Effect of surfactants on the stability of films between two colliding small bubbles

The stability of partially mobile drainage thin liquid film formed between two slightly deformed approaching bubbles or drops is studied. The intervening film is assumed to be thermodynamically unstable. The material properties of the interfaces (surface viscosity, Gibbs elasticity, surface and bulk diffusion) are taken into account. To examine the stability of the thin film we consider the coupling between the drainage and the disturbance flows. The velocity and pressure distributions due to the drainage flow are obtained by using the lubrication approximation. The disturbance flow is examined by imposing small perturbations on the film interfaces and liquid flow. The long wave approximation is applied. We solved the linear problem for the evolution of the fluctuations in the local film thickness, interfacial velocity and pressure. The linear stability analysis of the gap region allows us to calculate the critical thickness, at which the system becomes unstable. Quantitative explanation of the following effects is proposed, (i) the increase of critical thickness with the increase of the interfacial mobility; (ii) the role of surface viscosity, compared with that of the Gibbs elasticity; (iii) the significant destabilization of the gap region with the decreasing droplet radius in the case of buoyancy driven motion. The analytical expressions for critical thickness in the case of negligible surface viscosity and tangentially immobile interfaces are presented.