zbMATH — the first resource for mathematics

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.

76D45 Capillarity (surface tension) for incompressible viscous fluids
76D08 Lubrication theory
76T99 Multiphase and multicomponent flows
Full Text: DOI
[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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.