Sauter mean drop size

The predictive method for drop size is given in the Kenics Bulletin (May 1988, p. 28, Fig. 5-1) and in Figure 10.34. The ratio of Sauter mean drop size to the mixer ID (d/D) is a function of the Weber Number (V Dp/cr) and the ratio of dispersed phase to continuous phase viscosity (p-j/p.,). Now let s do two examples for static mixers. 

The Sauter mean drop size is reduced to 100 pm or halved by reducing the phase volume from 40-10%. 

To define the iramiscible-liquid-segregation problem, the drop size range of the dispersed phase must be known or approximated. Weinstein and Middleman present drop correlations for pipeline contacting and static mixers while Coulaloglou and Tavlarides present correlations of liquid in liquid drop sizes for agitated vessels. All use the Sauter mean drop size definitions and involve use of the Weber number, a... 

Drop dispersions are hardly ever uniform, and size distribution must be allowed for in calculating a. This can be done by means of the Sauter mean drop diameter, based on the average volume-to-area ratio for N drops. 

In liquid-liquid reacting systems, one of the important parameters is the surface area per unit volume, a, in the dispersion, which can be related to the Sauter mean drop diameter dn- In some processes, the drop size distribution and especially the minimum drop size or the maximum stable drop diameter are also important factors in analysing the process results. 

The Sauter mean drop diameter, d M or (32, defined by Equation (9.45), is most commonly used to characterize drop size because it relates to the volume fraction of the dispersed phase, O, and the interfacial area, a. The Sauter mean drop diameter is also known as the volume-to-surface average drop diameter. The interfacial area, a, in Equation (9.45) is also used to deal with mass transfer, such as ki a. Other commonly used terms are d o, dgo, and d They represent the midsize, the 90th percentile, and the largest size in the drop size distribution, respectively, on a volume basis. The... 

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-... 

Terms Used to Represent Mean Drop Size and Drop Size Distribution. The following expressions describe the common drop size notation used in this chapter. The volume fraction of dispersed phase is ( ), the total interfacial area per unit volume of mixed phases is ay, and dmax is the maximum drop size. The Sauter mean diameter, Ayi, is defined by... 

The drop size achieved is important in estimating the mass-transfer surface area developed in the dispersion. In certain situations, the surface area of the dispersion per unit volume of the total liquid phase, a, is available from measurements. The average or mean drop size appropriately defined can then be related to For example, the Sauter mean diameter ( 2 of the drop size number density distribution has been related to via the following relation and the dispersed phase volume fraction... 

Sauter mean drop diameter A method used to characterize the average drop size in a population of droplets in immiscible liquid-liquid dispersions. It is related to the volume fraction of the dispersed phase, <1> and the interfacial area, a. It is also known as the volume-to-area average drop diameter ... 

Thep and q denote the integral exponents of D in the respective summations, and thereby expHcitiy define the diameter that is being used. and are the number and representative diameter of sampled drops in each size class i For example, the arithmetic mean diameter, is a simple average based on the diameters of all the individual droplets in the spray sample. The volume mean diameter, D q, is the diameter of a droplet whose volume, if multiphed by the total number of droplets, equals the total volume of the sample. The Sauter mean diameter, is the diameter of a droplet whose ratio of volume-to-surface area is equal to that of the entire sample. This diameter is frequendy used because it permits quick estimation of the total Hquid surface area available for a particular industrial process or combustion system. Typical values of pressure swid atomizers range from 50 to 100 p.m. 

Sauter mean D39. This has the same ratio of surface to volume as the total drop population. It is typically 70 to 90 percent of D. n- II is frequently used in transport processes and is used here to characterize drop size. 

Most of the investigators have assumed the effective drop size of the spray to be the Sauter (surface-mean) diameter and have used the empirical equation of Nuldyama and Tanasawa [Trons. Soc. Mech. Eng., Japan, 5, 63 (1939)] to estimate the Sauter diameter ... 

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Fig. 9.3 Sauter mean diameter < 32 calculated from drop size measurements at single nozzles of liquid systems (a) toluene (dispersed phase d) water (continuous phase c) and (b) butanol d) water (c), is dependent on the mean velocity Vjv of the dispersed phase in the nozzle. (From Ref. 5.)... 

B) have found excellent correlation between the measured sizes of drops atomized by high-velocity gas streams with the equations developed by Nukiyama and Tanasawa (6L), so long as conditions are held within certain limits. The behavior of sprays of 7i-heptane, benzene, toluene, and other fuels has been studied by Garner and Henny (SB) by use of a small air-blast atomizer under reduced pressures. A marked increase in the Sauter mean diameter was obtained for benzene and toluene as compared with n-heptane, which parallels their poor performance in gas turbines. Duffie and Marshall (2B) give a theoretical analysis of the breakup characteristics of a viscous-jet atomizer and show high-speed photographs of the process. 

The mass transfer coefficient kL of oxygen transfer in fermenters is a function of Sauter mean diameter D32, diffusivity DAB, and density p, viscosity pc of continuous phase (liquid phase). Sauter-mean diameter D32 can be calculated from measured drop-size distribution from the following relationship,... 

The Sauter-mean diameter, a surface-volume mean, can be calculated by measuring drop sizes directly from photographs of a dispersion according to Eq. (9.21). 

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