液滴热毛细迁移的准定态假设适用性与稳定性研究

Quasi-steady state assumption has been widely applied in the studies on thermocapillary migration of bubbles and drops, since it was proposed in thermocapillary bubble migration at small Marangoni(Ma) numbers. However, its applicability at any Reynolds(Re) and Ma numbers has not been mentioned up to now. This defect may be the key point of the qualitative difference among the results of the steady theoretical analysis, numerical simulation and space experimental investigation at large Ma numbers. This project focuses on whether the steady solutions exist in the differential momentum and energy equations with boundary condisions for the thermocapillary droplet migration in the moving-body coordinate system as the changes of Re and Ma numbers, i.e., whether the solutions can satisfy the global integral momentum and energy conversation with boundary conditions. The physical mechanism for the applicable or not of quasi-steady state assumption will be determined. For the Re and Ma numbers, where the quasi-steady state assumption is not applicable, the force and temperature fileds inside/outside the droplet will be changed, so that the steady solutions can satisfy the global integral momentum and energy conversation with boundary conditions. The steady solutions are then determined. For the special (small and large) Re and Ma numbers, stability of steady thermocapillary droplet migration will be analyzed to show the thersholds of stabilty. It will be provided whether the perturbation solutions can change the global integral momentum and energy conversation with boundary conditions. The relation of the stibility of the steady solutions to the applicability of quasi-steady state assumtption will be determined.

自从在研究小Marangoni(Ma)数气泡热毛细迁移时提出准定态假设以来，定态迁移已被广泛地应用于气泡、液滴热毛细迁移的研究中，然而在任意Reynolds(Re)和Ma数下它的适用性却未被言及，这可能是导致现有的大Ma数下液滴热毛细迁移的定态理论分析和数值模拟与空间实验测量结果存在定性差别的根本原因。本项目通过采用理论分析和数值模拟方法研究随体坐标系下液滴热毛细迁移微分形式的动量和能量方程及边界条件随着Re和Ma的变化是否存在定态解，即定态解能否满足整体积分形式的动量和能量平衡，阐明准定态假设适用与否的物理机制。对于准定态假设不适用的Re和Ma数范围，通过改变液滴内或外的力场和温度场使得定态解满足整体动量和能量平衡并求出定态解。对于特定的（小和大）Re和Ma数确定定态液滴热毛细迁移的稳定性，给出稳定性判据，并分析微扰解能否改变整体动量和能量平衡，揭示定态解稳定性与准定态假设适用性的关系。

围绕着液滴热毛细迁移的准定态假设的适用性的主题开展了系统研究，研究结果包括发现了液滴热毛细迁移存在三个不同物理过程的无量纲时间尺度，而以Marangoni(Ma)数为特征量的热扩散过程时间尺度确定为判定系统演化达到终态的时间判据；数值确定了中等Ma数下液滴热毛细迁移的终态表现为定态，而大Ma数下液滴热毛细迁移的终态仍处于非定常状态，液滴内部温度场保持”冷眼”状态；理论分析了大Ma数下液滴热毛细迁移的动量方程能够获得解析解，而无论假设定态迁移速度与Ma数的关系如何均不能保证其能量方程守恒；理论设计了在外场附加热辐射下大Ma数下液滴热毛细迁移可以达到定态迁移，并求解出其理论解，为实现液滴热毛细迁移的主动控制设计了实验手段；分析了双滴热毛细迁移的物理过程并给出了理论解析解。所设计的液滴主动控制措施为解决实验和理论数值解的历史遗留问题提供了新的诠释途径。