A Hydrodynamic Interpretation of the Interchange

In reality, the bubble is not spherical, but more like that shown on the right-hand side of Fig. 13.5.3-1. Partridge and Rowe [1966] found experimentally that the wake occupies 25 percent of the spherical bubble volume. They also found that the ratio of the sum of the volumes of the bubble and the interchange zone to the volume of the bubble itself is given by a/(a - 1), where a = Ubsju f [Partridge and Rowe, 1966]. From this fundamental picture, the interchange coefficient has been derived in several ways. 

Krishna [1981] tried to confirm values and trends for A/starting from the model of Davidson and Harrison [1971] derived from hydrodynamic observations and theory. Davidson and Harrison expressed the interaction between the bubble phase and the emulsion in terms of two contributions cross flow and diffusion. The total rate of gas transfer, Q (in m%), is derived to be 

Gas streamlines for a real three-dimensional bubble when a = UiJ uJeJ) = 1.5. (a) Murray streamlines for spherical bubble, (b) Streamlines for bubble with particle wake. From Partridge and Rowe [1966]. 

The first term in (13.5.3-1) is the flow term. It dominates in the range of flow rates encountered in commercial practice. The second term expresses the transfer by effective diffusion. The interchange coefficient ki is related to ( by 

Since (4 varies with the bed height, 1/also depends on Z It follows from (13.5.3-2) that kjlfb is independent of dt, in contradiction with the van Swaaij-Zuiderweg correlation. One should keep in mind, however, that ki derived from experiments is really an integral over the total bed height of point values, kj  

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