Stick-slip dynamics of an oscillated sessile drop

TL;DR

This paper investigates the stick-slip behavior of a sessile drop on an oscillating substrate, revealing how contact line hysteresis leads to unique resonance phenomena and antiresonant frequency bands.

Contribution

It introduces a theoretical model incorporating contact angle hysteresis and analyzes the resulting complex resonance and antiresonance behaviors in oscillated drops.

Findings

Identification of antiresonant frequency bands due to hysteresis

Observation of nontrivial resonance competition

Analysis of surface oscillation responses

Abstract

The dynamics of an oscillated sessile drop of incompressible liquid with the focus on the contact line hysteresis is under theoretical consideration. The solid substrate is subject to transverse oscillations, which are assumed small amplitude and high frequency. The dynamic boundary condition that involves an ambiguous dependence of the contact angle on the contact line velocity is applied: the contact line starts to move only when the deviation of the contact angle exceeds a certain critical value. As a result, the stick-slip dynamics can be observed. The frequency response of surface oscillations on the substrate and at the pole of the drop are analyzed. It is shown that novel features such as the emergence of antiresonant frequency bands and nontrivial competition of different resonances are caused by contact line hysteresis.