Dynamics of gravity driven three-dimensional thin films on hydrophilic-hydrophobic patterned substrates

We investigate numerically the dynamics of unstable gravity driven three-dimensional thin liquid films on hydrophilic-hydrophobic patterned substrates. We explore longitudinally striped and checkerboard arrangements. Simulations show that for longitudinal stripes, the thin film can be guided preferentially on the hydrophilic stripes, while fingers develop on adjacent hydrophobic stripes if the width of the stripes is large enough. On checkerboard patterns, the film develops as a finger on hydrophobic domains, while it spreads laterally to cover the 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 toward potential techniques that control thin film growth in experimental setups.