On the rising and sinking motion of bouncing oil drops in strongly stratified liquids

TL;DR

This study investigates the bouncing motion of oil drops in stratified liquids, analyzing how parameters like drop size and viscosity influence bouncing behavior through experiments, scaling analysis, and simulations.

Contribution

It provides new insights into the bouncing dynamics of oil drops in stratified liquids, including empirical and numerical determination of drag coefficients for different viscosities.

Findings

Bouncing height and times depend on drop size, viscosity, and stratification strength.

Drag coefficients vary with viscosity and are validated by experiments and simulations.

Scaling relations accurately predict bouncing characteristics across different conditions.

Abstract

When an immiscible oil drop is immersed in a stably stratified ethanol-water mixture, the Marangoni flow on the surface of the drop can experience an oscillatory instability, so that the drop undergoes a transition from levitating to bouncing. The onset of the instability and its mechanisms have been studied previously, yet the bouncing motion of the drop itself, which is a completely different problem, has not yet been investigated. Here we study how the bouncing characteristics (jumping height, rising and sinking time) depend on the control parameters (drop radius, stratification strength, drop viscosity). We first record experimentally the bouncing trajectories of drops of different viscosities in different stratifications. Then a simplified dynamical analysis is performed to get the scaling relations of the jumping height and the rising and sinking times. The rising and sinking time scales are found to depend on the drag coefficient of the drop $C_D^S$ in the stratified liquid, which is determined empirically for the current parameter space. For low viscosity (5 cSt) oil drops the results on the drag coefficient match the ones from the literature. For high viscosity (100 cSt) oil drops the parameter space had not been explored and the drag coefficients are not readily available. Numerical simulations are therefore performed to provide external verification for the drag coefficients, which well match with the experimental results.