  We present a lattice-gas (generalised Ising) model for liquid droplets on
solid surfaces. The time evolution in the model involves two processes: (i)
Single-particle moves which are determined by a kinetic Monte Carlo algorithm.
These incorporate into the model particle diffusion over the surface and within
the droplets and also evaporation and condensation, i.e. the exchange of
particles between droplets and the surrounding vapour. (ii) Larger-scale
collective moves, modelling advective hydrodynamic fluid motion, determined by
considering the dynamics predicted by a thin-film equation. The model enables
us to relate how macroscopic quantities such as the contact angle and the
surface tension depend on the microscopic interaction parameters between the
particles and with the solid surface. We present results for droplets joining,
spreading, sliding under gravity, dewetting, the effects of evaporation, the
interplay of diffusive and advective dynamics, and how all this behaviour
depends on the temperature and other parameters.
