Sauter mean particle diameter

For non-spherical particles, the Sauter mean diameter ds should be used in place of d. This is given in Chapter 1, equation 1.15. 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

For a single particle, Dp can be taken as 2 (hydraulic radius), and the Sauter mean diameter for hindered particles. 

For the analysis of primary particles it is possible to calculate the spherical diameter for a particle from Rg described above as P = (5/3) Pg or 2.6 Rg. It is also possible to calculate diameter for a particle through the volume/surface ratio, which is called the Sauter mean... 

For a mixture of particles of several sizes, one evaluation of a mean diameter is the volume surface mean, or Sauter mean. When ws is the weight or volume fraction of particles of diameter ds the mean is... 

For both bubbles and particles, there will be a distribution of sizes in the dispersion. The above quantities can be related to the volume/surface or Sauter mean bubble and particle diameters <4 and dp (see Volume 2, Chapter 1). 

The results of the normal-designed experiments are listed in Table 13.3, where I, II, and III denote the summations of the Sauter mean diameters, d22, at Levels 1, 2, and 3, respectively and R is the extreme difference at a certain level. From Table 13.3 it follows that the order of influence of various factors on the mean size of the particles in the precipitate is D>C>B>F>H>G>E>A. The influences of the latter three factors, G, E, and A, can be considered as very weak, while the most serious factors leading to gelation of the reaction mixture are, in order, A and G, suggesting the reaction temperature cannot be too high and the amount of dispersion agent cannot be too large. 

From the data listed in Table 13.5 it can be seen that the Sauter mean diameter of the dried product, di2, is larger than that of the wet precipitate obtained under the same reaction conditions by about 10%, or by 0.15 pm. An obvious fact is that no matter whether at the bottom of the dryer or in the cyclone or in the bag filter, the recovery of the finer particles must be lower than that of the larger particles. These differences between the recoveries of particles of different sizes must lead to an increased mean diameter of the product. If this fact is taken into account, the sizes of the particles can be considered to be stable enough during the final treatment of the precipitate, without coalescence of particles occurring. 

Only a minority of systems of industrial interest contain powders with a uniform particle size, i.e. monodisperse. Most systems generally show a distribution of sizes (polydisperse) and it is then necessary to define the average dimension. There are many different definitions of particle size,1 2 the most commonly used, particularly in fluidisation, is the so called volume-surface mean or the Sauter mean diameter. This is the... 

Figure 15. Enhancement factor for hydrogen absorption in an aqueous hydroxylamine solution as a function of the reciprocal Sauter mean diameter of Pd/activated carbon catalyst particles esPs = 1.5 kgm-3, flat interface stirred cell (from Wimmers et al. [123]).

We get particles of different sizes. Each has a mass equivalent diameter," which is the diameter of a sphere with the same mass as the particle. One can characterize the sizes with a cumulative mass distribution such as in the upper part of Figure 14-6. This shows which mass fraction is in the particle with a diameter smaller than a certain value. The frequency distribution underneath is derived from the upper diagram it gives an indication of which diameters are most common. We can try to characterize the drops with a single diameter there are many different ways in which this can be done. They lead to parameters such as the c 32 (Sauter diameter), dso (mean diameter) and dmax (maximum... 

Aerodynamic diameter of a real median size particle Diffusion coefficient Sauter mean diameter Volume mean diameter Entrainment, mass liquid/mass gas Plate or stage efficiency, fractional Power dissipation per mass Murphree plate efficiency, with entrainment, gas concentrations, fractional... 

Some of the heterogeneous flow difficulties in the throat section can be avoided if the particle surface per unit volume is maintained constant. If the Sauter mean diameter of sprayed particles could be held constant during scale-up, the surface area per unit volume (or mass for constant density) of feed would be fixed. Because the ratio of heat carrier to feed... 

Consistent performance of the ACR during scale-up depends upon thermal and kinematic similarity throughout, but with a dynamic influence on kinematic similarity in the throat and chemical similarity in the diffuser. As a result of the above considerations, it was felt that the ACR process could be scaled in a geometrically similar reactor based on matching Mach numbers, S F ratio, and residence time in the reaction section, provided two critical conditions could be met. When scaled, the sprayed particle size distributions would have to be approximately equal (i.e., equality of Sauter mean diameter) while a kinematically similar oil-particle trajectory also would be required. 

FIGURE 10.1 (a) Effect of the number of particles counted on the average mean primary particle diameter, r/j (circles), and Sauter mean primary particle diameter, (squares), as well as the geometric standard deviation (that is, a measure of the width of the size distribution, triangles), (b) The corresponding primary particle size distribution and a TEM picture of the investigated titania nanoparticles collected with a thermophoretic sampler directly from a premixed TiOj flame at a height of 0.5 cm above the burner. (Courtesy of H.K. Kammler and S.E. Pratsinis.)... 

Effect of Solids Addition. Figure 16 shows the variation of the viscosity with shear stress when solids are added to a synthetic OAV emulsion. The solids are sand particles with a Sauter mean diameter of 9 xm. The... 

Example 2 The Sauter mean diameter and the volume weighted particle size and distribution given in Table 21-1 can be calculated by using FDIS-ISO 9276-2, Representation of Results of Particle Size Analysis—Part 2 Calculation of Average Particle Sizes/Diameters and Moments from Particle Size Distributions via Table 21-2. 

TABLE 21 -2 Table for Calculation of Sauter Mean Diameter and Volume Weighted Particle Size... 

The ratio of the Sauter mean diameter to the drag diameter appears as a shape factor. It is noted that for non-spherical particles or for systems with a particle size distribution, the various shape factors may not be unity. However, for a distribution of spherical particles, the shape factor, is unity regardless... 

One of the unique rheological features of emulsions is that the apparent viscosity of the emulsion can drop below the viscosity of the continuous phase when the concentration of the dispersed phase is low, normally below 0.1 in volume fraction (194). When solids are added to the emulsion, the apparent viscosity can decrease even further and the volume fraction of the dispersed phase at which minimum viscosity occurs increases with increasing solids content. Figure 30 shows the apparent viscosity of water-and-sand-in-bitumen, pwsh, variation with the solid-free water volume fraction, j8w, for two shear rate values. The experimental data were provided by Yan (private communication), where the system consists of 52 pm sand particles treated with hexadecyltri-methylammonium bromide (HAB) and water droplets of a Sauter mean diameter of 9 pm dispersed in bitumen at 60 °C. The sand particle volume fraction on water-free basis is j8s = 0.193. The range of the water droplet volume fraction, on a solid-free basis, jfrw is between 0 and 0.4. It can be observed that a minimum viscosity is present at a solid-free water droplet volume fraction of about 0.1. For a lower solid concentration, Ps = 0.113, the minimum apparent viscosity is found at /3W = 0.05... 

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