Bubble diameter class model

The two bubble class model is applied here to the absorption of CO2 in NaOH, which conforms to a fast pseudo-first order reaction under certain operating conditions (15). In the data reported by Schumpe et al. ( 7 ), COo was absorbed during cocurrent flow in NaOH solution in a 0.102 m diameter bubble column. The gas phase consisted of approximately 10 vol % of CO2 in N2. The gas velocities ranged from 0.025 to 0.15 m/s. Since the churn turbulent regime prevailed for gas velocities greater than approximately 0.07 m/s, only the data in the range 0.07 m/s to 0.15 m/s were considered. 

Figure 3 shows a comparison between the conversions predicted by the two bubble class model and the experimentally measured values of Schumpe et al. ( 7). In the theoretical calculations, the small bubble diameter was chosen to be 1 mm based on physical observations made by several investigators. As shown in Table III, the predicted conversions were, however, found to be relatively insensitive to the small bubble diameter. In these calculations, the small bubble diameter was varied from 1 mm to 3 mm and little effect on the conversions was observed. 

From the results described above, it is seen that the two bubble class model predicts conversions that fit the experimental data. The predicted conversions were obtained with the assumption that the large bubble size varies somewhat with the gas velocity. Thus it is required to have a knowledge of the large bubble diameter (as a function of gas velocity) to properly evaluate the validity of this model. 

The heuristic methodology we utilize is illustrated in Fig. 3. There are two kinds of resolution in the model, viz., the resolution of structure and dominant mechanisms. First, it is reasonable to resolve the flow structure into small bubbles, large bubbles, and hquid since there are plenty of reports in literature about the coexistence of small and large bubbles or a bimodal bubble size distribution (De Swart et al, 1996). This structure resolution is different from the spatial—temporal resolution of fluid domain in CFD models, and the significance fies in that the two bubble classes (TBCs) are actually relevant to the two kinds of dominant mechanisms. We will also show later that further resolution with more bubble classes in the model is not necessary and the MBSs are reduced to the TBCs. We use the following structure parameters for the description of the TBCs bubble diameters... 

With such an understanding on system complexity in mind, the DBS model is composed of two simple force balance equations, respectively, for small or large bubble classes, and one mass conservation equation as well as the stability condition serving as a variational criterion and a closure for conservative equations. For a given operating condition of the global system, six structure parameters for small and large bubble classes (their respective diameters dg, dL, volume fraction... 

The main contribution from the work of Luo [95, 96] was a closure model for binary breakage of fluid particles in fully developed turbulence flows based on isotropic turbulence - and probability theories. The author(s) also claimed that this model contains no adjustable parameters, a better phrase may be no additional adjustable parameters as both the isotropic turbulence - and the probability theories involved contain adjustable parameters and distribution functions. Hagesaether et al [49, 50, 51, 52] continued the population balance model development of Luo within the framework of an idealized plug flow model, whereas Bertola et al [13] combined the extended population balance module with a 2D algebraic slip mixture model for the flow pattern. Bertola et al [13] studied the effect of the bubble size distribution on the flow fields in bubble columns. An extended k-e model was used describing turbulence of the mixture flow. Two sets of simulations were performed, i.e., both with and without the population balance involved. Four different superficial gas velocities, i.e., 2,4,6 and 8 (cm/s) were used, and the superficial liquid velocity was set to 1 (cm/s) in all the cases. The population balance contained six prescribed bubble classes with diameters set to = 0.0038 (m), d = 0.0048 (m), di = 0.0060 (m), di = 0.0076 (m), di = 0.0095 (m) and di = 0.0120 (m). 

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