Faculty Advisor

Burt Tilley

Abstract

We consider the flow of two immiscible fluids in a thin inclined channel subject to gravity and a change in pressure. In particular, we focus on the effects of Navier slip along the channel walls on the long-wave linear stability. Of interest are two different physical scenarios. The first corresponds to two incompressible fluid layers separated by a sharp interface, while the second focuses on a more dense fluid below a compressible gas. From a lubrication analysis, we find in the first scenario that the system is stable in the zero-Reynolds number limit with the slip effects modifying the decay rate of the stable perturbation. In the case of the Rayeligh-Taylor problem, slip along the less dense fluid wall has a destabilizing effect. In the second scenario, fluid inertia is pertinent, and we find neutral stability criteria are not significantly affected with the presence of slip.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2013-04-25

Accessibility

Unrestricted

Subjects

lubrication analysis, linear stability, laminar fluid flow

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