresis. J. Am. Chem. Soc. 74, 5041-5042.
21. Greenwood, J. A. & Williamson, J. B. P. 1966 Nominally flat surfaces. Proc. R. Soc. Lond. A 295 (1442), 310-319.
22. Hazlett, R. D. 1990 Fractal applications: wettability and contact angle. J. Colloid Interface Sci. 173 (2), 527-533.
23. Hazlett, R. D. 1992 On surface roughness effects in wetting phenomena. J. Adhes. Sci. Technol. 6 (6), 625-633.
24. Hitchcock, S. J., Carroll, N. T. & Nicholas, M. G. 1981 Some effects of substrate roughness on wettability. J. Mater. Sci. 16, 714-732.
25. Huh, C. & Mason, S. G. 1977 Effects of surface roughness on wetting (theoretical). J. Colloid Interface Sci. 60 (1), 11-38.
26. Jansons, K. M. 1985 Moving contact lines on a two-dimensional rough surface. J. Fluid Mech. 154, 1-28.
27. Joanny, J. & de Gennes, P.-G. 1984 A model for contact angle hysteresis. J. Chem. Phys. 81 (1), 552-562.
28. Johnson, R. E. & Dettre, R. H. 1964 Contact angle hysteresis. I. Study of an idealized rough surface. In Advances in Chemistry Series, vol. 43, Contact Angle, Wettability and Adhesion (ed. F. M. Fowkes), pp. 112-135. American Chemical Society.
29. van Kampen, N. G. 2007 Stochastic Processes in Physics and Chemistry, 3rd edn. Elsevier.
30. Katzav, E., Adda-Bedia, M. & Derrida, B. 2007 Fracture surfaces of heterogeneous materials: a 2D solvable model. Europhys. Lett. 78, 46006.
31. Krishnamoorthy, K. 2006 Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC.
32. Longuet-Higgins, M. S. 1958 On the intervals between successive zeros of a random function. Proc. R. Soc. Lond. A 246, 99-118.
33. Majumdar, A. & Tien, C. L. 1990 Fractal characterization and simulation of rough surfaces. Wear 136, 313-327.
34. Mandelbrot, B. B. 1982 The Fractal Geometry of Nature. Freeman.
35. McHale, G. 2007 Cassie and Wenzel: were they really so wrong? Langmuir 23, 8200-8205.
36. Mulvaney, D. J., Newland, D. E. & Gill, K. F. 1989 A complete description of surface texture profiles. Wear 132, 173-182.
37. Øksendal, B. 2003 Stochastic Differential Equations, 6th edn. Springer.
38. Oliver, J. F., Huh, C. & Mason, S. G. 1977 The apparent contact angle of liquids on finely-grooved solid surfaces - a SEM study. J. Adhes. 8, 223-234.
39. Oliver, J. F., Huh, C. & Mason, S. G. 1980 An experimental study of some effects of solid surface roughness on wetting. Colloids Surf. 1, 79-104.
40. Palasantzas, G. & De Hosson, J. Th. M. 2001 Wetting on rough surfaces. Acta Mater. 49, 3533-3538.
41. Pomeau, Y. & Vannimenus, J. 1985 Contact angle on heterogeneous surfaces: weak heterogeneities. J. Colloid Interface Sci. 104 (2), 477-488.
42. Poon, C. Y. & Bhushan, B. 1995 Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler. Wear 190, 76-88.
43. Rice, S. O. 1945 The mathematical analysis of random noise. Bell Syst. Tech. J. 24, 46-156.
44. Robbins, M. O. & Joanny, J. F. 1987 Contact angle hysteresis on random surfaces. Europhys. Lett. 3 (6), 729-735.
45. Roberts, A. P. & Torquato, S. 1999 Chord-distribution functions of three-dimensional random media: approximate first-passage times of Gaussian processes. Phys. Rev. E 59 (5), 4953-4963.
46. Savva, N. & Kalliadasis, S. 2009 Two-dimensional droplet spreading over topographical substrates. Phys. Fluids 21, 092102.
47. Savva, N., Pavliotis, G. A. & Kalliadasis, S. 2011 Contact lines over random topographical substrates. Part 2. Dynamics. J. Fluid Mech. 672, 384-410.
48. Sayles, R. & Thomas, T. R. 1978 Surface topography as a non-stationary random process. Nature 271, 431-434.
49. Shibuichi, S., Onda, T., Satoh, N. & Tsujii, K. 1996 Super water-repellent surfaces resulting from fractal structure. J. Phys. Chem. 100, 19512-19517.
50. Thomas, T. R. 1999 Rough Surfaces, 2nd edn. Imperial College Press.
51. VanMarcke, E. 1983 Random Fields: Analysis and Synthesis. MIT Press.
52. Wenzel, R. N. 1936 Resistance of solid surfaces to wetting by water. Ind. Engng Chem. 28, 988-994.
53. Whitehouse, D. J. 2001 Fractal or fiction. Wear 249, 345-353.
54. Whitehouse, D. J. & Archard, J. F. 1970 The properties of random surfaces of significance in their contact. Proc. R. Soc. Lond. A 316 (1524), 97-121.
55. Zeitak, R. 1997 Short time expansion for first-passage distributions. Phys. Rev. E 56 (3), 2560-2567.
56. Zhou, X. B. & De Hosson, J. Th. M. 1995 Influence of surface roughness on the wetting angle. J. Mater. Res. 10 (8), 1984-1992.