Figure 1

(Color online) Schematic of the heterogeneous coating. (a) both the walls of the channel are partitioned in an alternate sequence of strips $A$ and $B$, with different chemical properties (${\theta }_A$ and ${\theta }_B$) and different lengths ($w_A$ and $w_B$). (b) force $f\left(z\right)$ as a function of $z$. In the hydrophilic regions (A) the front is pushed rightwards, while in the hydrophobic ones (B) it is pulled leftwards.Reuse & Permissions

Figure 2

(Color online) Potential $V\left(q\right)$ as a function of $q$: the ratchet form is clearly visible, as well as the position-increasing potential barriers.Reuse & Permissions

Figure 3

(Color online) Normalized pinning length ${\tilde{L}}_p$ as a function of ${\tilde{w}}_B$ for $\mid \cos \left({\theta }_A\right)∕\cos \left({\theta }_B\right)\mid =10,20,30$. The lines represent the prediction given by Eq. (18), while the symbols are the result of the LB simulations. To match theory and simulation, we have taken ${\tilde{w}}_B^{\mathit{eff}}={\tilde{w}}_B-\tilde{\delta }$ in Eq. (18), where $\tilde{\delta }=\delta ∕H=0.025$. The other parameters used are $\alpha =0.028$, $\tilde{L}=20$, ${\tilde{C}}_{\mathit{cap}}=5.7$, and ${\theta }_B=92$. Inset: normalized pinning length ${\tilde{L}}_p$ as a function of $\mid \cos \left({\theta }_A\right)∕\cos \left({\theta }_B\right)\mid$. Note the two distinct fast-filling and slow-filling regimes, as discussed in the text.Reuse & Permissions

Figure 4

(Color online) Time evolution of the front coordinate in the LB simulation (symbols) and as numerical solution of Eq. (17) (solid line). The simulation was performed using the following parameters: $\alpha =0.028$, $L=3600$, $H=200$, $w_A=144$, $w_B=56$, $\gamma =0.14$, and $\nu =1∕6$. For this case $\delta ∕H=0.025$, in lattice units. The dashed line marks the prediction of Eq. (18). Inset: comparison between imposed (line) and observed (dots) contact angles: note that while the imposed (static) angle $\cos \left[\theta \left(z\right)\right]$ is a stepwise function, the dynamic one deviates from it during the hydrophilic-hydrophobic transition. The observed contact angle was obtained by interpolating the front shape with a circle of radius $R$, so that $\cos \left(\theta \right)=H∕2R$. Note that, due to the convex shape of the interface, the front coordinate (calculated at $y=H∕2$) always precedes the location where the front first meets the hydrophobic region.Reuse & Permissions