We investigate numerically the dynamics of unstable gravity driven
three-dimensional thin liquid films on hydrophilic-hydrophobic patterned
substrates of longitudinal stripes and checkerboard arrangements. The thin film
can be guided preferentially on hydrophilic longitudinal stripes, while fingers
develop on adjacent hydrophobic stripes if their width is large enough. On
checkerboard patterns, the film fingering occurs on hydrophobic domains, while
lateral spreading is favoured on hydrophilic domains, providing a mechanism to
tune the growth rate of the film. By means of kinematical arguments, we
quantitatively predict the growth rate of the contact line on checkerboard
arrangements, providing a first step towards potential techniques that control
thin film growth in experimental setups.Comment: 30 pages, 12 figure