Stability bubble columns

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

Equation (61) is the transition criterion provided the conditions given by equation (52) are satisfied. From Table I it can be seen that these conditions are satisfied only in the case of gas-solid fluidized beds and in some cases of solid-liquid fluidized beds where ps Pl- Therefore, for other multiphase dispersions [such as gas-liquid (bubble columns) and solid-liquid fluidized beds (where pl is not negligible)] the comparison of dynamic wave velocity with continuity wave velocity is not valid for deciding the bed stability. Further, the above analysis holds for transition from region I to II (point P in Fig. 1) and not for III to II (point Q). Therefore, the criterion does not hold for bubble columns and dilute dispersions. 

Various model parameters involved in the derivation of the stability criterion need to be specified in order to use the stability criterion for quantitative predictions. Model parameters essential for this purpose include the slip velocity, the virtual mass coefficient, and the dispersion coefficient. The procedure for estimation of these parameters is given for gas-solid (and solid-liquid) fluidized beds and bubble columns. 

Parameters Appearing on the Stability Criterion (Bounded Analysis) for Rectangular Bubble Columns Cartesian Coordinates... 

Following a procedure analogous to that used in derivation of the stabihty criterion for two-dimensional bubble columns, the stability criterion for cyhndrical bubble columns is given as... 

Height of the column, m Dimensionless height of bubble column Parameter of the stability criterion The drift velocity, m/s Separation constant in (166)... 

FIGURE 11.17 (a) Schematic representation of the homogeneous regime uniform concentration and size distributions of bubbles in the transverse direction, (b) Schematic representation of the heterogeneous regime nonuniform concentration and bubble size distributions in the transverse direction. (From Bhole, M. R. and Joshi, J. B. Stability analysis of bubble columns Predictions for regime transition. Chem. Engr. Set, 4493-4507 (2005).)... 

Le6n-Becerril, E., Cockx, A., and Lind, A. (2002), Effect of bubble deformation on stability and mixing in bubble columns, Chemical Engineering Science, 57(16) 3283-3297. 

Le6n-Becerril, E., and Line, A. (2001), Stability analysis of a bubble column, Chemical Engineering Science, 56(21-22) 6135-6141. 

Ruzicka MC, Vecer MM, Orvalho S, Drahos J. (2008) Effect of surfactant on homogeneous regime stability in bubble column. Chem. Eng. Sci., 63 951-967. 

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