GENERALIZED NAVIER BOUNDARY CONDITION FOR THE MOVING CONTACT LINE

Communications in Mathematical Sciences

Volumn 1, Issue 2, 2003, Pages 333-341

  Qian, Tiezheng ^a   Wang, Xiao Ping ^a   Sheng, Ping ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144510803     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2003.v1.n2.a7     Document Type: Article

References (21)

1. 1] C. Huh and S.G. Mason, The steady movement of a liquid meniscus in a capillary tube. J. Fluid Mech., 81:401-419, 1977.
2. [2] E.B. Dussan, V., On the spreading of liquids on solid surfaces: static and dynamic contact lines.Ann. Rev. Fluid Mech., 11:371-400, 1979.
3. [3] J.F. Joanny and P.G.de Gennes, A model for contact angle hysteresis. J. Chem. Phys., 81:552-562, 1984.
4. [4] P.G.de Gennes, Wetting: statics and dynamics. Rev. Mod. Phys., 57:827-863, 1985.
5. [5] R.G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J.Fluid. Mech., 168:169-194, 1986.
6. [6] J. Koplik, J.R. Banavar, and J.F. Willemsen, Molecular dynamics of poiseuille flow and moving contact lines. Phys. Rev. Lett., 60:1282-1285, 1988.
7. [7] J. Koplik, J.R. Banavar, and J.F. Willemsen, Molecular dynamics of fluid flow at solid surfaces.Phys. Fluids A, 1:781-810, 1989.
8. [8] P.A. Thompson and M.O. Robbins, Simulations of contact-line motion: slip and the dynamic contact angle. Phys. Rev. Lett., 63:766-769, 1989.
9. [9] P.A. Thompson, W.B. Brinckerhoff, and M.O. Robbins, Microscopic studies of static and dy-namic contact angles. J. Adhesion Sci. Tech., 7:535-554, 1993.
10. [10] M.Y. Zhou and P. Sheng, Dynamics of immiscible-fluid displacement in a capillary tube. Phys.Rev. Lett., 64:882-885, 1990.
11. [11] G.J. Merchant and J.B. Keller, Contact angles. Phys. Fluids A, 4:477-485, 1992.
12. [12] Blake first proposed that the uncompensated Young stress contributes to the relative slipping, in the context of an adsorption/desorption model. See T. D. Blake, Dynamic contact angles and wetting kinetics, in Wettability (ed J.C. Berg) 251-309 (Marcel Dekker, Inc., 1993).
13. [13] H.Y. Chen, D. Jasnow, and J. Vinals, Interface and contact line motion in a two phase fluid under shear flow. Phys. Rev. Lett., 85:1686-1689, 2000.
14. [14] D. Jacqmin, Contact-line dynamics of a diffuse fluid interface. J. Fluid. Mech., 402:57-88, 2000.
15. [15] For technical details of the MD simulations, we followed those described in M. Allen and D.Tildesley, Computer Simulation of Liquids (Clarendon, New York, 1987).
16. [16] J.H. Irving and J.G. Kirkwood, The statistical mechanical theoryof transport processes. IV. The equations of hydrodynamics. J. Chem. Phys., 18:817-829, 1950.
17. [17] P.A. Thompson and S.M. Troian, A general boundary condition for liquid flow at solid surfaces.Nature, 389:360-362, 1997.
18. [18] J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy. J.Chem. Phys., 28:258-267, 1958.
19. [19] H. Johnston and J.G. Liu, Finite difference schemes for incompressible flow based on local pressure boundary conditions. J. Comput. Phys., 180:120-154, 2002.
20. [20] Weinan E, Numerical Methods for Viscous Incompressible Flow: Some Recent Advances. Ad-vances in scientific computing, p. 29 (Science Press, 2001).
21. [21] Nanometer-scale details may be resolved through the grid iteration method without significantly compromising the calculation efficiency. See W. Ren and X.P. Wang, An iterative grid redistribution method for singular problems in multiple dimensions. J. Comput. Phys., 159:246-273, 2000.