Summary
A recently developed model of dynamic wetting (Shikhmurzaev [1]) is applied to the spreading of a liquid over a smooth solid surface in the limit of weak viscosity effects. In this model, experimentally observed deviations of the dynamic contact angle from the static one are attributed to non-equilibrium values of the surface tensions. The limiting case of small capillary numbers and large Reynolds numbers is considered, with the Reynolds number being based upon the relaxation length. The results are compared with experimental data. Reasonable agreement is only partially obtained, and possible sources of the discrepancies are discussed.
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Shikhmurzaev, Y. D.: The moving contact line on a smooth solid surface. Int. J. Multiphase Flow 19, 589–610 (1993).
Dussan V., E. B., Davis, S. H.: On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65, 71–95 (1974).
Dussan V., E. B.: On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371–400 (1979).
Weidner, D., Schwartz, L.: Contact-line motion of shear-thinning liquids. Phys. Fluids 6, 3535–3538 (1994).
Dussan V., E. B.: The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665–684 (1976).
Hocking, L. M.: A moving fluid interface on a rough surface. J. Fluid Mech. 76, 801–817 (1976).
Cox, R. G.: The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169–194 (1986).
Zhou, M. Y., Sheng, P.: Dynamics of immiscible fluid displacement in a capillary tube. Phys. Rev. Lett. 64, 882–885 (1990).
Stoev, K., Ramé, E., Garoff, S.: Effects of inertia on the hydrodynamics near moving contact lines. Phys. Fluids 11, 3209–3216 (1999).
Cox, R. G.: Inertial and viscous effects on dynamic contact angles. J. Fluid Mech. 357, 249–278 (1998).
Lindner-Silwester, T.: Die bewegte Kontaktlinie mit schwachen Reibungseffekten. Technische Universität Wien, Dissertation, 2003.
Zunzer, J.: Experimentelle und numerische Untersuchungen zur bewegten Kontaktlinie. Technische Universität Wien, Dissertation, 2002.
Blake, T.: Dynamic contact angles and wetting kinetics. In: Wettability (Berg, J. C. ed.). Marcel Dekker 1993.
Shikhmurzaev, Y. D.: Dynamic contact angles and flow in vicinity of moving contact line. AIChE J. 42, 601–612 (1996).
Shikhmurzaev, Y. D.: Coalescence and capillary breakup of liquid volumes. Phys. Fluids 12, 2386–2396 (2000).
Kochurova, N. N., Rusanov, A. I.: Dynamic surface properties of water: Surface tension and surface potential. J. Colloid Interface Sci. 81, 297–303 (1981).
Batchelor, G. K.: On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177–190 (1956).
Shikhmurzaev, Y. D.: On metastable regimes of dynamic wetting. J. Phys. Condens. Matter 14, 319–330 (2002).
Churaev, N. V., Sobolev, V. D., Somov, A. N.: Slippage of liquids over lyophobic solid surfaces. J. Colloid Interface Sci. 97, 574–581 (1984).
Kistler, S. F.: Hydrodynamics of wetting. In: Wettability (Berg, J.C., ed). Marcel Dekker 1993.
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Dedicated to Prof. Dr.-Ing. Dr. techn. E.h. J. Zierep on the occasion of his 75th birthday
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Lindner-Silwester, T., Schneider, W. The moving contact line with weak viscosity effects – an application and evaluation of Shikhmurzaev’s model. Acta Mechanica 176, 245–258 (2005). https://doi.org/10.1007/s00707-004-0091-4
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DOI: https://doi.org/10.1007/s00707-004-0091-4