Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T18:25:02.154Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability and chaotic behaviour in a free-surface flow

Published online by Cambridge University Press:  21 April 2006

W. G. Pritchard
W. G. Pritchard
Affiliation:
Mathematics Research Center, University of Wisconsin-Madison, 610 Walnut Street, Madison, WI 53705 Permanent address: Department of Mathematics, University of Essex, Colchester CO4 3SQ, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes some experimental observations of free-surface flows arising when fluid is poured over the end of a flat plate into a reservoir well below the plate. This class of flows was found to be highly unstable with over seven hundred qualitatively different flows being observed in the experiment. At very small values of the flux the liquid fell from the plate into the reservoir in the form of droplets which developed periodically at a number of sites on the underside of the plate. As the flux was increased these 'sites’ were able to sustain continuous, unbroken streams, and combinations of drip sites and continuous streams were possible. At still larger values of the flux there was a tendency for the liquid to fall in 'sheets’ and several combinations of’ sheet flows’ and continuous streams were observed, some of which flows exhibited a rather chaotic temporal behaviour. At even larger flux values the flow resembled that of the classic waterfall, but here there were also some unexpected instabilities where the attachment line of the free surface of the liquid with the plate developed corrugations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 165 , April 1986 , pp. 1 - 60
Copyright
© 1986 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

Cuvelibr, C. 1981 On the numerical solution of a capillary free boundary problem governed by the Navier-Stokes equations. Seventh Intl Conf. on Num. Methods in Fluid Dynamics (ed. W. C. Reynolds & R. W. MacCormack). Lecture Notes in Physics, vol. 141. Springer.
Dutta, A. & Ryan, E. 1982 Dynamics of a creeping Newtonian jet with gravity and surface tension: a finite difference technique for solving steady free-surface flows using orthogonal curvilinear coordinates. AIChE J. 28, 220.CrossRefGoogle Scholar
Jean, M. 1980 Free surface of the steady flow of a Newtonian fluid in a finite channel. Arch. Rat. Mech. Anal. 74, 197.Google Scholar
Jean, M. & Pritchard, W. G. 1980 The flow of fluids from nozzles at small Reynolds numbers. Proc. R. Soc. Lond. A 370, 61.Google Scholar
Kistler, S. 1983 The fluid mechanics of certain coating and related viscous free-surface flows with contact lines. Ph.D. dissertation, University of Minnesota.
Nickell, R. E., Tanner, R. I. & Caswell, B. 1974 The solution of viscous incompressible jet and free-surface flows using finite-element methods. J. Fluid Mech. 65, 189.Google Scholar
Omodei, B. J. 1980 On the die swell of an axisymmetric Newtonian jet. Computers and Fluids 8, 275.Google Scholar
Saito, H. & Scriven, L. E. 1981 Study of coating flow by the finite element method. J. Comp. Phys. 42, 53.Google Scholar
Silliman, W. J. & Scriven, L. E. 1978 Slip of liquid inside a channel exit. Phys. Fluids 21, 2115.Google Scholar
Solonnikov, V. A. 1980 Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container. Math. USSR Izvestia 14, 193.Google Scholar
Tanner, R. I., Lam, H. & Bush, M. B. 1984 On the separation of viscous jets. Phys. Fluids 28, 23.Google Scholar
Yih, C.-S. 1969 Fluid Mechanics: A Concise Introduction to the Theory. McGraw-Hill.