Moving Common Lines, Thin Films, and Dynamic Contact Angles

  • J. C. Slattery
Chapter
Part of the International Centre for Mechanical Sciences book series (CISM, volume 318)

Abstract

When a common line or three-phase line of contact moves over a rigid solid, an unbounded force must be generated at the common line, if the usual no-slip boundary condition of fluid mechanics is valid.

Since an unbounded force is unrealistic, our description of the physics in this statement must be incorrect. There are various possibilities. Real solids are not rigid. Perhaps the no-slip boundary condition fails within the immediate neighborhood of the common line. In some situations there is undoubtedly mass transfer in the neighborhood of the apparent common line, and there is displacement over an existing film of fluid without a common line ever having been formed. In other situations, a sequence of stationary common lines may be formed in the thin film of fluid within the immediate neighborhood of the apparent common line, giving the appearance of a moving common line to an observer on the macroscale.

Section 1 is a review of what is known about moving common lines on relatively rigid solids. In Sec. 2, I illustrate with at least one computation that continuum mechanics can be applied successfully to very thin films, such as those within the immediate neighborhood of the common line. In Sec. 3 I discuss contact angles, with a demonstration computation for the dynamic contact angle as a function of the apparent speed of displacement of the common line.

Keywords

Contact Angle Disjoin Pressure Dynamic Contact Angle Common Line Precursor Film 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ablett, R., Philos. Mag. (6) 46, 244 (1923).CrossRefGoogle Scholar
  2. [2]
    Adamson, A. W., Physical Chemistry of Surfaces, fourth edition, John Wiley, New York (1982).Google Scholar
  3. [3]
    Allen, R. F., and P. R. Benson, J. Colloid Interface Sci. 50, 250 (1975).CrossRefGoogle Scholar
  4. [4]
    Bascom, W. D., R. D. Cottington, and C. R. Singleterry, in Contact Angles, Wettability and Adhesion, Advances in Chemistry Series No. 43, p. 355, American Chemical Society, Washington, D.C. (1964).CrossRefGoogle Scholar
  5. [5]
    Bayramli, E., and S. G. Mason, J. Colloid Interface Sci. 66, 200 (1978).CrossRefGoogle Scholar
  6. [6]
    Black, T. D., VDI-Berichte Nr. 182, 117 (1972).Google Scholar
  7. [7]
    Blake, T. D., D. H. Everett, and J. M. Haynes, in Wetting, S. C. I. Monograph No. 25, Society of Chemical Industry, London (1967).Google Scholar
  8. [8]
    Blake, T. D., and J. M. Haynes, J. Colloid Interface Sci. 30, 421 (1969).CrossRefGoogle Scholar
  9. [9]
    Buff, F. P., Handbuch der Physik, vol. 10, edited by S. Flügge, Springer- Verlag, Berlin (1960).Google Scholar
  10. [10]
    Buff, F. P., and H. Saltsburg, J. Chem. Phys. 26, 23 (1957).CrossRefGoogle Scholar
  11. [11]
    Burley, R., and B. S. Kennedy, Br. Polym. J. 8, 140 (1976a).CrossRefGoogle Scholar
  12. [12]
    Burley, R., and B. S. Kennedy, Chem. Eng. Sci. 31, 901 (1976b).CrossRefGoogle Scholar
  13. [13]
    Cain, J. B., D. W. Francis, R. D. Venter, and A. W. Neumann, J. Colloid Interface Sci. 94, 123 (1983).CrossRefGoogle Scholar
  14. [14]
    Cassie A. B. D., Fiscuss Faraday Soc. 3, 11 (1948).CrossRefGoogle Scholar
  15. [15]
    Chen, J. D., J. Colloid Interface Sci. 122, 60 (1988).CrossRefGoogle Scholar
  16. [16]
    Chen, J. D., and N. Wada, Phys. Rev. Letters 62, 3050 (1989).CrossRefGoogle Scholar
  17. [17]
    Cherry, B. W., and C. M. Holmes, J. Colloid Interface Sci. 29, 174 (1969).CrossRefGoogle Scholar
  18. [18]
    Coney, T. A., and W. J. Masica, NASA Tech. Note TN D-5115 (1969).Google Scholar
  19. [19]
    Cox, B. G., J. Fluid Mech. 168, 169 (1986).CrossRefGoogle Scholar
  20. [20]
    de Gennes, P. G., Rev. Mod. Phys. 57, 827 (1985).CrossRefGoogle Scholar
  21. [21]
    Dettre, R. H., and R. E. Johnson Jr., in Contact Angle, Wettability, and Adhesion, Advances in Chemistry Series No. 43, p. 136, American Chemical Society, Washington, D.C. (1964).CrossRefGoogle Scholar
  22. [22]
    Dussan V., E. B., J. Fluid Mech. 77, 665 (1976).CrossRefGoogle Scholar
  23. [23]
    Dussan V., E. B., Ann Rev. Fluid Mech. 11, 371 (1979).CrossRefGoogle Scholar
  24. [24]
    Dussan V., E. B., and S. H. Davis, J. Fluid Mech. 65, 71 (1974).CrossRefGoogle Scholar
  25. [25]
    Eick, J. D., R. J. Good, and A. W. Neumann, J. Colloid Interface Sci. 53, 235 (1975).CrossRefGoogle Scholar
  26. [26]
    Elliott, G. E. P., and A. C. Riddiford, Nature London 195, 795 (1962).CrossRefGoogle Scholar
  27. [27]
    Elliott, G. E. P., and A. C. Riddiford, Recent Progr. Surface Sci. 2, 111 (1965).CrossRefGoogle Scholar
  28. [28]
    Elliott, G. E. P., and A. C. Riddiford, J. Colloid Interface Sci. 23, 389 (1967).CrossRefGoogle Scholar
  29. [29]
    Ellison, A. H., and S. B. Tejada, NASA Contract Rep. CR 72441 (1968).Google Scholar
  30. [30]
    Fermigier, M. and P. Jenffer, Annales de Physique (Colloque n° 2, supplement au n° 3) 13, 37 (1988).Google Scholar
  31. [31]
    Gaydos, J., and A. W. Neumann, J. Colloid Interface Sci. 120, 76 (1987).CrossRefGoogle Scholar
  32. [32]
    Gibbs, J. W., The Collected Works, vol. 1, Yale University Press, New Haven, Conn. (1948).Google Scholar
  33. [33]
    Giordano, R. M., personal communication, April 25, 1979.Google Scholar
  34. [34]
    Goldstein, S., Modern Developments in Fluid Dynamics, Oxford University Press, London (1938).Google Scholar
  35. [35]
    Greenspan, H. P., J. Fluid Mech. 84, 125 (1978).CrossRefGoogle Scholar
  36. [36]
    Hahn, P. S., J. D. Chen, and J. C. Slattery, AIChE J. 31, 2126 (1985).Google Scholar
  37. [37]
    Hansen, R. S., and M. Miotto, J. Am. Chem. Soc. 79, 1765 (1957).CrossRefGoogle Scholar
  38. [38]
    Hansen, R. J., and T. Y. Toong, J. Colloid Interface Sci. 36, 410 (1971).CrossRefGoogle Scholar
  39. [39]
    Hardy, W. B., Phil. Mag. (6) 38, 49 (1919).Google Scholar
  40. [40]
    Heslot, F., N. Fraysse, and A. M. Cazabat, Nature London 338, 640 (1989).CrossRefGoogle Scholar
  41. [41]
    Hocking, L. M., J. Fluid Mech. 76, 801 (1976).CrossRefGoogle Scholar
  42. [42]
    Hocking, L. M., J. Fluid Mech. 79, 209 (1977).CrossRefGoogle Scholar
  43. [43]
    Hocking, L. M., and A. D. Rivers, J. Fluid Mech. 121, 425 (1982).CrossRefGoogle Scholar
  44. [44]
    Hoffman, R. L., J. Colloid Interface Sci. 50, 228 (1975).CrossRefGoogle Scholar
  45. [45]
    Hopf, W., and H. Stechemesser, Colloids Surf. 33, 25 (1988).CrossRefGoogle Scholar
  46. [46]
    Hough, D. B., and L. R. White, Adv. Colloid Interface Sci. 14, 3 (1980).CrossRefGoogle Scholar
  47. [47]
    Huh, C., and S. G. Mason, J. Colloid Interface Sci. 60, 11 (1977).CrossRefGoogle Scholar
  48. [48]
    Huh, C., and S. G. Mason, J. Fluid Mech. 81, 401 (1977).CrossRefGoogle Scholar
  49. [49]
    Huh, C., and L. E. Scriven, J. Colloid Interface Sci. 35, 85 (1971).CrossRefGoogle Scholar
  50. [50]
    Inverarity, G., Ph.D. dissertation, Victoria University of Manchester (1969).Google Scholar
  51. [51]
    Israelachvili, J. N., J. Chem. Soc. Faraday Trans. 1169, 1729 (1973).CrossRefGoogle Scholar
  52. [52]
    Israelachvili, J. N., Intermolecular and Surface Forces, p. 157, Academic Press (1985).Google Scholar
  53. [53]
    Israelachvili, J. N., and M. L. Gee, Langmuir 5, 288 (1989).CrossRefGoogle Scholar
  54. [54]
    Israelachvili, J. N., and P. M. McGuiggan, Science 241, 795 (1988).CrossRefGoogle Scholar
  55. [55]
    Jasper, J. J., and E. V. Kring, J. Phys. Chem. 59, 1019 (1955).CrossRefGoogle Scholar
  56. [56]
    Jiang, T. S., S. G. Oh, and J. C. Slattery, J. Colloid Interface Sci. 69, 74 (1979).CrossRefGoogle Scholar
  57. [57]
    Joanny, J. F., and P. G. de Gennes, J. Chem. Phys. 81, 552 (1984).CrossRefGoogle Scholar
  58. [58]
    Johnson, R. E. Jr., and R. H. Dettre, in Contact Angle, Wettability, and Adhesion, Advances in Chemistry Series No. 43, p. 136, American Chemical Society, Washington, D.C. (1964).Google Scholar
  59. [59]
    Johnson, R. E. Jr., and R. H. Dettre, J. Phys. Chem. 68, 1744 (1964).CrossRefGoogle Scholar
  60. [60]
    Johnson, R. E. Jr., and R. H. Dettre, Surface and Colloid Science, 2, 85, edited by E. Matijevic, Wiley-Interscience, New York (1969).Google Scholar
  61. [61]
    Johnson, R. E. Jr., R. H. Dettre, and D. A. Brandreth, J. Colloid Interface Sci. 62, 205 (1977).CrossRefGoogle Scholar
  62. [62]
    Kafka, F. Y., and E. B. Dussan V., J. Fluid Mech. 95, 539 (1979).CrossRefGoogle Scholar
  63. [63]
    Kennedy, B. S., and R. Burley, J. Colloid Interface Sci. 62, 48 (1977).CrossRefGoogle Scholar
  64. [64]
    Kralchevsky, P. A., A. D. Nikolov, and I. B. Ivanov, J. Colloid Interface Sci. 112, 132 (1986).CrossRefGoogle Scholar
  65. [65]
    Legait, B., and P. Sourieau, J. Colloid Interface Sci. 107, 14 (1985).CrossRefGoogle Scholar
  66. [66]
    Lester, G. R., J. Colloid Sci. 16, 315 (1961).CrossRefGoogle Scholar
  67. [67]
    Li, D., and J. C. Slattery, J. Colloid Interface Sci. (1991).Google Scholar
  68. [68]
    Lin, C. Y., and J. C. Slattery, AIChE J. 28, 147 (1982a).CrossRefGoogle Scholar
  69. [69]
    Lin, C. Y., and J. C. Slattery, AIChE J. 28, 786 (1982b).CrossRefGoogle Scholar
  70. [70]
    Ludviksson, V., and E. N. Lightfoot, AIChE J. 17, 1166 (1971).CrossRefGoogle Scholar
  71. [71]
    Miller, C. A., and P. Neogi, Interfacial Phenomena, Marcel Dekker, New York (1985).Google Scholar
  72. [72]
    Mori, Y. H., T. G. M. van de Ven, and S. G. Mason, Colloids Surfaces 4, 1 (1982).CrossRefGoogle Scholar
  73. [73]
    Morra, M., E. Occhiello, and F. Garbassi, Langmuir 5, 872 (1989).CrossRefGoogle Scholar
  74. [74]
    Morrow, N. R., J. Can. Pet. Technol. 14, 42 (1975).Google Scholar
  75. [75]
    Myers, G. E., Analytical Methods in Conduction Heat Transfer, p. 274, McGraw-Hill, New York (1971).Google Scholar
  76. [76]
    Neumann, A. W., and R. J. Good, J. Colloid Interface Sci. 38, 341 (1972).CrossRefGoogle Scholar
  77. [77]
    Ngan, C. G., and E. B. Dussan V., J. Fluid Mech. 118, 27 (1982).CrossRefGoogle Scholar
  78. [78]
    Oliver, J. F., C. Huh, and S. G. Mason, J. Adhes. 8, 223 (1977).CrossRefGoogle Scholar
  79. [79]
    Padday, J. F., and N. D. Uffindell, J. Phys. Chem. 72, 1407 (1968).CrossRefGoogle Scholar
  80. [80]
    Petrov, J. G., and B. P. Radoev, Colloid Polym. Sci. 259, 753 (1981).CrossRefGoogle Scholar
  81. [81]
    Platikanov, D., M. Nedyalkov, and V. Nasteva, J. Colloid Interface Sci. 75, 620 (1980).CrossRefGoogle Scholar
  82. [82]
    Poynting, J. H., and J. J. Thomson, A Text-Book of Physics - Properties of Matter, p. 142, Charles Griffin, London (1902).Google Scholar
  83. [83]
    Radigan, W., H. Ghiradella, H. L. Frisch, H. Schonhorn, and T. K. Kwei, J. Colloid Interface Sci. 49, 241 (1974).CrossRefGoogle Scholar
  84. [84]
    Richards, T. W., and E. K. Carver, J. Am. Chem. Soc. 43, 827 (1921).CrossRefGoogle Scholar
  85. [85]
    Richardson, S., J. Fluid Mech. 59, 707 (1973).CrossRefGoogle Scholar
  86. [86]
    Rose, W., and R. W. Heins, J. Colloid Sci. 17, 39 (1962).CrossRefGoogle Scholar
  87. [87]
    Ruckenstein, E., and C. S. Dunn, J. Colloid Interface Sci. 59, 135 (1977).CrossRefGoogle Scholar
  88. [88]
    Schonhorn, H., H. L. Frisch, and T. K. Kwei, J. Appl. Phys. 37, 4967 (1966).CrossRefGoogle Scholar
  89. [89]
    Schwartz, L. W., and S. Garoff, Langmuir 1, 219 (1985).CrossRefGoogle Scholar
  90. [90]
    Schwartz, A. M., and S. B. Tejada, NASA Contract Rep. CR 72728 (1970).Google Scholar
  91. [91]
    Schwartz, A. M., and S. B. Tejada, J. Colloid Interface Sci. 38, 359 (1972).CrossRefGoogle Scholar
  92. [92]
    Sheludko, A., Adv. Colloid Interface Sci. 1, 391 (1967).CrossRefGoogle Scholar
  93. [93]
    Slattery, J. C., Momentum, Energy, and Mass Transfer in Continua, McGraw-Hill, New York (1972); second edition, Robert E. Krieger, Malabar, FL 32950 (1981).Google Scholar
  94. [94]
    Slattery, J. C., Interfacial Transport Phenomena, Springer-Verlag, New York (1990).CrossRefGoogle Scholar
  95. [95]
    Teletzke, G. F., H. T. Davis, and L. E. Scriven, Chem. Eng. Commun. 55, 41 (1987).CrossRefGoogle Scholar
  96. [96]
    Wayner, P. C., J. Colloid Interface Sci. 77, 495 (1980).CrossRefGoogle Scholar
  97. [97]
    Wayner, P. C., J. Colloid Interface Sci. 88, 294 (1982).CrossRefGoogle Scholar
  98. [98]
    Wickham, G. R., and S. D. R. Wilson, J. Colloid Interface Sci. 51, 189 (1975).CrossRefGoogle Scholar
  99. [99]
    Williams, R., Nature London 266, 153 (1977).CrossRefGoogle Scholar
  100. [100]
    Williams, R., personal communication (1988).Google Scholar
  101. [101]
    Wilson, S. D. R., J. Colloid Interface Sci. 51, 532 (1975).CrossRefGoogle Scholar
  102. [102]
    Yarnold, G. D., Proc. Phys. Soc. London 50, 540 (1938).CrossRefGoogle Scholar
  103. [103]
    Yarnold, G. D., and B. J. Mason, Proc. Phys. Soc. London B62, 125 (1949).CrossRefGoogle Scholar
  104. [104]
    Young, T., Philos. Trans. R. Soc. London (4 to.) 95, 65 (1805).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • J. C. Slattery
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA

Personalised recommendations