EFFECTS OF GEOMETRY AND UNIDIRECTIONAL BODY FORCES ON THE STABILITY OF LIQUID LAYERS
STANFORD UNIV CA
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The stability of liquid layers with a prescribed interface geometry in the presence of surface tension and unidirectional body forces is investigated theoretically by means of a small vibration analysis. The fluid of the layers is assumed to be incompressible and inviscid and the flow irrotational. Particular emphasis is given to the effects of geometry and unidirectional body forces on the stability of such layers. They are studied by means of a semi-inverse method which allows the exact determination of particular eigenvibrations. Following the classical method of investigating the stability of systems, equations of motion are established for small perturbations of the equilibrium configuration and the boundary conditions for both two and three-dimensional layers with interface surfaces having a constant mean curvature are formulated. Pertinent equations are linearized and expressed in terms of the velocity potential. By separating the time and space variables, the vibration problem is reduced to an eigenvalue problem.
- Fluid Mechanics