Evaporating solvent-polymer mixtures play an im portant role in a number of modern industrial applications. We focus on developing a two-phase model for a fluid composed of a volatile solvent and a nonvolatile polymer in a thin-film geometry. The model accounts for density differences between the phases as well as evaporation at a fluid-air interface. We use the model in one dimension to explore the interplay between evaporation and compositional buoyancy; the former promotes the growth of a polymer-rich skin at the free surface while the latter tends to pull the denser polymeric phase to the substrate. We also examine how these mechanisms influence the drying time of the film. In the limit of dilute polymer, the model can be reduced to a single nonlinear boundary value problem. The nondilute problem has a rich asymptotic structure. We find that the shortest drying times occur in the limit of strong gravitational effects due to the rapid formation of a bilayer with a polymer-rich lower layer and a solvent-rich upper layer. In addition, gravity plays a key role in inhibiting the formation of a skin and can prevent substantial increases in the drying time of the film.
ASJC Scopus subject areas
- Applied Mathematics