Dynamics of insoluble surfactant-laden thin films flow over inclined random topography

Abstract

For the flow of an insoluble surfactant-laden thin film and droplet on inclined random topography, the lubrication theory is used to derive the evolution equations of thin liquid film thickness and interfacial surfactant concentration. Characteristics of thin film flow and droplet spreading, as well as the influence of topography structure are numerically simulated with PDECOL code. Results show that under the action of gravitational component and Marangoni effects, the thin film flow and droplet spreading is accelerated; the capillary ridge emerges at the thin film edge and the droplet center; and at the bottom of the thin film and droplet, the depression is generated. While the deformation of liquid film free surface is more significant due to the effect of random topography. The increasing θ has a role of enhancing gravitational component and Marangoni effects, leading to the enhancement of the capillary ridge and depression. The increase of D promotes the thin film flow and droplet spreading, but causes the deformation amplified; and the increased k0 can induce the evolutions of thin film flow and droplet spreading to slow down and inhibit the formation of capillary ridge and depression. In addition, compared with the thin film flow, the impact of D and k0 on the speed of droplet spreading is relatively weak.