Bingham流体双自由面热毛细液层的稳定性分析

热毛细对流是流体界面温度分布不均导致的表面张力梯度驱动的流动. 它主要存在于空间等微重力环境或小尺度流动等表面张力占主导的情况中. 在很多工业领域, 如晶体生长、聚合物加工、喷墨打印、微流控, 产品质量都与热毛细对流密切相关. 空间3D打印是太空制造的重要技术, 可以支持空间站的在轨长期有人照料的运行和维护, 实现按需制造. 本文以聚合物流体的空间3D打印为应用背景, 采用线性稳定性理论研究了Bingham流体双自由面热毛细液层的稳定性, 得到了在不同Bingham数(B)下的临界Marangoni数(Ma_c)与Prandtl数(Pr)的函数关系,分析了临界模态的流场和能量机制. 研究发现: 该流动的临界模态包括流向波和斜波模态, 与B, Bi和两界面垂直方向上的温差(Q)相关. B和Bi的增加会增强热毛细对流的稳定性. 当Q = 0时, 扰动温度分布分成对称和反对称两种情况. 当Q > 0时, Pr的增加会减弱流动稳定性. 在小Pr情况下, 扰动温度分布在整个流场, 在大Pr情况下, 扰动温度在栓塞区为零. 能量分析表明: 扰动动能的主要能量来源是表面张力做功, 但小Pr数下基本流也有一定贡献. 

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.