FIG. 12: Contact line growth rate as a function of hydrophobic domain length on checkerboard patterns. The growth rate decreases as the length of the hydrophobic domains increases. This effect is caused by the adjacent thin hydrophilic domains, whose length increases with l$_{φ}$ , thus making the trailing edge velocity larger and ˙ L smaller. The solid curve corresponds to the theoretical prediction, equation (12). The straight lines correspond to the limiting growth rates ˙ L ( l$_{φ}$ = 0) (dashed line) and ˙ L ( l$_{φ}$ → ∞ ) (solid line). Kinematical model for growth on checkerboard patterns To quantify the effect of the checkerboard pattern on the contact line growth, we charac- terize the motion of the thin film in terms of the velocities of the leading an trailing edges in the wide and thin domains. In general, the instantaneous leading and trailing edge ve- locities, v$_{l}$ and v$_{t}$ , will depend on the configuration of the pattern, i.e. , v$_{l}$ = v$_{l}$ ( w$_{φ}$, w$_{h}$, l$_{h}$, l$_{φ}$ ) and v$_{t}$ = v$_{t}$ ( w$_{φ}$, w$_{h}$, l$_{h}$, l$_{φ}$ ). We assume that these velocities relax to constant values as soon as the contact line comes into contact with a hydrophilic or a hydrophobic domain. For simplicity, we take these values as the ones corresponding to the limiting cases of very long domains. Therefore, at a hydrophobic domain, the leading and trailing edge velocities are approximated as v φ l = v$_{l}$ ( w$_{φ}$, w$_{h}$, l$_{h}$ = 0 , l$_{φ}$ → ∞ ) and v φ t = v$_{t}$ ( w$_{φ}$, w$_{h}$, l$_{h}$ → ∞ , l$_{φ}$ = 0), while at a hydrophilic domain we have v h l = v$_{l}$ ( w$_{φ}$, w$_{h}$, l$_{h}$ → ∞ , l$_{φ}$ = 0) and v h t = v$_{t}$ ( w$_{φ}$, w$_{h}$, l$_{h}$ = 0 , l$_{φ}$ → ∞ ) . We denote Δ t$_{l}$ and Δ t$_{t}$ the times in which the leading and trailing edges sweep a period of the underlying pattern, l$_{h}$ + l$_{φ}$ . It follows that In these expressions, the subscripts l and t , stand for the leading and trailing edges, while the superscripts h and φ stand for hydrophilic and hydrophobic domains respectively. The Δ t$_{l}$ = Δ t h l + Δ t φ l and Δ t$_{t}$ = Δ t h + Δ t φ . (10) 26