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The effect of the contact line on droplet spreading

Published online by Cambridge University Press:  26 April 2006

Patrick J. Haley  and
Michael J. Miksis
Patrick J. Haley
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Michael J. Miksis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

The motion of the free surface of a viscous droplet is investigated. By using lubrication theory a model is developed for the motion of the free surface which includes both the effect of slip and the dependence of the contact angle on the slip velocity. We solve the resulting nonlinear partial differential equation in several ways. First we investigate the initial motion of the drop at a non-equilibrium contact angle using the method of matched asymptotics. Then we develop a pseudo-spectral method to numerically solve the full nonlinear system. The dependence of the spreading rate of the drop on the various physical parameters and for different slip models is determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 57 - 81
Copyright
© 1991 Cambridge University Press

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References

Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A., 1988 Spectral Methods in Fluid Dynamics. Springer.
Chen, J.: 1988 Experiments on a spreading drop and its contact angle on a solid. J. Colloid Interface Sci. 122, 60–72.Google Scholar
Davis, S. H.: 1980 Moving contact lines and rivulet instabilities. Part 1. The static rivulet. J. Fluid Mech. 98, 225–242.Google Scholar
Davis, S. H.: 1983 Contact-line problems in fluid mechanics. Trans. ASMS E: J. Appl. Mech. 50, 977–982.Google Scholar
Dussan, V. E. B.: 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665–684.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, 371–400.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, 71–95.Google Scholar
Ehrhard, P. & Davis, S. H., 1990 Non-isothermal spreading of liquid drops on horizontal plates. Applied Mathematics Tech. Rep. 8920. Northwestern University, Evanston, IL.Google Scholar
de Gennes, P. G.: 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
Gottlieb, D. & Orszag, S. A., 1977 Numerical Analysis of Spectral Methods: Theory and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 26, SIAM.
Greenspan, H. P.: 1978 On the motion of a small viscous droplet that wets a surface. J. Fluid Mech. 84, 125–143.Google Scholar
Greenspan, H. P. & McCay, B. M., 1981 On the wetting of a surface by a very viscous fluid. Stud. Appl. Maths 64, 95–112.Google Scholar
Haley, P. J.: 1990 A numerical investigation of contact line motion. Thesis, Department of Applied Mathematics, Northwestern University, Evanston, IL.
Hocking, L. M.: 1977 A moving fluid interface. Part 2. The removal of the force singularity by a slip flow. J. Fluid Mech. 77, 209–229.Google Scholar
Hocking, L. M.: 1981 Sliding and spreading of thin two-dimensional drops. Q. J. Mech. Appl. Maths 34, 37–55.Google Scholar
Hocking, L. M.: 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Maths 36, 55–69.Google Scholar
Hocking, L. M. & Rivers, A. D., 1982 The spreading of a drop by capillary action. J. Fluid Mech. 121, 425–442.Google Scholar
Hoffman, R. L.: 1975 A study of the advancing interface. I. Interface shape in liquid-gas systems. J. Colloid Interface Sci. 50, 228–241.Google Scholar
Huh, E. & Mason, S. G., 1977 The steady movement of a liquid meniscus in a capillary tube. J. Fluid Mech. 81, 401–419.Google Scholar
Huh, E. & Scriven, L. E., 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.Google Scholar
Jansons, K. M.: 1986 Moving contact lines at non-zero capillary number. J. Fluid Mech. 167, 393–407.Google Scholar
Johnson, R. E., Dettre, R. H. & Brandreth, D. A., 1977 Dynamic contact angles and contact angle hysteresis. J. Colloid Interface Sci. 62, 205–212.Google Scholar
Koplik, J., Banavar, J. R. & Willemsen, J. F., 1989 Molecular dynamics of a fluid flow at solid surfaces. Phys. Fluids A 1, 781–794.Google Scholar
Rosenblat, S. & Davis, S. H., 1985 How do liquid drops spread on solids? In Frontiers in Fluid Mechanics (ed. S. H. Davis & J. L. Lumley), pp. 171–183. Springer.
Starov, V. M.: 1983 Spreading of droplets of nonvolatile liquids over a flat surface. Colloid. J. USSR (English Transl.) 45, 1009.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
Young, G. W. & Davis, S. H., 1987 A plate oscillating across a liquid interface: eifects of contact-angle hysteresis. J. Fluid Mech. 174, 327–356.Google Scholar