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.