Hydrodynamic Theory for Spontaneously Growing Dimple in Emulsion Films with Surfactant Mass Transfer

In this paper we propose a theory for the recently discovered phenomenon of spontaneous cycling dimpling. The latter is responsible for the high stability of non-equilibrium aqueous emulsion films when surfactant is transferred across the interfaces toward the surrounding oil phases. Our treatment is based on the lubrication approximation for the thin film hydrodynamics, with account for the surfactant fluxes due to convection and diffusion. A fourth-order differential equation is derived for the time evolution of the surface shape. This equation is solved numerically, and the results are compared with experimental profiles (determined by means of interferometry). Very good agreement is observed. It is proved that the surface viscosity and the surface diffusion are insignificant for the dimple growth. Quite essential is the Marangoni effect: the exhaustion of surfactant from the region around the film center gives rise to gradients of the interfacial tension which set the interface into motion, and consequently, liquid is dragged into the film, feeding the dimple.