Instabilities of thermocapillary liquid layers with two free surfaces

The instabilities of thermocapillary liquid layers with two free surfaces are examined by linear stability analysis. The surface tension is big enough to keep the liquid surfaces non-deformable. The effect of vertical temperature difference between two interfaces (Q) is considered. The critical parameters of preferred modes are determined, which depend on the Prandtl number (Pr) and Biot number (Bi). When Q=0, the preferred modes are the oblique wave at small Pr and the streamwise wave at large Pr. The perturbation is symmetric and anti-symmetric at small and large Pr, respectively. When Q>0, the preferred mode changes from the oblique wave to the streamwise wave, and finally the spanwise stationary mode with the increase of Pr. The instability mechanism is discussed. Comparisons are made with the liquid layer with a single free surface and previous results by numerical simulations and experiments. (C) 2021 Elsevier Ltd. All rights reserved