Breakup drop size

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Breakup of a. meet of liquid (Ih/elocity) . This governs drop size in most hydraulic spray nozzles. 

Further differences from hydraulic nozzles (controlled by sheet and ligament breakup) are the stronger increase in drop size with increasing surface tension and decreasing gas density. 

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

Pipe Lines The principal interest here will be for flow in which one hquid is dispersed in another as they flow cocurrently through a pipe (stratified flow produces too little interfacial area for use in hquid extraction or chemical reaction between liquids). Drop size of dispersed phase, if initially very fine at high concentrations, increases as the distance downstream increases, owing to coalescence [see Holland, loc. cit. Ward and Knudsen, Am. In.st. Chem. Eng. J., 13, 356 (1967)] or if initially large, decreases by breakup in regions of high shear [Sleicher, ibid., 8, 471 (1962) Chem. Eng. ScL, 20, 57 (1965)]. The maximum drop size is given by (Sleicher, loc. cit.)... 

For fluid particles that continuously coalesce and breakup and where the bubble size distributions have local variations, there is still no generally accepted model available and the existing models are contradictory [20]. A population density model is required to describe the changing bubble and drop size. Usually, it is sufficient to simulate a handful of sizes or use some quadrature model, for example, direct quadrature method of moments (DQMOM) to decrease the number of variables. 

It is also important to note Ca, , says nothing about the drop sizes produced upon breakup The value of Ca t only gives the maximum drop size that can survive in a given flow in the absence of coalescence. This result may appear to suggest that the most effective dispersion—leading to the finest drop sizes—occurs when viscosities are nearly matched. As we shall see later on, this perception turns out to be incorrect. Nevertheless, an understanding of Fig. 14 constitutes the minimum level of knowledge needed to rationalize dispersion processes in complex flows. 

Consider drops of different sizes in a mixture exposed to a 2D extensional flow. The mode of breakup depends on the drop sizes. Large drops (R > Caa,tal/xcy) are stretched into long threads by the flow and undergo capillary breakup, while smaller drops (R Cacri,oV/vy) experience breakup by necking. As a limit case, we consider necking to result in binary breakup, i.e., two daughter droplets and no satellite droplets are produced on breakup. The drop size of the daughter droplets is then... 

Fig. 23. (a) Distribution of drop sizes for mother droplets and satellite droplets (solid lines) produced during the breakup of a filament (average size = 2 x 10 5 m) in a chaotic flow. The total distribution is also shown (dashed line). A log-normal distribution of stretching with a mean stretch of 10 4 was used, (b) The cumulative distribution of mother droplets and satellite droplets (solid line) approaches a log-normal distribution (dashed line). 

Fig. 25. Drop size distributions f(V,p)] based on drop volume (V) obtained by repeated stretching and breakup in a journal bearing flow for different viscosity ratios (p) (left). The curves for the different distributions overlap when the distribution is rescaled (right) (Muzzio, Tjahjadi, and Ottino, 1991).

Muzzio, F. J., Tjahjadi, M., and Ottino, J. M., Self-similar drop size distributions produced by breakup in chaotic flows. Phys. Rev. Lett. 67, 54-57 (1991b). 

Because of such factors as wave formation, jet turbulence, and secondary breakup, the drops formed are not of uniform size. Various ways of describing the distribution, including the methods of Rosin and Rammler (R9) and of Nukiyama and Tanasawa (N3), are discussed by Mugele and Evans (M7). A completely theoretical prediction of the drop-size distribution resulting from the complex phenomena discussed has not yet been obtained. However, for simple jets issuing in still air, the following approximate relation has been suggested (P3) ... 

Two major contributions give an excellent view of the development of spray technology plus detailed summaries of current knowledge. Marshall (15A) presents such topics as jet breakup, performance characteristics of atomizers, and drop-size distributions. Miesse (lJfi) traces the theories of jet instability and has performed four series of experiments to verify them. 

Coalescence and Phase Separation. Coalescence between adjacent drops and between drops and contactor internals is important for two reasons. It usually plays a part in combination wilh breakup, in determining Ihe equilibrium drop size in a dispersion, and it can therefore affect holdup and flooding in a countercurrent extraction column. Secondly, it is an essential step in the disengagement of the phases and the control of entrainment after extraction has been completed. 

Single-droplet breakup at very high velocicty (1/velocity)2. This governs drop size in free fall as well as breakup when droplets impinge on solid surfaces. 

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

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, N (dimensionless). 

Most correlations show that di2 is proportional to the Weber number raised to the power of -0.6, which is consistent with the theory of drop breakup by turbulent shear forces. Strictly, these correlations should be applied only where the drop size is in the inertial subrange of turbulence, i.e.,... 

Although it may seem reasonable that an increase in viscosity of the spray fluid should increase the drop size, there is little fundamental information on the relationship between the drop size of the sprays and the viscosity of the spray liquid. Moreover, the information that is available is conflicting. Besides the work of Yeo and Dorman, where a viscosity term was found unnecessary when working with liquids having relatively low viscosities, other workers have found that a function of viscosity was necessary to describe drop size (16,17, 20), but the value of this function has varied from v01 to v106 (where v is the kinematic viscosity of the liquid). More recently, Dombrowsld and Johns (9) have examined the breakup of sheets of viscous liquids formed from fan-jet nozzles and have derived a theoretical expression for the size of drops produced. The expression is very complex and includes viscosity terms, but it is difficult to use in a practical fashion to predict drop size and its variation with a particular physical parameter of the spray fluid. 

In Range 3, the spray sheet is well developed, but the angle of the cone (a) becomes smaller as the viscosity is increased. This leads to a thicker sheet at the point of breakup, and hence the drop size increases. Eventually, at very high viscosities, a conical sheet is no longer formed. 

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