Self-ratcheting Stokes drops driven by oblique vibrations

TL;DR

This paper presents a hydrodynamic model explaining how oblique vibrations cause a drop to climb a smooth incline by inducing asymmetric shape responses, revealing scaling laws and flow reversal phenomena.

Contribution

It introduces a minimal hydrodynamic model that captures the nonlinear response of drops to oblique vibrations, explaining the climbing mechanism and flow reversal.

Findings

Vibration orthogonal to substrate causes nonlinear drop shape response.

Asymmetric drop response leads to net motion up the incline.

Scaling laws and flow reversal identified at high frequencies.

Abstract

We develop and analyze a minimal hydrodynamic model in the overdamped limit to understand why a drop climbs a smooth homogeneous incline that is harmonically vibrated at an angle different from the substrate normal [Brunet, Eggers and 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, in consequence, in the observed net motion. Beside establishing the basic mechanism, we identify scaling laws valid in a broad frequency range and a flow reversal at high frequencies.