Dynamics of Freely Suspended Drops Translating through Miscible Environments

TL;DR

This study experimentally investigates the behavior of water droplets rising through viscous, miscible liquids like glycerol and corn syrup, revealing shape changes, volume increase, and velocity decay over time, with proposed scaling laws.

Contribution

It provides new experimental insights and scaling relations for the shape, volume, and velocity evolution of miscible droplets in viscous environments.

Findings

Droplets initially prolate and rise at constant velocity.

Drops grow into oblate shapes after a critical time.

Velocity decreases following a power law over time.

Abstract

Our work focuses on an experimental investigation of droplets freely rising through a miscible, more viscous liquid. We report observations of water droplets rising through glycerol and corn syrup, which are common household ingredients. Immediately after the drops are formed, they take on prolate shapes and rise with constant velocity without expanding in size. However, after a critical time predicted by our theory, the drops continually grow into oblate spheroids, and as they mix with the ambient liquid, their volume increases and their velocity decreases, eventually following power laws. We present scaling relations that explain the main observed phenomena. However, the power laws governing the rate of the volumetric increase and the velocity decrease, namely $t^{1/2}$ and $t^{-1/2}$, respectively, remain points of further investigation.