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Apparent dynamic contact angle of an advancing gas-liquid meniscus. (English) Zbl 0838.76023
The dynamic contact anlge that the meniscus forms with the solid surface is derived as a function of the capillary number, the capillary radius, and the Hamaker’s constant for intermolecular forces. The method is based on a matched asymptotic analysis that links the outer capillary region to the precursor film in front of the meniscus through a lubricating film.

MSC:
76D45 Capillarity (surface tension) for incompressible viscous fluids
76D08 Lubrication theory
76T99 Multiphase and multicomponent flows
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[1] E. B. Dussan V., ”On the spreading of liquids on solid surfaces: Static and dynamic contact lines,” Annu. Rev. Fluid Mech. 11, 371 (1979).ARVFA30066-4189
[2] H. K. Moffatt, ”Viscous and resistive eddies near a sharp corner,” J. Fluid Mech. 18, 1 (1963).JFLSA70022-1120
[3] C. Huh and L. E. Scriven, ”Hydrodynamic model of steady movement of a solid/liquid/fluid contact line,” J. Colloid Interface Sci. 35, 85 (1971).JCISA50021-9797
[4] L. M. Hocking, ”A moving fluid interface. Part 2. The removal of the force singularity by a slip flow,” J. Fluid Mech. 79, 209 (1977).JFLSA70022-1120
[5] C. G. Ngan and E. B. Dussan V., ”On the dynamics of liquid spreading on solid surfaces,” J. Fluid Mech. 209, 191 (1989).JFLSA70022-1120
[6] E. B. Dussan V., ”The moving contact line: The slip boundary condition,” J. Fluid Mech. 77, 665 (1976).JFLSA70022-1120
[7] R. L. Hoffman, ”A study of the advancing interface I. Interface shape in liquid-gas systems,” J. Colloid Interface Sci. 50, 228 (1975).JCISA50021-9797
[8] L. Tanner, ”The spreading of silicone oil drops on horizontal surfaces,” J. Phys. D 12, 1473 (1979).JPAPBE0022-3727
[9] W. Rose and R. W. Heinz, ”Moving interfaces and contact angle rate dependency,” J. Colloid Sci. 17, 39 (1962).JCSCA70095-8522
[10] F. P. Bretherton, ”The motion of long bubbles in tubes,” J. Fluid Mech. 10, 166 (1961).JFLSA70022-1120 · Zbl 0096.20702
[11] H. Hervert and P. G. De Gennes, ”Dynamique du mouillage: Films précurseurs sur solide sec,” Comptes Rendus, Sér. II 299, 499 (1984).
[12] D. Ausserré, A. M. Picard, and L. Léger, ”Existence and role of the precursor film in the spreading of polymer liquids,” Phys. Rev. Lett. 57, 2671 (1986).PRLTAO0031-9007
[13] J. A. Nieminen, D. B. Abraham, M. Karttunen, and K. Kaski, ”Molecular dynamics of a microscopic droplet on solid surface,” Phys. Rev. Lett. 69, 124 (1992).PRLTAO0031-9007
[14] O. V. Voinov, ”Inclination angles of the boundary in moving liquid layers,” Zh. Prikl. Mekh. Tekh. Fiz. 2, 92 (1977). · doi:10.1007/BF00859809
[15] P. G. De Gennes, ”Dynamique d’étalement d’une goutte,” Comptes Rendus Sér. II 298, 111 (1984).
[16] G. Friz, ”Über den dynamischen randwinkel im fall der vollstandigen benetzung,” Z. Angew. Phys. 19, 374 (1965).ZAPHAX0044-2283
[17] C.-W. Park and G. M. Homsy, ”Two-phase displacement in Hele Shaw cells: Theory,” J. Fluid Mech. 139, 291 (1984).JFLSA70022-1120 · Zbl 0567.76092
[18] S. Davis, ”Rupture of thin liquid films,” in Waves on Fluid Interfaces, edited by R. E. Meyer (Academic, New York, 1982), p. 291. · Zbl 0569.76039
[19] C. A. Miller and P. Neogi, Interfacial Phenomena (Dekker, New York, 1985).
[20] L. M. Hocking, ”The influence of intermolecular forces on thin fluid layers,” Phys. Fluids A 5, 793 (1993).PFADEB0899-8213
[21] J. F. Joanny and P. G. De Gennes, ”Structure statique des films de mouillage et des lignes de contact,” Comptes Rendus Sér. II 299, 279 (1984).
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