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A new statistical parameter was de ned in order to determine the range of applicability of the mixing length concept in two bubble columns. Gas holdup time series (60,000 points) were measured in two bubble columns (0.15 and 0.4 m in i.d.) by a conductivity wire-mesh sensors. The new statistical parameter Φ was de ned as the ratio of the mean value of the signal to three times the average absolute deviation (3AAD) and it was correlated to the mixing length. It was found that this new correlation was not valid in all hydrodynamic regimes. It is applicable only in the transition ow regime. Such a clari cation has not been provided in the literature so far. In the narrow bubble column, the results were also conrmed on the basis of the Kolmogorov entropy and another statistical parameter. The new parameter Φ was also used for ow regime identi cation. In the narrow bubble column, the rst transition velocity Utrans was identi ed at 0.034 m/s; whereas, the second Utrans occurred at 0.112 m/s. In the large bubble column, the two Utrans values were identi ed at 0.045 and 0.101 m/s, respectively.

Statistical Validation of the Mixing Length Concept in Bubble Columns Operated in the Transition Flow Regime