Drainage of vertical foam film containing insoluble surfactant is investigated with consideration of combined effect of disjoining pressure and surface viscosity. Lubrication theory is applied to establish evolution equations of film thickness, surface concentration of insoluble surfactant and surface velocity. Film evolution under different initial surfactant concentration and gradient are simulated numerically. It shows that in the absence of initial surfactant concentration, film drainage process is very short and tends to break quickly, whereas lifetime of foam film is prolonged by adding surfactant to film surface. Under relatively low surfactant concentration, Marangoni effect is not enough to defeat gravity drainage, and "black film" cannot exist stably. Increasing concentration of initial surfactant reduces surface velocity of film and strengthens rigidity of film surface, and film stability is enhanced. Influence of concentration gradient of surfactant on drainage process is highlighted with evident reduction of surface velocity in initial stage of film drainage.

Coalescence of two surfactant-containing droplets on a topographic substrate was modeled with lubrication theory considering asymmetrically-arranged configuration. Effects of initial droplet spacing and height of substrate on coalescence evolution were investigated and compared with symmetrically-arranged droplets. It shows that variation of droplet height undergoes five stages, and variation of surfactant concentration experiences three stages in a short period; Coalescing time of droplets and surfactant is extended with increasing droplet spacing while shorten with increasing substrate height; Coalescence time of asymmetric droplets is distinctly less than that of symmetric droplets, resulting in a faster rate of coalescence.

For an insoluble surfactant-laden droplet spreading on corrugated topography,a disjoining pressure model induced by concentration of surfactant was established. Non-model stability theory was carried out to investigate stability of spreading. It indicates that compared with droplet spreading without disjoining pressure,under disjoining pressure advancing front height of droplet reduce apparently and spreading rate increases which improves stability of spreading. Long perturbation wave is conducive to enhance stability of droplet evolution and stability is enhanced with increasing wave number. However,spreading stability trends to deteriorate and even transit to unstable with increasing wave number of short perturbation waves. Reducing attraction strength coefficient α₁ and increasing repulsion strength coefficient α₂ promote spreading stability at small wave number(k=3). In addition,droplet displays more stable spreading with increasing α₁ and decreasing α₂ at large wave number(k=30).

For process of an ultrathin surfactant-laden droplet spreading on preset film, base state and disturbance evolution equations for film thickness, surfactant interfacial and bulk concentrations were established with lubrication approximation. Transient growth analysis (TGA) was carried out to investigate stability of evolution process. Effects of surfactant solubility and typical parameters were discussed. TGA indicates that introduction of perturbation wave is conducive to enhance stability of droplet evolution and stability degree is directly related with wave number (k). However, stability tends to be deteriorated with increment of k. Compared with insoluble surfactant, evolution with soluble surfactant slows down slightly and stability is improved. Increasing of b, M, C, K_s stabilize the spreading, especially Marangoni effect and capillary force. Thickness of preset film has a primarily role on stability of droplet thickness evolution.

For flowing of thin film containing insoluble surfactant over grooving substrate, lubrication theory is adopted for evolution equations of liquid film thickness and interfacial surfactant concentration. Film flowing characteristics and the effects of related parameters are numerically simulated. It shows that as thin film of insoluble surfactant flowing over grooving topography, gravity and Marangoni stress driven by surfactant promotes flow of liquid film. Gravity plays a leading role since influence of surfactant is limited by fl ows of surface liquid and adjacent bulk liquid. Viscous force associated with topography has an opposite effect. Film deformation is weak as improving Bond number or reducing capillary number. Increasing groove depth or decreasing groove steepness encourages film deformation as improving Marangoni stress.

Surfactant driven flows are simulated with three nonlinear partial differential evolution equations for film thickness, surfactant interracial and bulk concentrations based on lubrication theory via PDECOL program numerically, to investigate influence of Marangoni effect in positive, negative and neutral systems. Instability of droplet evolution in negative system is analyzed with method of transient growth analysis. It shows that Marangoni effect plays a positive role in promoting droplets non-uniform spreading and surfactant diffusion in a positive system. A system under negative Marangoni effect exhibits interfacial instability which resulted in spreading inhibited and violent fluctuations occurrence on droplet surface. Instability tends to be more obvious with strengthened effect. Marangoni stress is main driving force in transverse droplet evolution in both positive and negative systems.

Dewetting of thin films covered by insoluble surfactant in the presence of wall slippage is considered.PDECOL program is used to simulate evolutions of film thickness and surfactant surface concentration.With perturbation wave variation of film surface,effects of several parameters on dewetting dynamics are examined.It shows that Marangoni stress shortens unstability region at small Marangoni number(M) and the unstability region is extended at large M.Decreasing capillary number leads to shorten unstability region and even restrains dewetting phenomena.The influence of slipping is closely related to M,and it accelerates perturbation growth and shorten dewetted region at small M.Increasing equilibrium film thickness leads surface deformation degree weakened and unstability region extended.Compared with exogenous surfactant,endogenous forms a shorter dewetted region and hence film stability tends improved.