Gravity-driven thin liquid films over topographical substrates.

We investigate the time-dependent evolution of thin liquid films over inclined substrates using a multi-component lattice Boltzmann algorithm. Substrates with and without grooves are considered and the effects of the inclination angle on the dynamics and the coating of the substrates are studied. Our results indicate that the dynamics is enhanced and the ridge height and its displacement are increased by increasing the inclination angle. However, by increasing the inclination angle the maximum depth that can be successfully coated is reduced. Also, although for any given groove depth the width should be larger than a critical value for successful coating, the critical width decreases for smaller inclination angles. For different inclination angles we derive and report the critical sizes of the grooves for successful coating of the substrates.