STABILITY ANALYSIS OF THERMOCAPILLARY LIQUID LAYERS WITH TWO FREE SURFACES FOR A BINGHAM FLUID

Thermocapillary convection refers to the fluid motion driven by the temperature-induced surface tension gradient. It mainly exists in the microgravity environment such as space or small-scale flow dominated by surface tension. In many industrial fields, such as crystal growth, polymer processing, inkjet printing, and microfluidic, product quality is closely related to thermocapillary convection. 3D printing is an important technology in space manufacturing, which can support the long-term manned operation and maintenance of the space station in orbit and realize on-demand manufacturing. This paper takes the spatial 3D printing of polymer fluids as the application background, the stability of thermocapillary liquid layers with two free surfaces for a Bingham fluid is studied by using the linear stability analysis. The function relation between the critical Marangoni number (Ma_c) and Prandtl number (Pr) at different Bingham number (B) is obtained. The flow field and energy mechanism of the critical mode are analyzed. It is found that the critical modes include the streamwise wave and the oblique wave, which are related to B, Bi and the vertical temperature difference (Q) between two interfaces. The increase of B and Bi will enhance the stability. When Q = 0, there are two kinds temperature distribution, which are symmetric and antisymmetric. When Q > 0, the increase of Pr will destabilize the flow. The perturbation temperature is distributed in the whole flow field at small Pr, and the perturbation temperature is zero in the plug region at large Pr. The energy analysis shows that the main energy source of perturbation energy is the work done by surface tension,but for small Pr, the basic flow also makes some contributions.