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The hydrodynamics of bubble columns in the heterogeneous regime is revisited.Focusing on air-water systems at large aspect ratio, we show from dimensionalanalysis that buoyancy equilibrates inertia, and that velocities scale as$(gD\varepsilon)^{1/2}$, where $D$ is the bubble column diameter, $\varepsilon$the void fraction and $g$ the gravitational acceleration.  From new experiments in a $0.4$m diameter column with ${\cal{O}}(10^3)$particle Reynolds number bubbles and from a detailed analysis of publisheddata, we confirm the self-organization prevailing in the heterogeneous regime,and that the liquid flow rate is only set by the column diameter $D$. Besides,direct liquid and gas velocity measurements demonstrate that the relativevelocity increases above the terminal velocity $U_T$ in the heterogeneousregime, and that it tends to $\sim 2.4 U_T$ at very large gas superficialvelocities $V_{sg}$. The proposed velocity scaling is shown to hold for liquidand gas mean velocities and for their standard deviations. Furthermore, it isfound to be valid over a wide range of conditions, corresponding to Froudenumbers $Fr=V_{sg}/(gD)^{1/2}$ from 0.02 to 0.5. Then, the relevance of thisscaling for coalescing media is discussed. Moreover, following the successfulprediction of the void fraction with a Zuber \& Findlay approach at thebeginning of the heterogeneous regime, we show how the void fraction iscorrelated with $Fr$. Further investigations are finally suggested to connectthe increase in relative velocity with meso-scale structures known to exist inthe heterogeneous regime.

Buoyancy driven bubbly flows: scaling of velocities in bubble columns operated in the heterogeneous regime