THE HYDRODYNAMIC STABILITY OF A THIN FILM OF LIQUID IN UNIFORM SHEARING MOTION,
Abstract
The stability problem for a thin film of liquid having a linear mean-velocity profile and bounded by a fixed wall and free surface is solved asymptotically for large values of the Reynolds number R. The analysis is similar to that for plane Couette flow, but instability occurs for sufficiently large values of R in accordance with Heisenberg's criterion that neutral disturbances having finite wave numbers and phase velocities for R = infinity are necessarily unstable as R approaches infinity. It is found that a sufficient condi tion for stability is W<3, where W is the Weber number based on the mean speed at the free surface and the depth of the film. The minimum critical Reynolds number, also based on free surface speed and film depth, is found to be R = 203. Brief consideration also is given to the timerate-of-growth of unstable disturbances and to the lighter fluid that, in actual configurations, is responsible for the shear in the film. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 18, 1959
- Accession Number
- AD0605982
Entities
People
- John W. Miles
Organizations
- TRW Inc.