Study On The Instability And The Effect Of Wall Slip In The Process Of Vertical Liquid Film Drainage

Vertical liquid film drainage is widely used in the industrial fields.According to the difference of the substrate attached to the liquid film,the drainage process can be divided into bounded liquid film drainage and free liquid drainage,the former has been commonly applied in the field of dip coating,while the latter is evolved from the foam drainage process.It is of practical significance to study the drainage process of both,not only for the application of dip coating technology but also for the study of foam stability.Previous studies on free liquid film drainage model are numerous,and established the wire-frame liquid film drainage model containing surfactant,but the research on bounded plate liquid film drainage is less.Hence,this article simulates the research on the surface stability of film drainage,and considers the wall slip condition in vertical plate liquid film process,and establishes two-dimensional model for simulating surface perturbation phenomenon and one-dimensional vertical plate drainage model introduced wall slip.Some important parameters such as Marangoni effect,surface viscosity and slip length are analyzed.The main contents are as follows:(1)Aiming at the drainage process of the wire frame liquid film containing insoluble surfactant,based on the liquid film drainage model with the top pinned and the bottom connected to the meniscus,the Marangoni effect,dilatational viscosity and disturbance wave number are analyzed for the influence of liquid film surface perturbation.The Marangoni effect has the most significant impact on the stability of the liquid film.A weaker Marangoni effect will aggravate the instability of the liquid film,while a larger Marangoni number will rigidify the liquid film and cause backflow.The increase in dilatational viscosity will make the liquid film more rigid,and the film tends to be stable.The influence of the disturbance wave number is limited to the initial stage of liquid drainage,and has a slight influence on the change of the liquid film in the later stage of liquid drainage.(2)For the process of bounded liquid film drainage with insoluble surfactant,based on the vertical drainage model with the top pinning and the bottom connected to the liquid bath,the coupling nonlinear equations of the liquid film thickness,surface velocity and surfactant concentration are established.The Marangoni effect and the influence of dilatational viscosity are analyzed.Under the same initial disturbance,the bounded liquid film disturbance subsides later than the wire frame liquid film,and the disturbance can sustain a long time.With the increase of dilatational viscosity,the disturbance will last longer,and the Marangoni effect will extend the disturbance to the upper part of the liquid film,and also produces a tendency to expand the disturbance.(3)In order to analyze the effect of wall slip on the draining process,this article elaborates on three conditions: no slip,constant slip and variable slip.The results show that: the longer the slip length,the higher the concentration gradient,and the stronger Marangoni effect easily trigger backflow phenomenon.But the combination of slip and gravity can still suppress the thickening trend caused by the Marangoni effect and make the liquid film thinner.However,under the condition of variable slip length,slip only plays a role in accelerating the thinning of the liquid film in the early stage of drainage.The concentration and thickness distribution in the late stage of drainage are close to the no-slip condition,but it spreads evenly than the no-slip condition.