Mixing by a bubbly flow in a Hele-Shaw cell: time-resolved measurements and modelling

The present work investigates the mixing of a low diffusivity fluorescent dye within a homogeneous swarm of high-Re air bubbles rising in a vertical Hele-Shaw cell filled with water, for gas volume fractions from 1.4 to 5.4%. A given amount of Rhodamine WT is injected at a given location within the bubble swarm during a finite time at the beginning of the experiment. The bubbles motion generates liquid agitation, which causes a specific mixing of the dye. The local dye concentration at a given location is measured by an original Laser Induced Fluorescence (LIF) technique. On one side of the cell, a first optical fibre connected to a laser is used to light up a volume of 0.2 mm³. On the other side of the cell, a second optical fibre collects the emitted light in an observation volume of 7 mm³. Thanks to a spectrophotometer connected to this fibre, the fluoresced light, which intensity is proportional to the dye concentration, is separated from the incident light. This system allows us to record the time evolution of the local dye concentration at a frequency of 250 Hz. Concurrently, the distribution of the bubbles around the measurement volume is imaged with a high speed camera synchronized with the spectrometer. This camera is used to assess the LIF technique in bubbly flow. At a certain distance above the injection point, the dye concentration signal is characterized by rapid and intense fluctuations corresponding to the passages of patches of dye carried by individual bubbles superimposed to a slow global evolution. The global time evolution of the concentration shows two stages. It first increases as the injected dye is transported by the bubbles towards the measurement volume and then decreases as it moves farther. At large time, the global decrease is observed to be exponential, which is incompatible with a Fickian diffusive process but consistent with the transport of the dye by the mean wakes and the wake vortices that are quickly damped out by wall friction. The mixing by the bubble swarm is a convective intermittent process