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Many applications involve a three-step process with high velocity first tearing wave crests away from liquid sheets, followed by breakup of ligaments into large droplets, followed by breakup of the large droplets. The prediction of final droplet size based on power/mass works surprisingly well, as shown by Eqs. (14-198),(14-201), (14-202), and (14-203).

Liquid-Column Breakup Because of increased pressure at points of reduced diameter, the liquid column is inherently unstable. As a result, it breaks into small drops with no external energy input. Ideally, it forms a series of uniform drops with the size of the drops set by the fastest-growing wave. This yields a dominant droplet diameter about 1.9 times the initial diameter of the jet as shown by

FIG. 14-85 (a) Idealized jet breakup suggesting uniform drop diameter and no satellites. (b) and (c) Actual breakup of a water jet as shown by high-speed photographs. [From W. R. Marshall, "Atomization and Spray Drying," Chem. Eng. Prog. Monogr. Ser, no. 2 (1954).]

FIG. 14-85 (a) Idealized jet breakup suggesting uniform drop diameter and no satellites. (b) and (c) Actual breakup of a water jet as shown by high-speed photographs. [From W. R. Marshall, "Atomization and Spray Drying," Chem. Eng. Prog. Monogr. Ser, no. 2 (1954).]

Fig. 14-85. As shown, the actual breakup is quite close to prediction, although smaller satellite drops are also formed. The prime advantage of this type of breakup is the greater uniformity of drop size.

For high-viscosity liquids, the drops are larger, as shown by Eq. (14-191):

where

D = diameter of droplet Dj = diameter of jet |t = viscosity of liquid pt = density of liquid C = surface tension of liquid

These units are dimensionally consistent; any set of consistent units can be used.

As the velocity of the jet is increased, the breakup process changes and ultimately becomes a mix of various competing effects, such as the capture of small drops by bigger ones in the slowing jet and the "turbulent breakup" of the bigger drops. The high-velocity jet is occasionally used in process applications because of the very narrow spray angle (5-20°) and the high penetration into a gas it can give. The focused stream also aids erosion of a surface.

Liquid-Sheet Breakup The basic principle of most hydraulic atomizers is to form a thin sheet that breaks via a variety of mechanisms to form ligaments of liquid which in turn yield chains of droplets. See Fig. 14-86.

For a typical nozzle, the drop size varies with 1/(pressure drop)1/3. When (velocity)2 is substituted for pressure drop, droplet size is seen to vary with (velocity)-23.

Isolated Droplet Breakup—in a Velocity Field Much effort has focused on defining the conditions under which an isolated drop will break in a velocity field. The criterion for the largest stable drop size is the ratio of aerodynamic forces to surface-tension forces defined by the Weber number, NWe (dimensionless):

Nwe crit = constant = [pG (velocity)2(DmJ/(a)] (14-192)

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