The Case of Bubbles

FIGURE 8.17, Detailed structure of a bubble The thickness e depends on d. 

The variation of 7 with latitude [equation (8.39)] must be inserted into equation (8.41) to give finally 

In practice, a bubble is not quite the ideal object we have just described. At the moment of its birth, the thickness e is not the same everywhere. There are heavier regions and lighter regions. This gradient can generate flows akin to turbulent motions in films and gives rise to the shimmering iridescence of bubbles. 

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The gas-liquid flow characteristics of stirred vessels depend both on the level of agitation and the rate of gas flow and can vary from the case of bubble column type operation to that of a full circulating tank, as shown in Fig. 5.123. The mixing characteristics and gas distribution obtained, obviously exert a considerable influence on the rate of mass transfer obtained (Harnby et al., 1985). 

The influence of dispersed-phase viscosity was found to be negligible by Hayworth and Treybal (H5), but found to be significant (K2) when a greater range of dispered-phase viscosity was investigated. From the graph of Hayworth and Treybal, the influence of interfacial tension appears, as in the case of bubbles, to be more at low flow rates than at high flow rates. 

Smaller limestone particles possess shorter pores. Figure 44 shows that as particle diameter decreases, the pore volume increases, especially for particles measuring below 250 /im in diameter. Wu and Zhang (1988) attributed this phenomenon to increased absorption of mechanical energy as particles become smaller. An effective way to improve pore structure, and therefore, S02 capture, is to reduce particle size. For CFBC, addition of fine limestone is feasible without the carryover problem in the case of bubbling fluidization, often resulting in a calcium availability of as high as 50%. 

The above analysis can be applied for the case of bubble columns. From Figure I it can be seen that, near the wall the axial component of the liquid velocity is downwards, whereas the radial component of the liquid velocity is towards the wall in the top half of the circulation cell and away from the wall in the lower half of the circulation cell. As a result, for one circulation cell the enhancement factor is given by the following equation ... 

In bubble columns, the estimation of parameters is more difficult than in the case of either gas-solid or solid-liquid fluidized beds. Major uncertainties in the case of bubble columns are due to the essential differences between solid particles and gas bubbles. The solid particles are rigid, and hence the solid-hquid (or gas-solid) interface is nondeformable, whereas the bubbles cannot be considered as rigid and the gas-liquid interface is deformable. Further, the effect of surface active agents is much more pronounced in the case of gas-liquid interfaces. This leads to uncertainties in the prediction of all the major parameters such as terminal bubble rise velocity, the relation between bubble diameter and terminal bubble rise velocity, and the relation between hindered rise velocity and terminal rise velocity. The estimation procedure for these parameters is reviewed next. 

After completing reaction-engineering work, it is first necessary to evolve a reactor configuration before one can start evaluating whether such hardware can perform the expected duties. In the case of bubble columns, evolving reactor hardware involves at least the following (also see Fig. 11.2) ... 

The formulation of a proper e - equation for the case of bubbly flow was found to be more severe. As a first approach they adopted the above equation developed from the single phase transport equations (5.3). However, analyzing the two physical situations mentioned above, they found that this model formulation fails to produce both the asymptotic value and the time constant of homogeneous decay of grid generated bubbly flow turbulence. That is, the modified single-phase model did not break down, but it gave rise to unphysical solutions for such cases. 

Fig. 10.6. Illustrations of the impracticability of flotation at sufficiently great charges of the same sign of particle and bubble (a), the practicability of flotation in the case of bubble recharging of the bubble charge (b, curve 1). Curves 2 and 1 in (b) illustrate the possibility of flotation at the effective radius of the non electrostatic repulsion forces, which is smaller than the thickness of the double layer (2) and its impracticability in the opposite case (3).

Considerable work has been reported also for the case of bubble-liquid mass transfer and its associated coefficient kj. A general review of much of this was given by Calderbank [P.H. Calderbank in Mixing, Vol. II (V.W. Uhl and J.B. Gray, eds.). Academic Press, New York, NY, (1967)], and a correlation reported there has passed the test of time rather well. 

This error is large in the case of bubbles within a resonant field. In the light of this, Yosioka and Kawasima extended King s theory to allow for compressible spheres in 1955. They demonstrated that the time-averaged acoustic radiation force on a spherical particle of radius a, at position X within a one-dimensional standing wave of acoustic energy density e is... 

For most applications of interest, including cells in aqueous solution, the acoustic force will act towards the pressure node however, in the case of bubbles that are smaller than resmiant size, and certain two-phase fluid mixtures, the bubble, or second phase fluid, will experience... 

As in the case of bubble point pressures, the temperature dependence of normally or near-normally saturated cryogenic data is solely due to which type of pressurant gas is in... 

The converse of all the above is true for the case of bubble-point liquid feed. 

A stepwise illustration for the case of bubble-point feed is as follows. In this discussion, note that the x and y values refer to the light key mole fractions in a pseudobinary system consisting only of the keys. These concentration values are... 

Only a few recent results for co-current downflow packed bed and well stirred tank will be presented in the present review for the illustration of the previous considerations and because of the complex and simultaneous mechanism involved. A similar and complete review for the case of bubble columns may be obtained in the texts published by Deckwer et al. (72) and by Kastanek et al. (73). 

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