  Dynamic density functional theory (DDFT) is a promising approach for
predicting the structural evolution of a drying suspension containing one or
more types of colloidal particles. The assumed free-energy functional is a key
component of DDFT that dictates the thermodynamics of the model and, in turn,
the density flux due to a concentration gradient. In this work, we compare
several commonly used free-energy functionals for drying hard-sphere
suspensions including local-density approximations based on the ideal-gas,
virial, and Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of
state as well as a weighted-density approximation based on fundamental measure
theory (FMT). To determine the accuracy of each functional, we model one- and
two-component hard-sphere suspensions in a drying film with varied initial
heights and compositions, and we compare the DDFT-predicted volume-fraction
profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately
predicts the structure of the one-component suspensions even at high
concentrations and when significant density gradients develop, but the virial
and BMCSL equations of state provide reasonable approximations for smaller
concentrations at a reduced computational cost. In the two-component
suspensions, FMT and BMCSL are similar to each other but modestly overpredict
the extent of stratification by size compared to BD simulations. This work
provides helpful guidance for selecting thermodynamic models for soft materials
in nonequilibrium processes such as solvent drying, solvent freezing, and
sedimentation.
