Instability of Viscoelastic Thermocapillary Liquid Layers with Two Free Surfaces

In microgravity environments, dual-free surface liquid layer is a promising method for growing new material crystals, stability analysis of its flow is of great significance for applications such as thin film crystallization. The instability of viscoelastic thermocapillary liquid layers with two free surfaces is examined by linear stability analysis. The critical Marangoni number (Ma_c) is determined as a function of the elastic number (ε) and the Prandtl number (Pr). The flow fields and energy mechanisms of preferred modes are analyzed. Three kinds of instabilities are found: oblique wave, streamwise wave and spanwise stationary mode, whose properties are all significantly affected by the elasticity. The preferred modes are the oblique wave and streamwise wave at small and large Pr. When Pr = 1, the preferred mode changes from the oblique wave to the streamwise wave, and finally the spanwise stationary mode with the increase of ε. At small Pr, the hot spots move from the surface to the interior of the liquid layer with the increase of ε. The effect of the ratio ($\zeta $) of solvent viscosity to the total viscosity on the instability mechanism and the preferred modes are demonstrated. When Pr is large, the increase of $\zeta $ often makes the flow more stable. However, for small and moderate Pr, the flow is destabilized by the increase of $\zeta $ at weak ε. Energy analysis shows that at the small Pr, the perturbation stress at the weak ε dissipates energy while it provides energy at the strong ε. At the moderate and large Pr, the primary source of energy for perturbation energy is the work done by surface tension, and the contribution of the base flow can be neglected. Comparing the double free surface liquid layer with the single free surface liquid layer, it is found that the elastic instability of the double free surface liquid layer is more prominent when the Ma number is small.