Dimitrina S. Valkovska

Stability of draining plane-parallel films containing surfactants

The stability of partially mobile draining thin liquid films with respect to axisymmetric fluctuations was studied. The material properties of the interfaces (Gibbs elasticity, surface and bulk diffusions) were taken into account. When studying the long wave stability of films, the coupling between the drainage and perturbation flows was considered and the lubrication approximation was applied. Two types of wave modes were examined: radially-bounded and unbounded waves. The difference between the thickness of loss of stability, h(st), the transitional thickness, h(tr), at which the critical wave causing rupture becomes unstable, and the critical thickness, h(cr), when the film ruptures, is demonstrated. Both the linear and the non-linear theories give h(st) > h(tr) > h(cr). The numerical results show that the interfacial mobility does not significantly influence the thickness of the draining film rupture. The interfacial tension and the disjoining pressure are the major factors controlling the critical thickness. The available experimental data for critical thicknesses of foam and emulsion films show excellent agreement with the theoretical predictions. The important role of the electromagnetic retardation term in the van der Waals interaction is demonstrated. Other published theories of the film stability are discussed.

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

Abstract 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.

Surfactants role on the deformation of colliding small bubbles

Abstract 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 Waals interaction.

Hydrodynamic instability and coalescence in trains of emulsion drops or gas bubbles moving through a narrow capillary

We investigate the effect of surfactant on the hydrodynamic stability of a thin liquid film formed between two emulsion drops or gas bubbles, which are moving along a narrow capillary. A ganglion (deformed drop or bubble in a pore) is covered by an adsorption monolayer of surfactant. Due to the hydrodynamic viscous friction, the surfactant is dragged from the front part of a moving ganglion toward its rear part. Consequently, the front and rear parts are, respectively, depleted and enriched in adsorbed surfactant. When such two ganglia move one after another, surfactant molecules desorb from the rear part of the first ganglion and are transferred by diffusion, across the intermediate liquid film, to the front part of the second ganglion. This leads to the appearance of a diffusion-driven hydrodynamic instability, which may cause coalescence of the two neighboring drops or bubbles. The coalescence occurs through a dimple-like perturbation in the film thickness, which is due to a local lowering in the pressure caused by a faster circulation of the liquid inside the film, which in turn is engendered by the accelerated surfactant diffusion across the thinner parts of the film. The developed theory predicts the critical distance between the two ganglia, which corresponds to the onset of coalescence, and its dependence on the radius of the capillary channel, velocity of motion, surfactant concentration and type of the operative surface forces. The results can be useful for a better understanding and quantitative description of the processes accompanying the flow of emulsions and foams though porous media.