Interface bubble/cloud

For most practical conditions, a comparison of k and k from Equations (4) and (5) would suggest that the principal resistance to transfer resides at the outer cloud boundary. However, when (a), (b) and (c) are taken into account, this is no longer the case. In fact, experimental evidence (e.g. 30,31,32) indicates strongly that the principal resistance is at the bubble/ cloud interface. With this in mind, it is probably more sensible to include the cloud with the dense phase (as in the Orcutt (23, 27) models) rather than with the bubbles (as in the Partridge and Rowe (37) model) if a two-phase representation is to be adopted (see Figure 1). If three-phase models are used, then Equations (2) and (5) appear to be a poor basis for prediction. Fortunately the errors go in opposite directions. Equation (2) overpredicting the bubble/cloud transfer coefficient, while Equation (5) underestimates the cloud/emulsion transfer coefficient. This probably accounts for the fact that the Kunii and Levenspiel model (19) can give reasonable predictions in specific instances (e.g.20),... 

After defining the exchange coefficients for bubble-cloud and cloud-emulsion interfaces (Equations 22.30 and 22.31), and assuming a first-order reaction, we get the following equation ... 

The fourth term in Eq. 11.22 represents the mass transfer at the bubble-cloud interface. The mass balance for the cloud phase is ... 

From these data, it is possible to calculate the transfer coefficients at the bubble interface with the cloud, he, using the following empirical equation (Equation 22.30) ... 

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