Bubble rise in a Hele-Shaw cell: bridging the gap between viscous and inertial regimes

TL;DR

This study investigates the transition of a single bubble's rise in a Hele-Shaw cell from viscous to inertial regimes, analyzing changes in speed, shape, and drag across a wide Reynolds number range.

Contribution

It introduces a simple power balance model that accurately captures the transition of bubble velocity from viscous to inertial regimes and describes shape evolution.

Findings

Power balance model matches experimental data across regimes

Bubbles are elongated along motion in viscous regime

Bubbles are flattened perpendicular in inertial regime

Abstract

The rise of a single bubble confined between two vertical plates is investigated over a wide range of Reynolds numbers. In particular, we focus on the evolution of the bubble speed, aspect ratio and drag coefficient during the transition from the viscous to the inertial regime. For sufficiently large bubbles, a simple model based on power balance captures the transition for the bubble velocity and matches all the experimental data despite strong time variations of bubble aspect ratio at large Reynolds numbers. Surprisingly, bubbles in the viscous regime systematically exhibit an ellipse elongated along its direction of motion while bubbles in the inertia-dominated regime are always flattened perpendicularly to it.