The rolling and slipping of droplets on superhydrophobic surfaces

The leaves of many plants are superhydrophobic, a property that may have evolved to clean the leaves by encouraging water droplets to bead up and roll off. Superhydrophobic surfaces can also exhibit reduced friction and liquids flowing over such surfaces have been found to slip in apparent violations of the classical no-slip boundary condition. Here we introduce slip into a model for rolling droplets on superhydrophobic surfaces and investigate under what conditions slip might be important for the steady state motion. In particular, we examine three limiting cases where dissipation in the rolling droplet is dominated by viscous dissipation, surface friction, or contact line friction. We find that in molecular dynamics simulations of droplets on ideal superhydrophobic surfaces with large effective slip lengths, contact line dissipation dominates droplet motion. However, on real leaves, droplet motion is likely to be dominated by viscous shear, and slip, for the most part, can be neglected.