Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T04:53:42.857Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of a ridge of fluid

Published online by Cambridge University Press:  26 April 2006

Leslie M. Hocking  and
Michael J. Miksis
Leslie M. Hocking
Affiliation:
Department of Mathematics. University College London, Gower Street, London WC1E 6BT, UK
Michael J. Miksis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability and nonlinear evolution of a ridge of fluid on an inclined plane is investigated. This model was introduced by Hocking (1990). Here we present numerical solutions of the model showing the evolution of the ridge and in some cases the formation of droplets. Also, we investigate the linear stability of the fluid ridge allowing for contact-line motion. We find a preferred wavelength for the linear stability of spanwise disturbances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 247 , February 1993 , pp. 157 - 177
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
Dussan, V. E. B. & Chow, R. T-P. 1983 On the ability of drops and bubbles to stick to non-horizontal surfaces of solids. J. Fluid Mech. 137, 1– 29.Google Scholar
Greenspan, H. P. 1978 On the motion of a small viscous droplet that wets a surface, J. Fluid Mech. 84. 125– 143.CrossRefGoogle 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. & Miksis, M. J. 1991 The effect of the contact line on droplet spreading. J. Fluid Mech. 223, 57– 81.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. 1990 Spreading and instability of a viscous fluid sheet. J. Fluid Mech. 211, 373– 392 (referred to herein as I).Google Scholar
Hocking, L. M. 1992 Rival contact-angle models and the spreading of drops. J. Fluid Mech. 239, 671– 681.Google Scholar
Huppert, H. E. 1982 Flow and instability of viscous gravity currents down a slope. Nature 300, 427– 429.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water I. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1– 26.Google Scholar
Miksis, M. J., Vanden-Broeck, J.-M. & Keller, J. B. 1981 Axisymmetric bubble or drop in a uniform flow. J. Fluid Mech. 108, 89– 100.Google Scholar
Silvi, N. & Dussan, V., E. B. 1985 On the rewetting of an inclined solid surface by a liquid. Phys. Fluids 28, 5– 7.Google Scholar
Troian, S. M., Herbolzheimer, E., Safran, S. A. & Joanny, J. F. 1989 Fingering instabilities of driven spreading films. Europhys. Lett. 10, 25– 30.Google Scholar
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.Google Scholar