Evaporation maps for non-ideal ternary mixtures

Evaporation maps are a convenient way of representing the dynamic composition of evaporating liquid mixtures. Specifically, these maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly used residue curve maps of simple distillation processes. The evaporation process considered here involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one or more of the ternary components. The model developed here uses an exact solution to the Maxwell-Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperature-composition space, which are then projected onto a ternary diagram to form the map. Efficient Newton-based methods are used to calculate the composition and temperature of pseudo-azeotropes in the mixture, and to calculate the wet-bulb temperature at a given composition. A numerical continuation method is used for tracking the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal pseudo-azeotrope composition. Provided the gas-phase limited assumption applies, such analysis is applicable to applications such as drying of solvent-based coatings and tray-drying of granulated pharmaceutical products.