非平整基底上含表面活性剂的超薄液膜流动过程及稳定性研究

The flow and stability of ultrathin liquid films resting on solid substrates in microscale is of enormous significance in engineering and industrial applications, including coating, the thermal management of electronic devices, precision manufacturing techniques, heat exchangers,micro electro mechanical systems(MEMS). While the film thickness is in the scale of nanometers, the effects of intermolecular force (disjoining pressure), topography surface and impurity of liquid (the particles in the liquid serve as surface actives, or surfactants) on flow dynamics and stability should be considered. Although there have been lots of theoretical studies for flows of thin viscous films over surface features, about the spreading of surfactant solutions and on the effect of disjoining pressure separately, to date there has not been a complete study of the thin film flow considering the three important factor simultaneously. In this project, the dynamics and stability of ultrathin liquid films over topography will be studied in the presence of insoluble surfactants. The surfactants can drive a flow due to surface tension gradients and additionally the coefficients of the intermolecular potential can depend on the surfactant concentration. Coupled evolution equations for the film thickness and surfactant concentration will be derived using lubrication theory while there will be additional two terms relating to disjoining pressure and the non-flat wall. These equations will be numerical calculated over different substrates featuring rectangle trench or mound for steady flow and spreading process, then the combined effects of disjoining pressure, topography and surfactants on ultrathin film can be obtained. On the base of that, because of the base states of the ultrathin film are spatially non-uniform, the non-modal linear stability analysis will be constructed by calculating the transient amplification of perturbations and results on whether the thin film is stable or unstable under complicated conditions will be derived. Our investigations will provide theoretical foundations for the need to precise control of flow, making the fluid to have expected surface topography on an ever decreasing scale surface for different technological applications.

微尺度意义上超薄液膜的流动特性和稳定性对以微机电系统（MEMS）为主的技术发展和应用具有重要的理论意义。当液膜厚度为纳米级时，常常需要同时考虑分子间作用力（分离压）、基底表面性质以及液膜所含表面活性剂对流动特性和稳定性的影响，但目前这类研究尚未开展。为此，本课题研究非平整基底上含表面活性剂的超薄液膜流动过程及其稳定性，考虑与活性剂浓度有关的分离压的作用，采用润滑理论推导液膜厚度及表面活性剂浓度的演化方程。通过对所建立的演化方程在具有矩形沟槽和突起的基底表面进行稳态和非稳态（铺展）过程的数值求解，揭示分离压、基底特征和表面活性剂三种因素的耦合对超薄液膜流动的独特影响；采用非模态稳定性理论计算液膜厚度和活性剂浓度分布不均匀情况下，扰动能量的增长特性，分析流动的稳定性特征。本课题旨在为各应用领域实现微尺度液膜的精确控制提供理论基础。

本课题采用理论建模和数值计算相结合的方法研究了非平整基底上含表面活性剂的超薄液膜的流动过程，旨在为各应用领域实现微尺度液膜的精确控制提供理论基础。本项目取得的主要研究成果有：（1）采用润滑理论，建立了非平整基底上含不溶性表面活性剂的液滴/液膜流动（铺展）过程的数学模型，该模型考虑了活性剂浓度对表面张力的影响，以及液膜厚度超薄情况下分离压的作用，且分离压表达式与表面活性剂的浓度相关。该模型是以液膜厚度和表面活性剂浓度为特征量构成的无量纲形式的演化方程组。在此基础上，采用摄动展开法构建了上述特征量对应扰动量的演化方程组，作为采用非模态稳定性理论进行稳定性分析的基础。（2）通过数值计算，研究了以重力或活性剂浓度为驱动力时，液膜的稳态流动过程，得到了多种形式的非平整基底影响下液膜的表面形貌特征，如流经负向台阶前，液膜会先形成隆起的波峰；流经正向台阶前，液膜会先形成凹陷的波谷；流经连续的波纹状表面时，液膜表面也会形成波峰、波谷连续分布的形态，即基底形貌将在液膜表面有所反映。在重力，活性剂浓度梯度和毛细力同时存在时，毛细力的作用要强的多。（3）通过数值计算，研究了存在多个驱动力情况下，液膜/液滴铺展过程的演化特征。结果表明，不同的基底形貌都将在液膜外形上有所反映，波纹状基底上的液膜铺展速度最快，连续凹槽基底上次之，平整基底上的液膜铺展速度最慢，增加凹槽基底高度和宽度将加速铺展，分离压导致铺展更快，结合压导致铺展速度降低。非平整基底上液膜的铺展速度快于液滴的铺展速度。（4）通过数值计算，研究了存在多个驱动力情况下，液滴铺展过程的稳定性，当基底为正弦波纹状时，较小的扰动波数、较大的基底高度和适当的基底波数对铺展稳定性具有有利的影响；考虑分离压时，在小扰动波数下，减小引力强度系数，液滴铺展稳定性上升，而减小斥力强度系数对液滴铺展稳定性有不利影响，但在大扰动波数下，则存在相反的规律。依托本项目，目前已发表学术论文22篇，其中SCI检索论文6篇，包括1篇发表在本学科领域国际权威刊物《Physics of Fluids》上的国际领先水平论文；除此之外Ei检索7篇，参加国际会议4次，已培养研究生5人，其中1人被评为河北省优秀硕士论文，5人被评为我校优秀硕士论文。并且在项目执行后期，顺利完成原定研究计划后，开始了原计划未列出、但与本课题相关的研究工作，将该项目推向纵深发展