The influence of surfactants on the drainage and rupture of mobile liquid films between drops: A parametric numerical study
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2018-01-01
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Abstract
Film drainage and rupture during coalescence between two drops approaching each other under a constant force in the presence of insoluble surfactants affected by the van der Waals forces is studied numerically. The mathematical problem is based on the coupled equations of flow in each phase and the convection-diffusion equation governing the surfactant distribution at the interface as well as the related Marangoni effects. The latter are subject to the boundary conditions in the limit of gentle interactions (small-deformations) for which the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. The finite difference method is used to discretize the lubrication equation in the gap and the interfacial diffusion-convection equation while the boundary integral method is employed to solve the flow in the drops. In this work, a parametric study is carried out by a numerical simulation for Peclet numbers (Pe) ranging from 102 to 104, initial dimensionless surfactant concentrations (Γ0*) from 0 to 10 and dimensionless Hamaker parameter (A*) from 10-7 to 10. The results indicate that the critical film thickness (hc) is strongly dependent on the combination of the three parameters which determines the predominance of van der Waals forces or those of Marangoni.