Sessile drop on oscillating incline

TL;DR

This study numerically investigates how a droplet pinned on a hydrophilic patch deforms on an oscillating incline, revealing unique amplitude and phase lag behaviors akin to a driven over-damped oscillator.

Contribution

It introduces a numerical analysis of droplet deformation on an oscillating incline, highlighting non-linear amplitude scaling and phase lag characteristics.

Findings

Displacement behaves like a driven over-damped oscillator.

Amplitude scales as 1/ω at high frequencies.

Phase lag is proportional to ω at small frequencies.

Abstract

Natural or industrial flows of a fluid often involve droplets or bubbles of another fluid, pinned by physical or chemical impurities or by the roughness of the bounding walls. Here we study numerically one drop pinned on a circular hydrophilic patch, on an oscillating incline whose angle is proportional to $\sin(\omega\,t)$. The resulting deformation of the drop is measured by the displacement of its center of mass, which behaves like a driven over-damped linear oscillator with amplitude $A(\omega)$ and phase lag $\varphi(\omega)$. The phase lag is ${\cal O}(\omega)$ at small $\omega$ like a linear oscillator, but the amplitude is ${\cal O}(\omega^{-1})$ at large $\omega$ instead of ${\cal O}(\omega^{-2})$ for a linear oscillator. A heuristic explanation is given for this behaviour. The simulations were performed with the software Comsol in mode Laminar Two-Phase Flow, Level Set, with fluid 1 as engine oil and fluid 2 as water.