Stability of Marangoni Convection in a Fluid Layer with Temperature-Dependent Viscosity

The onset of steady Marangoni convection induced by surface tension gradients along the upper surface of a horizontal layer of fluid have been the subject of a great deal of theoretical work since the pioneering theoretical investigations of Pearson (1958). The system is heated from below and cooled from above. The purpose of the thesis is to study in detail the onset of Marangoni convection with temperature-dependent viscosity. Few cases of boundary conditions at the bottom surface are studied which are conducting with no-slip, conducting with free-slip and insulating with no-slip. We perform a detailed numerical calculation of the marginal stability curves. We showed that the effect of a temperature-dependent viscosity may be either stabilizing or destabilizing depending on the measurement of the relative variation of viscosity in the fluid volume (viscosity group, Rv). We also present the problem to a case where the fluid layer is overlying a solid layer and here, we undertake a detailed investigation to look at the effect of the thickness or the iv conductivity of the solid layer to the onset of Marangoni convection with temperature-dependent viscosity. Again we perform a detailed numerical calculation of marginal stability curves. We showed that the coupled effect of the solid layer depth (or its conductivity) and a temperature-dependent viscosity (with negative sign of variation of viscosity with temperature) is to stabilize the fluid layer.

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