Improved approximations for flows of thin films

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Title: Improved approximations for flows of thin films
Author: Lowry, Christine Elizabeth
Abstract: Film flow equations are simplified equations for modeling the flow of thin liquid films. They are ordinary differential equations in terms of the film thickness. Typically, the boundary-layer approximation to the Navier-Stokes equation is employed, a velocity profile is assumed, and conservation of momentum then yields a film equation. Surface tension is usually important in which case the film equations are third order. Existing film equations are adequate when the substrate is not moving and when the substrate is moving in the absence of inertial effects. These equations are deficient in the important case of a moving substrate when inertia is included and the film connects with a reservoir of liquid that is substantially hydrostatic. In that case, the inertial terms of the film equations do not die off as the film thickens, unlike the viscous terms or the inertial terms when the wall is stationary, and so a hydrostatic reservoir is not described. The main goals of this thesis are to explore the cause of the deficiency and, if possible, propose a remedy.
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Date: 2010-07-28

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