On the stability of thermocapillary convection of a Bingham fluid in an infinite liquid layer

The linear stability of thermocapillary liquid layer of a Bingham-plastic fluid is studied. Due to the yield stress of Bingham fluid, there is a plug region in the flow, which divides the yielded flow into two regions. When the flow is subjected to a small perturbation, the velocity perturbation below the upper surface of plug region is negligible, while the temperature perturbation can be found in all flow regions at moderate and small Prandtl numbers (Pr). The perturbation amplitude of the upper surface of plug region decreases rapidly with the increase of Pr. The preferred modes are the upstream oblique wave and the downstream streamwise wave at small and large Pr, respectively. The effects of the yield stress, gravity and the interfacial heat transfer on the flow stability are discussed. The perturbation amplitude only appears above the plug region, which differs from the cases in the plane Bingham-Poiseuille flow and the thermocapillary liquid layer of a Carreau fluid.