Skip to main content Accessibility help
×
Home

On the dynamics of liquid spreading on solid surfaces

  • C. G. Ngan (a1) and E. B. Dussan V. (a2)

Abstract

Our main objective is to identify a boundary-value problem capable of describing the dynamics of fluids having moving contact lines. A number of models have been developed over the past decade and a half for describing the dynamics of just such fluid systems. We begin by discussing the deficiencies of the methods used in some of these investigations to evaluate the parameters introduced by their models. In this study we are concerned exclusively with the formulation of a boundary-value problem which can describe the dynamics of the fluids excluding that lying instantaneously in the immediate vicinity of the moving contact line. From this perspective, many of the approaches referred to above are equivalent, that is to say they give rise to velocity fields with the same asymptotic structure near the moving contact line. Part of our objecive is to show that this asymptotic structure has only one parameter. A substantial portion of our investigation is devoted to determining whether or not the velocity field in a particular experiment has this asymptotic structure, and to measuring the value of the parameter.

More specifically, we use the shape of the fluid interface in the vicinity of the moving contact line to identify the asymptotic structure of the dynamics of the fluid. Experiments are performed in which silicone oil displaces air through a gap formed between two parallel narrowly-spaced glass microscope slides sealed along two opposing sides. Since we were unable to make direct measurements of the shape of the fluid interface close to the moving contact line, an indirect procedure has been devised for determining its shape from measurements of the apex height of the meniscus. We find that the deduced fluid interface shape compares well with the asymptotic form identified in the studies referred to above; however, systematic deviations do arise. The origin of these deviations is unclear. They could be attributed to systematic experimental error, or, to the fact that our analysis (valid only for small values of the capillary number) is inadequate at the conditions of our experiments.

Copyright

References

Hide All
Abramowitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. NBS Appl. Maths Series No. 55, US Government Prining Office, Washington DC.
Aussere, D., Picard, A. M. & Leger, L. 1986 Existence and role of the precursor film in the spreading of polymer liquids. Phys. Rev. Lett. 57, 2671.
Bach, P. & Hassager, O. 1985 An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow. J. Fluid Mech. 152, 173.
Bascom, W. D., Cottington, R. L. & Singleterry, C. R. 1964 Dynamics surface phenomena in the spontaneous spreading of oils on solids. In Adv. Chem.: Am. Chem. Soc. 43, 389.
Cox, R. G. 1986 The dynamics of the spreading of a liquid on a solid surface. J. Fluid Mech. 168, 169.
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665.
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid. Mech. 11, 371.
Dussan, V. E. B. & Davis, S. H. 1974 On the motion of a fluid—fluid interface along a solid surface. J. Fluid Mech. 65, 71.
de Gennes, P. G., 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827.
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, pp. 676680. Oxford University Press.
Gregory, R. D. 1980a The semi-infinite srip x >; 0, -1 < y < 1; completeness of the Papkovich—Fadle eigenfunctions when ϕxx(0,y),ϕyy(0,y) are prescribed. J. Elast. 10, 57.
Gregory, R. D. 1980b The traction boundary-value problem for the elastostatic semi-infinite strip; existence of solution and completeness of the Papkovich—Fadle eigenfunctions. J. Elast. 10, 295.
Hanse, R. J. & Toong, T. Y. 1971 Dynamic contact angle and its relationship to forces of hydrodynamic origin. J. Colloid Interface Sci. 37, 196.
Hardy, W. B. 1919 The spreading of liquids on glass. Philos. Mag. 38, 49.
Hocking, L. M. 1976 A moving fluid interface on rough surface. J. Fluid Mech. 76, 801.
Hocking, L. M. 1977 A moving fluid interface. Part 2. The removal of the force singularity by a slip flow. J. Fluid Mech. 77, 209.
Hocking, L. M. 1981 Sliding and spreading of two-dimensional drops. Q. J. Mech. Appl. Maths. 34, 37.
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillary. Q. J. Mech. Appl. Maths 36, 55.
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 motion of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401.
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.
Jansons, K. M. 1988 Determination of the macroscopic (partial) slip boundary condition for a viscous flow over a randomly rough surface with a perfact slip boundary condition microscopically. Phys. Fluids 31, 15.
Joseph, D. D. 1977 The convergence of biorthogonal series for biharmonic and Stokes flow edge problems. Part. I. SIAM J. Appl. Maths 33, 337.
Joseph, D. D. & Sturges, L. 1975 The free surface on a liquid filling a trench heated from its side. J. Fluid Mech. 69, 565.
Joseph, D. D. & Sturges, L. 1978 The convergence of biorthogonal series for biharmonic and Stokes flow edge problems. Part II. SIAM J. Appl. Maths 34, 7.
Joseph, D. D., Sturges, L. & Warner, W. H. 1982 Convergence of biorthogonal series of biharmonic eigenfunctions by the method of Titchmarsh. Arch. Rat. Mech. 78, 223.
Kafka, F. Y. & Dussan, V. E. B. 1979 On the interpretation of the dynamic contact angles in capillaries. J. Fluid Mech. 95, 539.
Lowndes, J. 1980 The numerical simulation of the steady motion of the fluid meniscus in a capillry tube. J. Fluid Mech. 101, 631.
Ngan, C. G. 1985 An assessment of the proper modelling assumptions for the spreading of liquids on solid surfaces. PhD thesis, University of Pennsylvania.
Ngan, C. G. & Dussan, V. E. B. 1982 On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech. 118, 27.
Ngan, C. G. & Dussan, V. E. B. 1984 The moving contact line with a 180 degree advancing contact angle. Phys. Fluids 27, 2785.
Pismen, L. M. & Nir, A. 1962 Motion of a contact line. Phys. Fluids 25, 3.
Richardson, S. 1973 On the no-slip boundary condition. J. Fluid Mech. 59, 707.
Rose, W. & Heins, R. W. 1962 Moving interfaces and contact angle rate-dependence. J. Colloid Interface Sci. 17, 39.
Smith, R. C. T. 1952 The bending of a semi-infinite strip. Austral. J. Sci. Res. A 5, 227.
White, C. 1983 Integration of stiff differential equations in chemical reactor modelling. PhD thesis, University of Pennsylvania.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

On the dynamics of liquid spreading on solid surfaces

  • C. G. Ngan (a1) and E. B. Dussan V. (a2)

Metrics

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.