Phase-field simulation of liquid-vapor equilibrium and evaporation of fluid mixtures

In solution-processing of thin films, the material layer is deposited from a solution composed of several solutes and solvents. The final morphology and hence the properties of the film often depend on the time needed for the evaporation of the solvents. This is typically the case for organic photoactive or electronic layers. Therefore, it is important to be able to predict the evaporation kinetics of such mixtures. We propose here a new phase-field model for the simulation of evaporating fluid mixtures and simulate their evaporation kinetics. Similar to the Hertz-Knudsen theory, the local liquid-vapor equilibrium is assumed to be reached at the film surface and evaporation is driven by diffusion away from this gas layer. In the situation where the evaporation is purely driven by the liquid-vapor equilibrium, the simulations match the behavior expected theoretically from the free energy: for evaporation of pure solvents, the evaporation rate is constant and proportional to the vaporpressure. For mixtures, the evaporation rate is in general strongly time-dependent because of the changing composition of the film. Nevertheless, for highly non-ideal mixtures, such as poorly compatible fluids or polymer solutions, the evaporation rate becomes almost constant in the limit of low Biot numbers. The results of the simulation have been successfully compared to experiments on a polystyrene-toluene mixture. The model allows to take into account deformations of the liquid-vapor interface and therefore to simulate film roughness or dewetting.