Skip to main content Accessibility help

On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation

  • E. B. Dussan V. (a1), Enrique Ramé (a2) and Stephen Garoff (a3)


Over the past decade and a half, analyses of the dynamics of fluids containing moving contact lines have specified hydrodynamic models of the fluids in a rather small region surrounding the contact lines (referred to as the inner region) which necessarily differ from the usual model. If this were not done, a singularity would have arisen, making it impossible to satisfy the contact-angle boundary condition, a condition that can be important for determining the shape of the fluid interface of the entire body of fluid (the outer region). Unfortunately, the nature of the fluids within the inner region under dynamic conditions has not received appreciable experimental attention. Consequently, the validity of these novel models has yet to be tested.

The objective of this experimental investigation is to determine the validity of the expression appearing in the literature for the slope of the fluid interface in the region of overlap between the inner and outer regions, for small capillary number. This in part involves the experimental determination of a constant traditionally evaluated by matching the solutions in the inner and outer regions. Establishing the correctness of this expression would justify its use as a boundary condition for the shape of the fluid interface in the outer region, thus eliminating the need to analyse the dynamics of the fluid in the inner region.

Our experiments consisted of immersing a glass tube, tilted at an angle to the horizontal, at a constant speed, into a bath of silicone oil. The slope of the air–silicone oil interface was measured at distances from the contact line ranging between O.O13a. and O.17a, where a denotes the capillary length, the lengthscale of the outer region (1511 μm). Experiments were performed at speeds corresponding to capillary numbers ranging between 2.8 × 10-4 and 8.3 × 10-3. Good agreement is achieved between theory and experiment, with a systematic deviation appearing only at the highest speed. The latter may be a consequence of the inadequacy of the theory at that value of the capillary number.



Hide All
Boender, W. & Chesters, A. K. 1986 The hydrodynamics of moving contact lines: an analytic approximation for the advancing liquid-gas case, private communications.
Cox, R. G. 1986 The dynamics of the spreading of a liquid on a solid surface. J. Fluid Mech. 168, 169.
Durbin, P. A. 1988 Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop. J. Fluid Mech. 197, 157.
DussanV., E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, pp. 67680. Oxford University Press.
Halst, H. van Dee 1979 Light Scattering by Small Particles. University Microfilms International, Ann Arbor.
Hocking, L. M. 1976 A moving fluid interface on a rough surface. J. Fluid Mech. 76, 801.
Hocking, L. M. & Rivers, A. D. 1982 The spreading of a drop by capillary action. J. Fluid Mech. 121, 425.
Huh, C. & Mason, S. G. 1977 The steady moti on of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401.
Huh, C. & Scriven, L. E. 1969 Shapes of axisymmetric fluid interfaces of unbounded extent. J. Colloid Interface Sci. 30, 323.
Jackson, R. 1977 Transport in Porous Catalysts. Elsevier.
Jansons, K. M. 1986 Moving contact lines at non-zero capillary number. J. Fluid Mech. 167, 393.
Koplik, J., Banavar, J. R. & Willemsen, J. F. 1988 Molecular dynamics of Poiseuille flow and moving contact lines. Phys. Rev. Lett.60, 1282.
Lowndes, J. 1980 The numerical simulation of the steady motion of the fluid meniscus in a capillary tube. J. Fluid Mech. 101, 631.
Ngan, C. G. & DussanV., E. B. 1989 On the dynamics of liquid spreading on solid surfaces. J. Fluid Mech. 209, 191.
Thompson, P. A. & Robbins, M. O. 1989 Simulations of contact-line motion: slip and dynamic contact angle. Phys. Rev. Lett. 63, 766.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation

  • E. B. Dussan V. (a1), Enrique Ramé (a2) and Stephen Garoff (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.