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 interven ing film is assumed to be thermodynamically unstable. The material properti es of the interfaces (surface viscosity, Gibbs elasticity, surface and bulk diffusion) are taken into account. To examine the stability of the thin fi lm we consider the coupling between the drainage and the disturbance flows. The velocity and pressure distributions due to the drainage flow are obtai ned by using the lubrication approximation. The disturbance Row is examined by imposing small perturbations on the film interfaces and liquid flow. Th e long wave approximation is applied. We solved the linear problem for the evolution of the fluctuations in the local film thickness, interfacial velo city and pressure. The linear stability analysis of the gap region allows u s to calculate the critical thickness, at which the system becomes unstable . Quantitative explanation of the following effects is proposed, (i) the in crease of critical thickness with the increase of the interfacial mobility; (ii) the role of surface viscosity, compared with that of the Gibbs elasti city; (iii) the significant destabilization of the gap region with the decr easing droplet radius in the case of buoyancy driven motion. The analytical expressions for critical thickness in the case of negligible surface visco sity and tangentially immobile interfaces are presented. (C) 2000 Elsevier Science B.V. All rights reserved.