Hydrodynamic model for drying emulsions.

We present a hydrodynamic model for film formation in a dense oil-in-water emulsion under a unidirectional drying stress. Water flow through the plateau borders towards the drying end leads to the buildup of a pressure gradient. When the local pressure exceeds the critical disjoining pressure, the water films between droplets break and the droplets coalesce. We show that, depending on the critical pressure and the evaporation rate, the coalescence can occur in two distinct modes. At low critical pressures and low evaporation rates, coalescence occurs throughout the sample, whereas at high critical pressures and high evaporation rate, coalescence occurs only at the front. In the latter case, an oil layer develops on top of the film, which acts as a diffusive barrier and slows down film formation. Our findings, which are summarized in a state diagram for film formation, are in agreement with recent experimental findings.