Pi

where U2J is the velocity of the swarm of bubbles, g is gravitational acceleration, pL is the density of liquid, Ap is the density difference, a is the surface tension, and u is the gas holdup. This equation is valid for bubble diameters of the order of 0.1 to 2 cm, which covers the population usually observed in ALRs.

It has, however, been shown (71) that a plot of UG versus J gives a straight line, suggesting that a constant value of the drift velocity satisfactorily represents the two-phase flow in the riser of an external-loop ALR. In this plot, the distribution parameter was C0 = 1.03, and UGS, the value of the slip velocity of a bubble, was taken as the mean drift velocity. Siegel et al. (35) applied the same model for the study of gas recirculation in a split-vessel ALR and obtained the values of C0 = 1.11. The slip velocity that they obtained fitting their data to equation 8 was 0.238 m/s. It has been suggested (71) that this simplification holds as long as coalescence is not a predominant factor in the process.

It is very important to stress the difference between holdup, u, and the flowing volumetric concentration (fi), which is defined as:

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