Gravity-driven thin-film flow using a new contact line model

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 73, Issue 1, 2008, Pages 4-36

  Billingham, John ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Moving contact line; Thin film flow

Indexed keywords

CONTACT ANGLE; FORECASTING; GRAVITY WAVES; NAVIER STOKES EQUATIONS;

GRAVITY-DRIVEN FLOW; MOVING CONTACT LINE; NAVIER SLIP; THIN-FILM FLOW;

OCEANOGRAPHY;

EID: 39049103025     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxm042     Document Type: Article

References (14)

1. BEDEAUX, D. (2003) Non-equilibrium thermodynamic description of the three phase contact line. J. Chem. Phys., 120, 3744-3748.
2. BEDEAUX, D., ALBANO, A. M. & MAZUR, P. (1976) Boundary conditions and non-equilibrium thermodynamics. Physica A, 82, 438-462.
3. BERTOZZI, A. L. & PUGH, M. (1994) The lubrication approximation for thin < viscous films: The moving contact line with a 'porous medium' cut-off of van der Waals interactions. Nonlinearity, 7, 1535-1564.
4. BELLINGHAM, J. (2006) On a model for the motion of a contact line on a smooth solid surface. Eur. J. Appl. Math., 17, 347-382.
5. BLAKE, T. D. & SHIKHMURZAEV, Y. D. (2002) Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci., 253 196-202.
6. BUCKINGHAM, R., SHEARER, M. & BERTOZZI, A. L. (2003) Thin film travelling waves and the Navier slip condition. SIAM J. Appl. Math. 63, 722-744.
7. DUFFY, B. R. & WILSON, S. K. (1997) A third-order differential equation arising in thin-film flows and relevant to Tanner's law. Appl. Math. Lett., 10, 63-68.
8. FORD, W. F. (1992) A third-order differential equation. SIAM Rev., 34, 121-122.
9. HOCKING, L. M. (1981) Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Math., 34, 37-55.
10. KONDIC, L. (2003) Instabilities in gravity driven flow of thin fluid films. SIAM Rev., 45, 95-115.
11. SHIKHMURZAEV, Y. D. (1993) The moving contact line on a smooth solid surface. Int. J. Multiphase Flow, 19, 589-610.
12. SHIKHMURZAEV, Y. D. (1996) Dynamic contact angles and flow in vicinity of moving contact line. AIChE J., 42, 601-612.
13. SHIKHMURZAEV, Y. D. (1997) Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech., 359, 313-328.
14. TUCK, E. O. & SCHWARTZ, L. W. (1990) A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. SIAM Rev., 32, 453-469.