  We use a three-dimensional lattice Boltzmann model to investigate the
spreading of mesoscale droplets on homogeneous and heterogeneous surfaces. On a
homogeneous substrate the base radius of the droplet grows with time as
$t^{0.28}$ for a range of viscosities and surface tensions. The time evolutions
collapse onto a single curve as a function of a dimensionless time. On a
surface comprising of alternate hydrophobic and hydrophilic stripes the wetting
velocity is anisotropic and the equilibrium shape of the droplet reflects the
wetting properties of the underlying substrate.
