Interaction between a particle and a liquid surface covered by a surfactant

The interaction of particles with liquid surfaces takes place in many engineering processes. When the liquid surface is covered by a surfactant, the liquid motion creates its nonuniform distribution, which generates a Marangoni stress acting on the flow. We consider the motion of a spherical particle rising in a viscous fluid towards a surface covered by a surfactant, in the framework of the Stokes equation. The presence of the surfactant changes the flow significantly. It is shown that with the decrease of the distance between the particle and the surface, a "hole" free of the surfactant is created. Analytical and numerical solutions of the problem are obtained.