FIG. 7: Grey scale maps of the y component of the local mass flow for a sawtooth and a neighboring finger in a pattern composed of longitudinal stripes. (a) Steady configuration at t/t$_{c}$ = 134 for stripes of width w/x$_{c}$ = 8. Early finger growth at t/t$_{c}$ = 33 . 5 for (b) w/x$_{c}$ = 13, (c) w/x$_{c}$ = 11 and (d) w/x$_{c}$ = 8 for an initial condition consisting of a slightly perturbed contact line with a transverse perturbation mode k = 2 π/w . The effect of the striped pattern is to decrease the finger growth rate on the hydrophobic stripe as the width of the stripe decreases. FIG. 8: Contact line growth in wide/thin longitudinal stripe arrangements of hydrophilic (grey) or hydrophobic (white) properties. (a) For a wide hydrophobic stripe in contact with a thin hydrophilic stripe the contact line destabilizes on the hydrophobic domain, while the trailing edge advances on the hydrophilic domain. (b) On a wide hydrophilic stripe, the contact line forms a sawtooth, while the trailing edge of the contact line advances much more slowly on the thin hydrophobic domain. Wetting properties are fixed to θ$_{e}$ = 0 ◦ at the grey zones, while at the white zones θ$_{e}$ = 90 ◦ . B. Checkerboard pattern Controlled tuning of the growth rate of the film is an appealing technique, that could be used, for instance, to control the filamenting of the film in chemical networks, where 21 (a) (b)