We present two statistical mechanics based methods for simulating the evaporation of droplets of nanoparticle suspensions from upon a heterogeneous surface. These are based on a generalised lattice-gas model. Properties such as wettability and the dynamic contact angle, are determined by the attraction strength parameters between particles and from the dynamic mobility coefficients. Both models incorporate the effects of surface roughness and slip at the surface. The two approaches used are Monte Carlo (MC) computer simulations and Dynamical Density Functional Theory (DDFT). We calculate the bulk fluid phase behaviour including the influence of the suspended nanoparticles, comparing results from the two approaches. We also calculate thermodynamic quantities such as the surface tensions. Our results show that the presence of steps in the surface can be crucial in controlling dewetting from heterogeneous surfaces. We also observe that coffee ring stains can be formed via the coupling of evaporation to phase separation and that the advective hydrodynamics within the droplets in not required for ring stains to form
