INSTABILITY IN THE SOLUTAL-THERMOCAPILLARY LIQUID LAYER WITH TWO FREE SURFACE

Solute-thermocapillary convection is a flow driven by a surface tension gradient caused by uneven concentration and temperature distribution at the fluid interface. It mainly appears in microgravity environment space or small-scale flow where the surface tension dominates, such as crystal growth, microfluidic, alloy pouring and solidification, organic thin liquid film growth, etc. The stability of this flow is of great significance of these applications. In the present work, the convective instability in the solutal-thermocapillary liquid layer with two free surfaces is examined by linear stability analysis. The relation between the critical Marangoni number and the Prandtl numbers (Pr) is obtained at different capillary ratio (η). The critical modes of solute-thermocapillary flow and pure thermocapillary flow are quite different. The former are downstream streamwise wave, upstream streamwise wave, spanwise stationary mode and upstream oblique waves, but the latter are upstream oblique waves and upstream streamwise wave. When Pr is larger, the flow stability will be weaker when Pr increases. At other parameters, the flow stability will be stronger when Pr increases. In the middle or low Pr, solute capillary force makes the flow more unstabler; at high Pr, solute capillary force may make the flow more stable. Flow stability does not change monotonously from η. In most cases, the distributions of perturbation concentration field and temperature field are similar. The energy analysis shows the main energy source of perturbation kinetic energy is the surface capillary force, but the work done by solute capillary force and thermal capillary force may be either positive or negative.