分离压和表面黏度的协同作用对液膜排液过程的影响

针对含不溶性活性剂的垂直液膜排液过程,在考虑分离压作用的前提下,引入随活性剂浓度变化的表面黏度模型,应用润滑理论建立了液膜厚度、活性剂浓度和液膜表面速度的演化方程组,通过数值计算分析了常表面黏度和变表面黏度情形下的液膜演化特征.结果表明:表面黏度是影响液膜排液过程的重要因素,当不考虑表面黏度时,液膜表面呈"流动"模式,反之呈"刚性"模式,且随表面黏度增加,液膜排液速率明显减缓.分离压对"黑膜"的形成至关重要,分离压单独作用时,其形成的"黑膜"长度较短,而只考虑表面黏度时,则不能形成稳定的"黑膜".而在二者协同作用下,液膜中部形成了向下扩展、厚度很薄但非常稳定的"黑膜",且"黑膜"厚度、出现时间均随表面黏度的增大而增加.当考虑活性剂浓度对表面黏度的影响时,表面速度受此影响显著;在形成"黑膜"长度及出现时间方面与相应常表面黏度的情形基本类似,但其"黑膜"厚度小于相应常表面黏度,故在液膜排液过程中更容易发生失稳.

Synergistic effects of disjoining pressure and surface viscosity on film drainage process

A mathematical model is established to investigate the gravity-driven draining process of a vertical thin liquid film containing insoluble surfactants when considering the synergistic effect of surface viscosity and disjoining pressure. Lubrication theory is used to derive a coupled equation set describing the evolution of the film thickness, surfactant concentration and surface velocity. The equation set is solved numerically by the FreeFem program based on the finite element method. The film is assumed to be supported by the wire frame at both the top and bottom, thus the mass of liquid and the mass of total surfactants are conserved in the simulation. The characteristics of film evolution under the constant and variable surface viscosity are examined. Simulation results show that the surface viscosity is a crucial factor affecting the film drainage process. When neglecting the effect of surface viscosity, the film surface exhibits the mobile mode, while the film surface presents the rigid mode in the case of the surface viscosity considered. Increasing the surface viscosity, the rate of film drainage is slowed down significantly, leading to a reduction of the film thinning and enhancement of film stability, which is consistent with the results obtained by Naire et al. The disjoining pressure is a key factor in the formation of “black film”. When the disjoining pressure is only involved in the model, the length of the “black film” region is relatively short, nevertheless, if the effect of surface viscosity is only considered, a stable “black film” does not form. Under the synergistic effect of the disjoining pressure and surface viscosity, a very long and thin but stable “black film” is found in the middle segment of the film. Additionally, the thickness of “black film” increases and the appearance time postpones with the increase of surface viscosity. Considering the influence of concentration-dependent surface viscosity, the drainage rate is greatly affected. In the early stage, due to the smaller overall surface viscosity, the surface velocity is relatively large. With increasing surface viscosity at the bottom of film, the strength of the film surface tends to be enhanced, and then the anti-perturbation ability of the film is promoted and the film thinning is retarded. There is no significant difference in the length nor the appearance time of “black film” except that the thickness of “black film” with concentration-dependent surface viscosity is lower than that with the constant viscosity, thus the flow stability is weaker than that with the constant viscosity. In addition, the presence of the disjoining pressure slows down the thinning of “blackest” portion of the film and the surfactant concentration at this position. In the numerical results of the variable surface viscosity given by Braun et al. it is observed that the concentration of surfactant could almost be swept to clean in the top part of film. That is possibly because the effect of the disjoining pressure is neglected by Braun et al. It should be pointed out that the surface elasticity plays an important role in the stability of film. Therefore, it is necessary to consider the effect of surface elasticity in the future investigation.