THE RAYLEIGH-TAYLOR STABILITY OF CONFINED VISCOUS FLUIDS WITH AN INTERFACE,

Abstract

The paper is concerned with the interfacial stability of two stationary superposed viscous fluids confined within a rigid container and subject to both capillary and gravity forces, the gravitational force being directed from the heavier toward the lighter fluid. The stability of a static 'equilibrium' interface when subject to a small disturbance is first posed as a linear initial boundary value problem and the solution obtained in terms of the normal modes associated with a normal mode analysis. The normal modes problem is then recast as a variational problem for the disturbance growth rates. Two parameters appear, the Bond number, and a viscous parameter. The linearization requires the viscous parameter to be of unit order. Using the method of undetermined functions, an approximate solution of the variational problem is obtained for the particular case of a right circular cylindrical container and a flat interface. The unstable growth rates are calculated and the critical Bond number determined to be 14.67. It is found that the viscous forces stabilize the interface. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0658548

Entities

People

  • Richard J. Prutow
  • Simon Ostrach

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Containers
  • Microvessels
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.