Drag of a solid particle trapped in a thin film or at an interface: Influence of surface viscosity and elasticity

We propose a theoretical model for the motion of a spherical particle entra pped in a thin liquid film or in a monolayer of insoluble surfactant at the air/water interface. Both surface shear and dilational viscosity, surface diffusion, and elasticity of the film are taken into consideration. The dra g force acting on the particle is analytically calculated and asymptotic ex pressions of the problem are provided, The relevance of the model is discus sed by comparing the calculated "viscoelastic" drag, gamma(vel), to the one predicted by Saffman's theory, gamma(s), for cylindrical inclusions in mem branes. Numerical analyses are performed to evaluate the contributions of t he surface viscosity and the diffusion coefficient of the layer on the hydr odynamical resistance experienced by the particle. (C) 2000 Academic Press.