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