There exists a narrow operating window in bubble columns

A new theory to predict liquid circulation was derived and compared with applicable literature data. A single dimensionless group, ?(gRd2/ v:), is shown to control mixing intensity under low-viscosity conditions, Richard G. Rice but two separate groups (z and gRd2/vz) are necessary for viscous Nicholas W. Geary systems. Closure was accomplished using the Prandtl model for Department of Chemical Engineering Reynolds stress. Locally varying mixing length was taken to be Louisiana State University proportional to bubble size and bubble concentration. The model was Baton Rouge, LA 70803constructed based on the premise that two distinct zones exist: a mainly turbulent core joined to a thin viscous wall layer.

The liquid circulation model of Rice and Geary (1990) is extended to include turbulence originating at the wall. Thus, two possible length scales are considered: one originating from rising bubbles and the other emanating from the wall. The appropriate scale for small columns should be based on bubble size, while for larger systems the proper mixing length is proportional to column diameter. It is proposed that the film Reynolds number may be the key in distinguishing the two cases.

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The prediction of mixing in bubble columns, especially that of axial dispersion coefficient, has received considerable attention in recent years, and it is clear that wide disagreement exists. A recent compilation of many results (Rice and Littlefield, 1987) showed order of magnitude differences among several research groups.Generally, mixing in unstirred vessels has been correlated with respect to two key parameters: column diameter and superficial gas velocity. However, two recent papers (Tinge and Drinkenburg, 1986;Rice and Littlefield, 1987) have shown that slight departure from true verticality ( t 2 degrees) had a much stronger effect than diameter and velocity. However, the former used very small diameter columns, while the latter presented sparse results. Predating these mixing studies, Valdes-Kreig et al. (1975) observed that vertical misalignment can strongly affect surfactant removal in a foam fractionation column.In this study, we present new visual VCR experimental evidence, using the acid-base technique described by Rice and Littlefield (1987). This technique allowed the following aspects to be studied:Entrance length for fully developed bubbly flow. Measurement of dispersion coefficient within the bubbly flow region, thereby mitigating inflation of values caused by the entrance region.Testing the "summation of resistance" hypothesis for twozone bubble columns.Measurement of enhanced mixing times and effective dispersion coefficient for controlled column tilt. Measurement TheoryThe basis for the batch acid-base technique is to set up two separated regions driven by the concentration gradient of AIChE Journal September 1990Fickian-like character. The measurement of the movement of the boundary can then be related to the effective dispersion coefficient. Baird et al. (1976) were perhaps the first to use the acid-base technique for dispersion measurement, although their solution of the Fickian equations differs slightly from that of Rice and Littlefield (1987) who gave the following result:where the pair [zn, t,] portrays the position-time movement of the LON (line of neutralization). For long times, because D, t,/ Lz > 0.3 the series terms can be ignored, so that A "one-shot'' experiment can be performed without using a VCR by measuring the time to neutralize the total column contents, denoted as t $ so when z, = L, then we have