Flow Dynamics Of Insoluble Surfactant Vertically-draining Film With Variable Surface Viscosity

The dynamics of drops and bubbles as well as their interaction are important issues in many multiphase systems that involve simultaneous flow and mass transport.Surfactant may give rise to interfacial stresses, which may cause the free surface to viscously entrain the fluid flow. These stresses may be in form of surface tension gradients at the free surface, which is the mechanism underlying the Marangoni effect,or such as those relating to the interfacial shear and dilatational viscosity, influencing the drops or films interfacial motion.In this paper, theoretical derivation and numerical simulation considering variable surface viscosity are conducted, and the spreading features of an insoluble surfactant-laden vertical films drainage with insoluble surfactant are investigated. The main contents of the paper are listed as follows:(1) A model of vertical drainage film with insoluble surfactant model is established. According to the lubrication theory, the evolution equations of film thickness, surface concentration and surface slip velocity are derived, including disjoining pressure model. Based on Dow Corning surfactant experiment data, the three equations are improved by introducing the Boussinesq-Scriven surface stress model and Hisa viscosity expression.(2) The evolution model is simulated with FREEFEM code and the effects of disjoining pressure, conjoining pressure, attraction strength coefficient, repulsion strength coefficient, surfactant concentration and Bond Number are examined.(3) Under the cases of constant viscosity and surface viscosity depending on local surfactant concentration, the dynamics characteristics of drainage are presented by the simulation with FREEFEM code, and the effect of viscosity on drainage is discussed.