  We develop a lattice gas model for the drying of droplets of a nanoparticle
suspension on a planar surface, using dynamical density functional theory
(DDFT) to describe the time evolution of the solvent and nanoparticle density
profiles. The DDFT assumes a diffusive dynamics but does not include the
advective hydrodynamics of the solvent, so the model is relevant to highly
viscous or near to equilibrium systems. Nonetheless, we see an equivalent of
the coffee-ring stain effect, but in the present model it occurs for
thermodynamic rather the fluid-mechanical reasons. The model incorporates the
effect of phase separation and vertical density variations within the droplet
and the consequence of these on the nanoparticle deposition pattern on the
surface. We show how to include the effect of slip or no-slip at the surface
and how this is related to the receding contact angle. We also determine how
the equilibrium contact angle depends on the microscopic interaction
parameters.
