Water drops in air

U. Single water drop in air, liquid side coefficient / jy l/2 ki = 2 ), short contact times / J 1 lcontact times dp [T] Use arithmetic concentration difference. Penetration theory, t = contact time of drop. Gives plot for k a also. Air-water system. [lll]p.. 389... 

FIG. 6-60 Drag coefficient for water drops in air and air hiihhles in water. Standard drag curve is for rigid spheres. (From Clift, Grace, and Weher, Biih-hles. Drops and Particles, Academic, New York, 1978. )... 

Terminal velocities for water drops in air have been correlated by Berry and Pruager (J. Appl. Meteoml., 13, 108-113 [1974]) as... 

When a fluid sphere exhibits little internal circulation, either because of high K = Pp/p or because of surface contaminants, the external flow is indistinguishable from that around a solid sphere at the same Re. For example, for water drops in air, a plot of versus Re follows closely the curve for rigid spheres up to a Reynolds number of 200, corresponding to a particle diameter of approximately 0.85 mm (B5). In fact, many of the experimental points used in Section II to determine the standard drag curve refer to spherical drops in gas streams, where high values of k ensure negligible internal circulation. 

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. 

Fig. 5.25 Dimensionless fluid velocities for water drops in air (/c predictions of LeClair et al. (L9).

Fig. 5.26 Streamlines and vorticity contours inside a water drop in air at Re y = 790). Numerical predictions of LeClair (L5).

Fig. 5.28 Distribution of dimensionless modified pressure at surface of spheres at Re = 100, compared with potential flow distribution. (A) Potential flow (p, — Px)/ipU = 1 — 2.25sin fl (B) Rigid sphere (L5) (C) Water drop in air k = 55, y = 790 (L9) (D) Gas bubble k — y 0 (H6).

Because of their practical importance, water drops in air and air bubbles in water have received more attention than other systems. The properties of water drops and air bubbles illustrate many of the important features of the ellipsoidal regime. 

As for other types of fluid particle, the internal circulation of water drops in air depends on the accumulation of surface-active impurities at the interface (H9). Observed internal velocities are of order 1% of the terminal velocity (G4, P5), too small to affect drag detectably. Ryan (R6) examined the effect of surface tension reduction by surface-active agents on falling water drops. 

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. 

This form of correlation was used by Beard (B3) to suggest a correlation for water drops in air under different atmospheric conditions. It should be used with caution for gases with properties widely different from air under atmospheric conditions, but the range of liquid properties covered is broad. 

In general, oscillations may be oblate-prolate (H8, S5), oblate-spherical, or oblate-less oblate (E2, FI, H8, R3, R4, S5). Correlations of the amplitude of fluctuation have been given (R3, S5), but these are at best approximate since the amplitude varies erratically as noted above. For low M systems, secondary motion may become marked, leading to what has been described as random wobbling (E2, S4, Wl). There appears to have been little systematic work on oscillations of liquid drops in gases. Such oscillations have been observed (FI, M4) and undoubtedly influence drag as noted earlier in this chapter. Measurements (Y3) for 3-6 mm water drops in air show that the amplitude of oscillation increases with while the frequency is initially close to the Lamb value (Eq. 7-30) but decays with distance of fall. 

Figure 6-60 gives the drag coefficient as a function of bubble or drop Reynolds number for air bubbles in water and water drops in air, compared with the standard drag curve for rigid spheres. Information on bubble motion in non-Newtonian liquids may be found in Astarita and Apuzzo (AIChE J., 11, 815-820 [1965]) Calderbank, Johnson, and Loudon (Chem. Eng. Sci., 25, 235-256 [1970]) and Acharya, Mashelkar, and Ulbrecht (Chem. Enz. Sci., 32, 863-872 [1977]). 

There is a critical drop radius, rcritkal, for equilibrium with the surrounding vapor pressure, because smaller drops have a higher vapor pressure and will spontaneously evaporate, and all drops larger than this size will grow at the expense of smaller (and unstable) droplets. For a water drop in air and also an air bubble in water, the effect of radius of curvature on equilibrium vapor pressures is given in Table 4.1. It can be seen that below a droplet size of lOnm, there is a considerable vapor pressure increase over the vapor pressure of flat surfaces due to the presence of curvature. 

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