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On the dynamics of liquid spreading on solid surfaces

Published online by Cambridge University Press:  26 April 2006

C. G. Ngan  and
E. B. Dussan V.
C. G. Ngan
Affiliation:
Millipore Corporation, 80 Ashby Road, Bedford, MA 01730, USA
E. B. Dussan V.
Affiliation:
Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108, USA
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 191 - 226
Copyright
© 1989 Cambridge University Press

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References

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.Google Scholar
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.Google Scholar
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.Google Scholar
Cox, R. G. 1986 The dynamics of the spreading of a liquid on a solid surface. J. Fluid Mech. 168, 169.Google Scholar
Dussan, V. E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665.Google Scholar
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid. Mech. 11, 371.Google Scholar
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.Google Scholar
de Gennes, P. G., 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827.Google Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, pp. 676–680. 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.Google Scholar
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.Google Scholar
Hanse, R. J. & Toong, T. Y. 1971 Dynamic contact angle and its relationship to forces of hydrodynamic origin. J. Colloid Interface Sci. 37, 196.Google Scholar
Hardy, W. B. 1919 The spreading of liquids on glass. Philos. Mag. 38, 49.Google Scholar
Hocking, L. M. 1976 A moving fluid interface on rough surface. J. Fluid Mech. 76, 801.Google Scholar
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.Google Scholar
Hocking, L. M. 1981 Sliding and spreading of two-dimensional drops. Q. J. Mech. Appl. Maths. 34, 37.Google Scholar
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillary. Q. J. Mech. Appl. Maths 36, 55.Google Scholar
Hocking, L. M. & Rivers, A. D. 1982 The spreading of a drop by capillary action. J. Fluid Mech. 121, 425.Google Scholar
Huh, C. & Mason, S. G. 1977 The steady motion of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401.Google Scholar
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.Google Scholar
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.Google Scholar
Joseph, D. D. 1977 The convergence of biorthogonal series for biharmonic and Stokes flow edge problems. Part. I. SIAM J. Appl. Maths 33, 337.Google Scholar
Joseph, D. D. & Sturges, L. 1975 The free surface on a liquid filling a trench heated from its side. J. Fluid Mech. 69, 565.Google Scholar
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.Google Scholar
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.Google Scholar
Kafka, F. Y. & Dussan, V. E. B. 1979 On the interpretation of the dynamic contact angles in capillaries. J. Fluid Mech. 95, 539.Google Scholar
Lowndes, J. 1980 The numerical simulation of the steady motion of the fluid meniscus in a capillry tube. J. Fluid Mech. 101, 631.Google Scholar
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.Google Scholar
Ngan, C. G. & Dussan, V. E. B. 1984 The moving contact line with a 180 degree advancing contact angle. Phys. Fluids 27, 2785.Google Scholar
Pismen, L. M. & Nir, A. 1962 Motion of a contact line. Phys. Fluids 25, 3.Google Scholar
Richardson, S. 1973 On the no-slip boundary condition. J. Fluid Mech. 59, 707.Google Scholar
Rose, W. & Heins, R. W. 1962 Moving interfaces and contact angle rate-dependence. J. Colloid Interface Sci. 17, 39.Google Scholar
Smith, R. C. T. 1952 The bending of a semi-infinite strip. Austral. J. Sci. Res. A 5, 227.Google Scholar
White, C. 1983 Integration of stiff differential equations in chemical reactor modelling. PhD thesis, University of Pennsylvania.