Relationship Between Kolmogorov Entropy and Characteristic Mixing Length in Narrow Bubble Columns Operated in the Transition Flow Regime

The mixing performance of bubble column reactors depends strongly on the prevailing flow regime. Kawase and Tokunaga (Can. J. Chem. Eng. 69, 1228-1231, 1991) introduced the characteristic mixing length L as an important mixing parameter. In the homogeneous regime the liquid mixing is at the scale of the bubble diameter, whereas in the heterogeneous regime it is at the scale of the column diameter. Our research is aimed at determining the scale of liquid mixing in the transition flow regime by using some advanced methods.
The Kolmogorov entropies (KE) were extracted from gas holdup time series measured (at 2000 Hz) by a new type of wire mesh sensor. It was found that in a relatively narrow bubble column (0.15 m in ID, clear liquid height = 2 m) operated with an air-water system in the transition flow regime the KE values could be correlated to L. The KE in the transition flow regime decreases monotonously and can be correlated to the superficial gas velocity (KE=1.5Ug^-0.38). The same exponent (-0.38) for UG was reported by Kawase and Tokunaga (1991) in their correlation for prediction of L. Therefore, the KE and L values (in a narrow bubble column) are correlated as follows: KE=222.222L.
A new parameter called maximum number of visits per region Nv-max was also introduced and in the same way was related to L in the transition flow regime.