Numerical Simulation Study of the Effect of Liquid Depth on the Stability of Thermal Marangoni Convection in a Shallow Cavity

Abstract

The effect of liquid depth on thermal Marangoni convection stability in a shallow cavity was investigated via three-dimensional (3D) numerical simulations. The liquid film in the cavity is silicone oil with a Prandtl number of 6.7. The cavity is subjected to perpendicular temperature gradients. The simulation results show that, for thinner films, a primary instability appears when the flow transits from a steady state to a 3D oscillatory pattern. In thicker films, a secondary instability appears when the flow changes from oscillatory to chaotic. The critical thermal Marangoni numbers (at which transitions occur) of thin films are higher than those of thicker films. The simulation results imply that the uniform steady flow behavior in thinner films can be utilized to a benefit in coating and thin film applications, while the chaotic flow behavior predicted in thicker films can be utilized to obtain better mixing in applications such as lubrication and mixing.