Drops in Liquids

Figure 7-23. Parameters for pressure drop in liquid/gas flow through horizontal pipes. (Source Lockheed and Martinelli, Chem. Engr. Prog., 45, 39, 1949.)...

Vh = vapor velocity through valve holes, ft/sec P = tray aeration factor, dimensionless AP = tray pressure drop, in. liquid pvm = valve metal density, tj = tray deck thickness, in. 

AP = pressure drop, in. liquid X, = slope ratio, slope equilibrium line/slope operating line. Equation 8-329 p = density, Ib/ft ... 

Dry Cray pressure drop, in. liquid hL = Clear liquid head, m... 

Actual tray pressure drop, in. liquid Prandtl number dimensionless Fractional opening in the circumference or a valve or. Pi... 

AP(j = dry bed pressure drop, in. water/ft AP = operating pressure drop, in. liquid/ft e = base of natural logarithms Xi,X2 = curve fit coefficients for C2, Table 9-32. 

AP = Wet pressure drop, in. liquid/ft packed height (Nutter)... 

Handlos, A. E. and Baron, T. A.I.Ch.E.Jl. 3 (1957) 127. Mass and heat transfer from drops in liquid-liquid extraction. 

Moore, G. R. (1956). Vaporization of superheated drops in liquids. Ph.D. Thesis, University of Wisconsin, Madison. 

Figure 5.24 shows predicted surface vorticity distributions at Re = 100 and for K = 0 (gas bubble), k = 1 (liquid drop in liquid of equal viscosity), and K = 55 (water drop in air), and for a rigid sphere. The results for the raindrop are very close to those for a rigid sphere. The bubble shows much lower surface vorticity due to higher velocity at the interface, while the k = 1 drop is intermediate. The absence of separation for the bubble and k = 1 drop is indicated by the fact that vorticity does not change sign. 

As indicated in Chapter 2, liquid drops falling through gases have such extreme values of y and k that they must be treated separately from bubbles and drops in liquids. Few systems have been investigated aside from water drops in air, discussed above, and what data are available for other systems (FI, G5, L5, V2) show wide scatter. Rarely have gases other than air been used, and some data for these cases [e.g. (L5, N2)] cannot be interpreted easily because of evaporation and combustion effects. Results for drops in air at other than room temperature (S8) differ so radically from results of other workers that they cannot be used with confidence. 

Fig. 7.13 Flow transitions for bubbles and drops in liquids (schematic).

The assumption of transfer by a purely turbulent mechanism in the Handlos-Baron model leads to the prediction that the internal resistance is independent of molecular diffusivity. However, such independence has not been found experimentally, even for transfer in well-stirred cells or submerged turbulent jets (D4). In view of this fact and the neglect of shape and area oscillations, models based upon the surface stretch or fresh surface mechanism appear more realistic. For rapid oscillations in systems with Sc 1, mass transfer rates are described by identical equations on either side of the drop surface, so that the mass transfer results embodied in Eqs. (7-54) and (7-55) are valid for the internal resistance if is replaced by p. Measurements of the internal resistance of oscillating drops show that the surface stretch model predicts the internal resistance with an average error of about 20% (B16, Yl). Agreement of the data for drops in liquids with Eq. (7-56) considerably improves if the constant is increased to 1.4, i.e.. 

For a bubble to grow, vapor must pass from the superheated liquid into the bubble. Thus latent heat of vaporization is removed from the surrounding liquid, and the liquid cools. The drop in liquid temperature near the bubble means a decrease in the driving force between liquid and bubble. This temperature drop strongly affects the bubble rate of growth. The rate can be shown to approach asymptotically a condition whereby the radius increases according to the square root of time. 

As the fluids travel down the bed, the energy losses decrease the pressure. As the pressure is dropped, the gas expands. The expansion results in a decrease in liquid holdup. However, the relative pressure drop for the commercial size bed at a depth of 3.8 m is 1.9% of the initial value while for the laboratory column at the same depth this value is 73%. The gas in the low pressure bed consequently expands five fold from 200cc/g to 1000 cc/g, at a pressure of 4 atm, while the high pressure bed gas specific volume remains nearly constant at 23.8cc/g for a pressure of 35 atm. It is this large expansion which is responsible for the appreciable drop in liquid holdup for the small reactor. 

Fig. 5.7. Shape regimes for bubbles and drops in liquid. Reprinted from Clift et al [22] with permission from Elsevier.

---