Maximum droplet sizes correlations

Table 4.3. Correlations for Mean, Minimum and Maximum Droplet Sizes Generated in Pressure Jet Atomization by Plain-Orifice Atomizers... 

Various correlations for mean and maximum droplet sizes generated by smooth flat vaneless disks, vaneless disks, and wheels are listed in Tables 4.11, 4.12 and 4.13, respectively. In these correlations, d is the diameter of disk/cup, ft) and (Orps are the rotational speed of disk/cup in radians/s and rps, respectively, 6 is the semi cone... 

Table 4.11a. Correlations for Mean and Maximum Droplet Sizes Generated by Smooth Flat Vaneless Disks in Direct Droplet Formation Regime...

Pinczewski and Fell [Trans. Inst. Chem E/ig., 55, 46 (1977)] show that the velocity at which vapor jets onto the tray sets the droplet size, rather than the superficial tray velocity. A maximum superficial velocity formulation that incorporates ( ), the fractional open area, is logical since the fractional open area sets the jet velocity. Stichlmair and Mers-mauu [Int. Chem. Eng., 18(2), 223 (1978)] give such a correlation ... 

In many atomization processes, physical phenomena involved have not yet been understood to such an extent that mean droplet size could be expressed with equations derived directly from first principles, although some attempts have been made to predict droplet size and velocity distributions in sprays through maximum entropy principle.I252 432] Therefore, the correlations proposed by numerous studies on droplet size distributions are mainly empirical in nature. However, the empirical correlations prove to be a practical way to determine droplet sizes from process parameters and relevant physical properties of liquid and gas involved. In addition, these previous studies have provided insightful information about the effects of process parameters and material properties on droplet sizes. 

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

Analytical and empirical correlations for droplet sizes generated by ultrasonic atomization are listed in Table 4.14 for an overview. In these correlations, Dm is the median droplet diameter, X is the wavelength of capillary waves, co0 is the operating frequency, a is the amplitude, UL0 is the liquid velocity at the nozzle exit in USWA, /Jmax is the maximum sound pressure, and Us is the speed of sound in gas. Most of the analytical correlations are derived on the basis of the capillary wave theory. Experimental observations revealed that the mean droplet size generated from thin liquid films on... 

For constant surfactant concentration there is a linear correlation between water concentration and the size of the water droplet in a W/O microemulsion [36]. Thus, droplet size is proportional to Wq. [For the most commonly used surfactant, AOT, the droplet radius, Rd, can be directly obtained from the Wq value from the relationship Rd (nm)=0.175 Wo [37].] In general, it seems that maximum activity occurs around a value of Wq at which the size of the droplet is equivalent to or slightly larger than that of the entrapped enzyme. Figure 5 shows data compiled for 17 different enzymes on the relationship between the hydrodynamic radius of the protein and droplet radius at optimum activity [38]. With only one exception (lipoxygenase), the correlation between the two radii is excellent. 

This method is an alternate to the HLB one and was presented by Lin et al. [12]. They found a correlation between the maximum amount of water which can be solubilized in the oil phase containing the emulsifier(s) and the average droplet size of the emulsion. Experimentally, they determined the solubilization by adding the aqueous phase, drop by drop, to the oily phase and recording the added volume of aqueous phase at the point of permanent turbidity. 

Alternative approaches to the selection of emulsifiers have been investigated. Prediction of optimum emulsifier mixtures has been made by way of solubilization measurements [44]. Lin et ai [44] found a correlation between the maximum amount of aqueous phase that could be solubilized in the oil phase containing the surfactant and the average droplet size of the emulsion subsequently formed (Fig. 8.9). The relationship held even when ionic-non-ionic mixtures of surfactants were used and thus displays an advantage over the PIT method as ionic surfactants do not produce PIT values. It is telling that the method works in the presence of additives such as lauryl alcohol. Fig. 8.9 shows the shift in optimum surfactant ratio when lauryl alcohol is added to the oil phase, in this case mineral oil. The addition of a polar oil to a non-polar oil will result in a predictable shift in required HLB. However, a shift of no more than 1 HLB unit would be expected from the linear additivity rule, while Fig. 8.9 shows a shift of some 2.4 HLB units. In some systems that Lin and his colleagues [44] investigated, the position of maximum solubilization did not coincide with the optimal O/W emulsion, an effect believed to be due to phase inversion at the point of maximum solubilization. 

Figure 9 shows the relaxation time T2 of micelles of sodium dodecyl sulfate (SDS) as a function of SDS concentration [13,16,17], It is evident that the maximum relaxation time of micelles is observed at an SDS concentration of 200 mM. This implies that SDS micelles are most stable at this concentration. For several years researchers at the CSSE have tried to correlate the measured T2 with various equilibrium properties such as surface tension, surface viscosity, and others, but no correlation could be found. However, a strong correlation of t2 with various dynamic processes such as foaming ability, wetting time of textiles, bubble volume, emulsion droplet size, and solubilization of benzene in micellar solution was found [18]. 

Here the dimensionless time z=t/t is normalized by the characteristic relaxation time t, the time required for a charge carrier to move the distance equal to the size of one droplet, which is associated with the size of the unit cell in the lattice of the static site-percolation model. Similarly, we introduce the dimensionless time zs = ts/t where ts is the effective correlation time of the s-cluster, and the dimensionless time z = tm/t. The maximum correlation time t, is the effective correlation time corresponding to the maximal cluster sm. In terms of the random walker problem, it is the time required for a charge carrier to visit all the droplets of the maximum cluster sm. Thus, the macroscopic DCF may be obtained by the averaging procedure... 

A determination of the particle size, which is independent from the distance of the particle to the detector, assumes that the extinction coefficients for the minimum and the maximum aperture angle do not differ significantly. Water droplets in air whose diameters are less than 1000 pm result in nearly identical extinction coefficient when the aperture is less than 0.01"". The smaller the particles, the larger the aperture angles are which lead to significantly different extinction coefficients. Water droplets with diameters less than 100 pm arise in almost identical extinction cross sections when the aperture is less than 0.1°. For other particle systems the qualitative correlation is similar. The determination of particle size that is independent of the position of the particle in the measurement volume requires an optical construction of the SE-Sensor with a correspondingly small aperture angle. 

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