Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

Dewetting on the Surface of Rutile

After annealing a continuous SiO2 film on the (001) surface of TiO2, the film dewets and then spreads to form a complex pattern. The final droplet morphology displays a densely branching morphology similar to those seen in computer-simulated models. It is proposed that Bénard-Marangoni convection cells form within the film before dewetting occurs. The formation of Bénard-Marangoni convection cells prior to dewetting results in the uniform size and spacing of the droplets on the surface. These convection cells form at temperature when the TiO2 substrate dissolves into the SiO2 thin film. The change in composition results in regions of differing surface tensions and therefore leads to the formation of the convection cells.