表面弹性对含可溶性活性剂垂直液膜排液的影响

针对含可溶性活性剂的垂直液膜排液过程，在考虑表面弹性作用的基础上，采用润滑理论建立了液膜厚度、表面速度、表面和内部活性剂浓度的演化方程组，通过数值计算分析了表面弹性和活性剂溶解度耦合作用下的液膜演化特征.结果表明：表面弹性是影响可溶性活性剂垂直液膜排液过程中必不可少的因素.排液初期，随表面弹性增加，液膜初始厚度增大，表面更趋于刚性化.随排液进行，弹性不同的液膜呈现不同的典型排液特征：当弹性较小时，液膜上部表面张力高，下部表面张力低，产生正向的马兰戈尼效应，与重力作用相抗衡.当弹性较大时，膜上部表面张力低，下部表面张力高，产生逆向的马兰戈尼效应，促使液膜排液加速，更易发生失稳.活性剂溶解度通过控制液膜表面的活性剂分子吸附量，进而影响表面弹性：当活性剂溶解度较大时，液膜厚度较小，很快发生破断；随溶解度降低，液膜稳定性增加，初始表面弹性也随之增大，并随液膜变薄逐渐接近极限膨胀弹性值.

Effect of surface elasticity on drainage process of vertical liquid film with soluble surfactant

The aim of the present paper is to investigate the gravity-driven draining process containing soluble surfactant when considering the coupling effects of surface elasticity and surfactant solubility. A nonlinear coupling evolution equation including liquid film thickness, surface velocity and surfactant concentration (both on the surface and in the bulk) is established based on the lubrication theory. Assuming that the top of liquid film is attached to the wireframe and the bottom is connected to a reservoir, the drainage evolution is simulated with the software called FreeFem. The effects of surface elasticity and solubility on liquid film draining are discussed under their coupling. The simulation results show that the surface elasticity is an indispensable factor in the process of liquid film drainage with soluble surfactant, and the surfactant solubility also has an important influence on the process. At the initial stage of liquid draining, the initial thickness of liquid film increases with increasing surface elasticity, and the surface tends to be more rigid; with the drainage proceeding, the liquid film with high and low elasticity illustrate different notable draining features:in the case of low surface elasticity, the distribution of surfactant forms a surface tension gradient from top to bottom on the film surface, leading to positive Marangoni effect that counteracts gravity. However, in the case of high elasticity, the film surface presents a surface tension gradient from bottom to top, resulting in a reverse Marangoni effect, which accelerates the draining and makes the film more susceptible to instability. The solubility of surfactant dominates the number of adsorbent molecules on the film surface, which affects the surface elasticity. When the solubility of the surfactant is great (β → 0), the film is extremely unstable, and it breaks down quickly. As the solubility decreases (namely, β increases), the stability of the film increases, and the initial surface elasticity also rises. The surface elasticity gradually approaches to the limiting dilational elasticity modulus due to the film being thinner.