Self-ratcheting Stokes drops driven by oblique vibrations.

John K, Thiele U

Abstract

We develop and analyze a minimal hydrodynamic model to understand why a drop climbs a smooth homogeneous incline that is harmonically vibrated at an angle different from the substrate normal [P. Brunet, J. Eggers, and R. D. Deegan, Phys. Rev. Lett. 99, 144501 (2007)]. We find that the vibration component orthogonal to the substrate induces a nonlinear (anharmonic) response in the drop shape. This results in an asymmetric response of the drop to the parallel vibration and, as a consequence, in the observed net motion. In addition to establishing the basic mechanism, we identify scaling laws valid in a broad frequency range and a flow reversal at high frequencies.