Similarity drop size distribution

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). 

Much ingenious and painstaking work has been done by more than 40 investigators seeking methods for describing fuel sprays in terms of drop-size distribution. In many instances the methods are similar consequently, the procedures have been divided into six general types, or classes of methods. 

Other studies were conducted by the FS in 1976 to expand the data base on the size of drops which deposited on Douglas-fir needles. These studies provided an opportunity to determine if the drop size distribution would be similar to drop size distributions of tank mixes studied earlier. The 1976 study involved aerial application of acephate and trichlorfon, and the 1981 study involved Bacillus thuringiensis (Dipel 4L and Thuricide 16B). These data have not been published or reported previously. The chemical tank mixes were applied by helicopter and the B.t. tank mixes were applied by fixed-wing aircraft. 

The B.t. drop stain sizes from the 1981 study were assessed in a similar manner as the chemical tank mixes. Results (Table X) differed, however, from the 1976 chemical applications. Sixty percent of the Dipel 4L drop stains were less than 42 pm in diameter and 42 percent of the Thuricide 16B drop stains were less than 31 pm in diameter. Differences between the chemical and biological spray drop size distribution, however, may be due to variation in spreading of the drop after it deposits on the needle. There was no statistical difference in percent distribution of the drop stain sizes between the two B.t. tank mixes or between the two chemical tank mixes. 

Erickson et al. (E3) developed a model for batch growth in fermentations with two liquid phases present in which the growth-limiting substrate is dissolved in the dispersed phase. The model accounts for drop size distribution and considers the effect of droplet coalescence and redispersion by an interaction model similar to that of Eq. (110). Droplet interactions were shown to be important if drop size distributions have large variance. 

The maximum surviving drop diameter, is approximately 1.6 times d M- The Sauter mean drop diameter can be calculated using Equation (9.45) from a population of n drops of different sizes, 4. 4+1 4- The drop size distribution often becomes self-preserving (similar shape distri-... 

Junge and McLaren (1971) have studied the effect that the presence of insoluble material has on the capacity of aerosol particles to serve as cloud condensation nuclei. Using Eq. (7-25) they calculated the supersaturation needed for an aerosol particle to grow to the critical radius at the peak of the Kohler curve, from where spontaneous formation of cloud drops becomes feasible. The results are shown in Fig. 7-8. They indicate that the difference is less than a factor of two in radius for particles whose soluble fraction is greater than e =0.1. The majority of particles can be assumed to meet this condition (see Fig. 7-19). By assuming particle size distributions similar to those of Fig. 7-1 for continental and maritime background aerosols, Junge and McLaren also calculated cloud nuclei spectra as a function of critical supersaturation and compared them with observational data. These results are shown in Fig. 7-8b. We shall not discuss the data in detail. The results make clear, however, that the presence of insoluble matter in aerosol particles does not seriously reduce their capacity to act as cloud condensation nuclei. 

The purpose of this section is not to analyze drop size statistics. Therefore, only basic featores are discussed here. Depending on the way the emulsion is manufactirred, particularly the fluid mechanical conditions in which the shear or turbulence have produced the droplets, the emulsion should contain drops of similar or very different sizes, with the associated variety in statistical distribution. Figure 5 illustrates the aspect of typical drop size distribution which... 

Regardless of which constraints are chosen, it is necessary to estimate the parameters that appear there. When this is dmie, there is similarity between predicted and measured drop size distributions, and the predicted drop velocity distribution is consistent with measured profiles. However, agreement with experimental data is achieved by adjusting the source term magnitudes. Hence, the MEF is similar to curve fitting. 

FIGURE 5.2.1 Evidence of self-similarity in experimental data of Madden and McCoy (1969) on drop size distributions from Ramkrishna (1974). Evolution of drop size is assumed to be by breakage process only. Reprinted with permission from Elsevier Science. 

FIGURE 5.2.3 Evidence of self-similarity in drop size distributions evolving purely by breakage obtained by Narsimhan et al (1984). (Reproduced with permission of the American Institute of Chemical Engineers. Copyright 1984 AIChE. All rights reserved.)... 

The expression in (6.1.13) above was obtained from the correlation developed by Narsimhan et al, (1984) (referenced in Chapter 5) from drop size distribution data on the breakage of liquid drops in a manner very similar to that of Sathyagal et al (1995). Although their methodology of Narsimhan et al (1984) was similar to that of Sathyagal et al (1995), their solution to the inverse problem was vastly improved in the latter publication. 

There have been a few studies of drop size distributions, and they appear to be similar. Calabrese et al. (1988) give... 

Therefore the system of stretched, reshaping, and cross-wind affected threads was transferred to a similarity trial. Threads form capillary nozzles are exposed to cross-wind flow set by an axial fan, in the field of gravity. With the exception of the very slow and negligible radial component of the emerging threads from the rotary device both systems are similar. In both systems, the acceleration of the liquid phase is constant [11, 14]. Within the similarity trials, all parameters can be controlled individually regarding their impact on the breakup length Lb as well as on the mean drop size and the drop size distribution expressed by the span value. 

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