耦合多场动态变化的固着双组分液滴蒸发对流失稳机理研究

In order to improve the production accuracy impaired by the coffee-ring effect in evaporating sessile droplets, the flow control inside sessile droplets has been studied chronically in industrial circle (such as ink-jet printing field). In the evaporation of sessile solution droplets, there are the effects of the thermo-solutal Marangoni convection and the dynamic changes of droplet shape, flow, temperature, concentration and density, thus it is very difficult to completely describe the internal flow of sessile droplets by an effective theoretical model. Currently, the convection control in the evaporation process of sessile droplets is still in an exploration stage. The present project will build a single-phase Marangoni convection model in evaporating sessile bi-component droplets, which is solved by the spectral element method. The dynamic mesh technology is used to research the free-surface deformation and the thermal and mass transport in the evaporating progress, and the linear stability theory is used to reveal the instability mechanism of Marangoni convection in the initial transition. Moreover, experiments of the sessile droplet evaporation will be designed to validate the numerical results. This project attempts to throw light on the internal heat and mass transport process and explore the flow instability mechanism in evaporating sessile droplets, so as to provide theoretical guidance for optimizing the scheme of controlling the internal flow in the droplet evaporation.

工业领域（如喷墨打印）一直在研究固着液滴内部流动的控制方式，以解决因液滴蒸发产生咖啡环效应而导致工艺精度降低的问题。溶液液滴蒸发过程中含有热-溶质Marangoni对流，同时液滴形状、液滴内流场、温度场、组分浓度场及溶液密度场也处于动态变化，这使得当前缺乏合适的理论模型来完整描述固着液滴的内部流动，因而目前对固着液滴蒸发过程的对流失稳机理研究及其控制仍处于探索阶段。本项目将建立固着双组分液滴蒸发过程的单相Marangoni对流模型，以谱元法和动网格技术研究蒸发液滴表面的动态变化及其内部热质输运，并结合线性稳定性理论揭示液滴内部Marangoni对流转捩初期的失稳机理；同时，本项目也将设计固着液滴蒸发实验，实现对数值结果的验证。本项目试图揭示固着液滴蒸发过程的内部热质输运过程和流动失稳机理，这为控制蒸发液滴内部流动的优化方案提供理论指导。

长期以来，固着液滴蒸发问题被流体力学领域高度关注，其中涉及的Marangoni对流则一直是工业应用研究中的难点和热点。基于恒温缓慢蒸发假设，本项目建立了固着双组份液滴Marangoni对流模型来描述咖啡环现象；针对液滴的几何特性，发展出一种适用于广义三角形计算域的Legendre谱元法，并结合动网格技术模拟了固定接触线模式下液滴内溶质的动态变化现象；运用线性稳定性分析捕捉了一系列Marangoni对流的失稳临界参数，并通过能量分析相应Marangoni对流在转捩初期的失稳机理，发现两种以上的流动驱动力会共存并相互竞争，使得流动失稳机制更加复杂，并可能使流动出现多次失稳现象。相关结果揭示了Marangoni对流的失稳机理，丰富了分岔理论，为Marangoni对流的流动控制提供指导，也为解决大量相关流体力学问题奠定基础。