Bubbles and Drops

Fig. 11-16. Shapes of sessile and hanging drops and bubbles (a) hanging drop (b) sessile drop (c) hanging bubble (d) sessile bubble.

The cases of the sessile drop and bubble are symmetrical, as illustrated in Fig. n-16. The profile is also that of a meniscus 0 is now positive and, as an... 

Fig. 6. Shape of drops and bubbles, (a) Bubble rising in sparged tower system air-water. Courtesy of Shell Development Co. (b) Bubble and droplet...

TABLE 5-25 Mass-Transfer Correlations for Drops and Bubbles... 

TABLE 5-26 Mass-Transfer Correlations for Particles, Drops, and Bubbles in Agitated Systems... 

G. Highly agitated systems solid particles, drops, and bubbles continuous phase coefficient [E] Use arithmetic concentration difference. Use when gravitational forces overcome by agitation. Up to 60% deviation. Correlation prediction is low (Ref. 118). (PA, ar.k) = power dissipated by agitator per unit volume liquid. [79][83]p.231 [91] p. 452... 

Numerous studies of the formation and flow of gas bubbles in liquids have appeared in the literature, and a complete review will not be attempted. Attention is drawn to two recently published reviews, that of Jackson (Jl) on the formation and coalescence of drops and bubbles in liquids, and that of Govier (G6) on developments in the understanding of the vertical flow of two phases. 

Acrivos, A., The breakup of small drops and bubbles in shear flows. 4th International Conference on Physicochemical Hydrodynamics, Ann. N. Y. Acad. Sci., 404, 1-11 (1983). 

Rallison, J. M., The deformation of small viscous drops and bubbles in shear flows. Ann. Revs. Fluid Mech. 16, 45-66 (1984). 

Harmathy, T., 1960, Velocity of Large Drops and Bubbles in Media of Infinite and Restricted Extent, AIChE J. 6 281. (3)... 

For larger Reynolds numbers (1 < NRe < 500), Rivkind and Ryskind (see Grace, 1983) proposed the following equation for the drag coefficient for spherical drops and bubbles ... 

Kendall JM, Chang M, WangTG (1989) Third International Conference on Drops and Bubbles, Monterey, CA, American. Institute of Physics Proceedings, p 197... 

Grace, J.R., Wairegi, T. and Nguyen, T.H., Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Transactions of the Institution of Chemical Engineers, 54, pp. 167-73 (1976). 

Harmathy, T.Z., Velocity of large drops and bubbles in media of infinite and restricted extent, AIChE Journal, 6, pp. 281-88 (1960). 

Wallis, G.B., The terminal speed of liquid drops and bubbles in an infinite medium, International Journal ofMultiphase Flow, l,pp. 491-511 (1974). 

Passerone, A. and Ricci, E. (1998) High Temperature Tensiometry Drops and Bubbles in Interfacial Research, eds. Mobius, D. and Miller, R. (Elsevier, Amsterdam), p. 475. 

Calderbank (C3) has given different correlations for drops and bubbles as well as for coalescing and noncoalescing systems. However, Jackson (Jl) has pointed out that it is unlikely that an absolute classification of this type is possible in practice, where speed of coalescence is continuously varying. 

The rates at which drops and bubbles rise and fall are rather more sensitive to traces of surface-active materials than are the mass-transfer coeflScients 77a, 77b). Whereas, for example, the rate of fall of CCh drops... 

A major point we emphasize is that, from a reaction engineering viewpoint, these are all essentially identical problems. The fluid may be a gas or a liquid, and the particle may be a liquid, gas, or a solid, but the geometries and the reactions are very similar. The interfaces may be gas-liquid, liquid-liquid, gas-soHd, or liquid-solid. For gas-Hquid problems we have drops and bubbles rather than particles, but the geometries are identical. These systems are the subject of Chapter 12. The applications are also quite different, but, once one realizes the similarities, the same ideas and equations unify all these problems. 

We title this chapter the reactions of sohds and we deal mostly with gaseous and sohd reactants and products, but the same ideas and equations apply to gas-hquid and liquid-liquid systems. For example, in fiying of foods, the fluid is obviously a liquid that is transferring heat to the sohd and carrying off products. The same equations also apply to many gas-hquid and liquid-hquid systems. The drops and bubbles change in size as reactions proceed so the same equations we derive here for transformation of sohds wiU also apply to those situations. 

Of course, the growth or dissolution of bubbles from liquid solution has the same geometry and equations. In both drops and bubbles the situation could involve chemical... 

In some multiphase reactors, stirring with an impeller or the flow pattern caused by gravity will control the interfacial area. By suitably designing and positioning propellers and reactant injection orifices or by using static mixers, it is possible to provide very efficient breakup of hquids into drops and bubbles. A factor of two decrease in drop or bubble size means a factor of four increase in interfacial area. 

Surface tension can be very important in deternhning drop and bubble sizes and shapes. This ultimately controls the size of drops and the breakup of films and drops. The presence of surface active agents that alter the interfacial tension between phases can have enormous influences in multiphase reactors, as does the surface tension of sohds and the wetting between solids and liquids. 

If an isolated drop or bubble rises or falls in the reactor, then the flow pattern in this phase is clearly unmixed, and this phase should be described as a PFTR. However, drops and bubbles may not have simple trajectories because of stirring in the reactor, and also drops and bubbles can coalesce and breakup as they move through the reactor. 

The bubble column and spray tower depend on nozzles to disperse the drop or bubble phase and thus provide the high area and small particle size necessary for a high rate. Drop and bubble coalescence are therefore problems except in dilute systems because coalescence reduces the surface area. An option is to use an impeller, which continuously redisperses the drop or bubble phase. For gases this is called a sparger reactor, which might look as shown in Figure 12-16. 

Thus this reactor requires mass transfer between the gas and hquid phases and between the organic and aqueous liquid phases. Stirring to mix phases, make small drops and bubbles, and increase inter-facial mass transfer is crucial in designing an alkylation reactor. 

As noted in Chapter 2, bubbles and drops remain nearly spherical at moderate Reynolds numbers (e.g., at Re = 500) if surface tension forces are sufficiently strong. For drops and bubbles rising or falling freely in systems of practical importance, significant deformations from the spherical occur for all Re > 600 (see Fig. 2.5). Hence the range of Re covered in this section, roughly 1 < Re < 600, is more restricted than that considered in Section II for solid spheres. Steady motion of deformed drops and bubbles at all Re is treated in Chapters 7 and 8. 

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