Sliding drops across alternating hydrophobic and hydrophilic stripes

We perform a joint numerical and experimental study to sistematically characterize the motion of drops sliding over a periodic array of alternating hydrophobic and hydrophilic stripes with large wettability contrast, and typical width of hundreds of $\mu \textrm{m}$. The fraction of the hydrophobic stripes has been varied from about 20% to 80%. The effects of the heterogeneous patterning can be described by a renormalized value of the critical Bond number, i.e. the critical dimensionless force needed to depin the drop before it starts to move. Close to the critical Bond number we observe a jerkily motion characterized by an evident stick-slip dynamics. As a result, dissipation is strongly localized in time, and the mean velocity of the drops can easily decrease by an order of magnitude compared to the sliding on homogeneous surface. Lattice Boltzmann (LB) numerical simulations are crucial for disclosing to what extent the sliding dynamics can be deduced from the computed balance of capillary, viscous and body forces at varying the Bond number, the surface composition and the liquid viscosity. Away from the critical Bond number, we characterize both experimentally and numerically the dissipation inside the droplet by studying the relation between the average velocity and the applied volume forces.

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