  We introduce a mesoscopic hydrodynamic model for drops of binary mixtures of
volatile partially wetting liquids on brush-covered substrates, i.e., we model
the coupled dynamics of spreading, evaporation, imbibition, diffusion and
partial demixing of the two volatile components across the three phases -
brush, drop and gas. The formulation of the model as gradient dynamics on an
underlying free energy functional allows us to systematically account for
cross-couplings between the six scalar fields needed to describe the dynamics
of both components within each of the three phases. The energy accounts for
concentration- and brush state-dependent capillarity and wettability,
miscibility of the two components within drop and brush, and entropy in the
gas. Finally, the usage of the model is illustrated by employing numerical time
simulations to study the dynamics of a sessile drop.
