A mathematical model of droplet spreading on surface of an immiscible liquid based on lubrication approximation was used. Influence of viscosity ratio on evolution and equilibrium state of droplet at high viscosity ratios was investigated. Crucial parameters including droplet thickness and spreading radius were examined. It shows that deformation of the liquid-liquid interface near the contact line is affected by the viscosity ratio and the surface tension ratio; Increase of viscosity ratio reduces the spreading rate and the time constant, thereby, prolongs the spreading evolution. It does not affect the final stable shape of the droplet; Relation between spreading radius and time satisfies x_max= 1 - 0.2 exp(- βt). Inertial oscillation does not appear at the final stage of droplet spreading in the case of high viscosity ratios.

To analyze instability on surface of liquid film in a wire-frame drainage experiment, we establish a three-dimensional mathematical model for drainage process of a wire-frame containing insoluble surfactants, and simulate instability at bottom of the liquid film. Influence of factors including Marangoni effect, dilational viscosity and disturbance wave number are analyzed. It shows that bottom perturbation is severe at beginning of drainage, then quickly weakens, and gradually increases in the late drainage. Perturbation at the beginning is caused by initial perturbation, and instability at the late of the drainage is related to the distribution of surfactant. A weaker Marangoni effect enhances the surface disturbance, while a stronger Marangoni effect inhibits the bottom perturbation, making the liquid film rigid and causing surface countercurrent. Higher dilational viscosity slows down the drainage process and reduces the surface velocity. It suppresses the countercurrent phenomenon caused by the Marangoni effect. A greater disturbance wave number makes the perturbation stronger in the early stage of drainage, while it does not affect the stability of late stage of the drainage.