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The Effects of a Navier-Slip Boundary Condition on the Flow of Two Immiscible Fluids in a Microchannel

By Charles Edward Fisher

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

Topics: lubrication analysis, linear stability, laminar fluid flow
Publisher: Digital WPI
Year: 2013
OAI identifier: oai:digitalcommons.wpi.edu:etd-theses-1293
Provided by: DigitalCommons@WPI

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