Velocity of a large bubble rising in a stagnant liquid inside an inclined rectangular channel

Abstract

The velocity of large air bubbles rising in an inclined rectangular channel filled up with stagnant water is investigated within the inertial flow regime. The experiments based on bubble observation by means of a high-speed camera are carried-out in a versatile channel with easily adaptable geometry over a wide range of inclination angles. The results obtained in vertical channels of various aspect ratios are confronted with the previous analytical predictions to confirm bubble velocity scaling based on the channel perimeter. The extrapolation of velocity measurements done at very low inclinations then provides the translation velocities of large bubbles corresponding to horizontal channel placements. These velocities agree well with the results of previous channel emptying experiments and suggest velocity scaling based on the channel height. Markedly different dependences of the bubble rise velocity on the channel inclination are observed in flat and tall channels. The analysis of our experimental data provides a simple model for the prediction of the bubble rise velocity in inclined rectangular channels. The effects of leveling and buoyancy, which are jointly acting on bubbles in inclined channels, are incorporated into the model through two principal parameters: the limiting bubble velocities achieved at the horizontal and vertical channel placement. Considering the inertial regime of large Taylor bubbles, these limiting velocities are predictable with a sufficient accuracy.