Surfactants role on the deformation of colliding small bubbles

The mutual approach of two bubbles and the rate of thinning and the deformation of the partially mobile thin liquid film intervening between them is studied. The material properties of the interfaces (surface viscosity, Gibbs elasticity, surface and:or bulk diffusivity) are taken into account. In the normal stress balance at the fluid interfaces we include the contribution of the intermolecular forces. To obtain the liquid velocity and pressure distribution the lubrication approximation is used. From the normal stress boundary condition the first order (with respect to the capillary number) shape function is derived. It provides information on the inversion thickness, at which the curvature in the gap between the drops changes from convex to concave, and the pimple thickness, at which the curvature of the interfaces spontaneously increases due to the action of the attractive intermolecular forces. The analytical and numerical investigations reveal significant influence of the disjoining pressure and the surfactant on both thicknesses. Explanation of the following effects is proposed: (i) increase of the pimple thickness and decrease of the inversion thickness with the increase of the interfacial mobility; (ii) role of the surface viscosity; (iii) role of the van der Waal