Effects of gravity levels on Marangoni-Stokes flows in Plateau configurations

A numerical model is developed for combined free convection in the Stokes regime, and a solution is derived for a plane configuration. General properties of free convection flows produced by the actions of imposed temperature differences and gravity fields when Stokes regimes prevail are formulated. The model is based on nonelastic, nonmicropolar Newtonian interfacing fluids, negligible bulk viscosity, interfaces that are massless surface phases with a single degree of freedom, and a linear equation of state for the interfacial tension. Use is made of the Boussinesq and constant transport property approximation, and steady motion is assumed. It is shown that, for Plateau conditions, the zeroth order problem is fully linear and Marangoni and buoyancy effects are superposable. A solution is found for the case of plane geometry through application of biorthogonal complex functions. Comparisons are made between Marangoni, buoyant, and combined free convection in terms of streamlines, velocity profiles, and dynamic interface shapes.