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Viscous fluid instabilities under an elastic sheet Khomenko, Maria

Abstract

This thesis considers the flow of thin fluid film between an elastic sheet and a rigid plane. We derive a mathematical model for the flow from the Navier-Stokes equations using the lubrication approximation and develop numerical and similarity solutions to this problem. An experimental apparatus was developed to investigate this phenomenon, and the results of the mathematical model were compared with experimental data. Chapter 3 examines the evolution of a fixed fluid volume under gravitational forces on a horizontal plane. The evolution of the fluid mass profile and the progression of the fluid front are determined from the numerical solutions, as well as experimentally. The favourable comparison between the numerical solutions and the experimental results establishes the validity of the model. Chapters 4-5 considers the evolution of a thin fluid flow under an elastic on an inclined plane. We establish a traveling wave solution for this flow. A linear stability analysis yields the criterion for the existence of unstable modes and establishes the growth rate and wavelength of the most unstable mode. Instability is promoted by increasing the inclination of the plane. For low angles, the numerical and experimental growth rates were in good agreement, while the wavelengths were experimentally of the same order and numerically computed wavelengths had little variation. The long term behaviour of the fluid front is studied analytically via a similarity solution in Chapter 6.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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