Volume surface-weighted mean diameter

Volume surface-weighted mean diameter d,s = di = S3 /S2 Volume moment-weighted mean diameter d,m = dt 3 = S4/S3... 

Table 5.3. Fat globule size (volume surface-weighted mean diameter, dys) in milk...

Example 1-3 The optical microscope analysis given in Table 1-5 was performed for a particulate sample of ground Pittsburgh seam coal that was to be fed to a combustor. Determine the length, surface, volume, and weight mean diameters. Using the equations in Table 1-4, one finds... 

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... 

Substituting all the possible combinations of characteristics, i.e. values of p and q, info equation 1.10 gives rise to a number of differenf definitions of the mean size of a distribution. At minimum fluidization the drag force acting on a particle due to the flow of fluidizing gas over the particle is balanced by the net weight of fhe particle. The former is a function of surface area and the latter is proportional to particle volume. Consequently the surface-volume mean diameter, with p = 2 and = 3, is the most appropriate particle size to use in expressions for minimum fluidizing velocity. It is defined by equafion 1.11... 

Because the inequalities among the various mean diameters are usually strengthened when the drop sizes are widely dispersed, the ratio of some higher-order moment to a lower-order moment is often useful as a measure of the dispersion of the drop sizes. For example, the coefficient of variation for the surface-weighted size distribution is a function of the ratio of the weight-weighted mean drop size to the volume-surface mean drop size. The variance of the drop-size distribution may also be expressed in terms of the moments of the unweighted size distribution. 

Table 9 shows the results of the sieve analysis obtained for a sample of a FCC1 powder. The values reported in the first two columns of the table are the standard diameters of the sieve apertures. From these the mean diameter dp is obtained for each two adjacent sieve sizes and the values are reported in the third column. From the mass fraction of powder in each sieve (values in the fourth column) the weight percentage is obtained and reported in the fifth column. Thus, the sum of the mass fraction over the mean diameter allows the calculation of the volume-surface mean particle diameter of the distribution using Equation (1) ... 

For an open circuit ball mill 5 liters in volume operating at a flow rate of 1 liter per hr the product is a Z1O2 suspension with a Ros-lin-Rammler size distribution with a weight mean size of 0.5 jam and a volume to surface mean diameter of 0.7 jam. Determine the feed distribution to the mill assuming the value of j3 the grinding selectivity factor is 1.0 and k is 0.5 (hr/jam) . ... 

A summary of these different types of averages can be found in Table 3. Example 5. Using the particle count data given in Example 4 and Table 2, compute the statistical mean diameters for the number-length, number-surface, number-volume, length-surface, length-volume, surface-volume, volume-moment and weight-moment mean diameters. 

TABLE 4 Calculation of the Number-Length. Number-Surface. Number-Volume. Length-Surface, Length-Volunne, Surface-Volume, Volume-Moment and Weight-Moment Mean Diameter... 

Droplet-size distributions and average droplet sizes (volume-surface mean diameter d32 and weighted average mean diameter d43) of O/W emulsions were... 

From the extent of reduction and the surface area of the metal, as calculated from the extent of chemisorption, the mean size of the metal can be calculated. The broadening of the maxima in the X-ray diffraction pattern also measures a mean particle size. Usually the mean particle size calculated from the X-ray line-broadening is larger than that calculated from the extent of reduction and the surface area of the metal particles. The difference is because X-ray line-broadening provides a weight-mean particle size, Ln d l Ln- di, whereas the extent of chemisorption and the extent of reduction result in a volume-surface mean diameter, Lnid /Lrijdj. ... 

Accuracy has to be carefully defined, particularly for a (drop or particle) population containing a range of sizes. Tlie simplest description is via some appropriate mean size such as the Sauter Mean Diameter (d32, particle with the same volume /surface area ratio as ensemble of particles, sphere equivalent) or the mass median diameter (dso, size below which lie 50% by weight of the sample). The next step is to consider a second parameter describing the width of the distribution. A simple definition is a dimensionless span,... 

In this expression, Wp is the weight of particles titrated (g), Cb and Vb are the concentration of the base (i.e., titrant) and the volume of the base at equivalence point. The surface charge density can be calculated for the particles having a known diameter by means of the following expression ... 

In which the ratio m/n is close to 3. The silane was produced by free radical copolymerization of vinyltriethoxysilane with N-vinylpyrrolidone. Its number-average molecular weight evaluated by vapour-phase osmometry was 3500. Porous silica microballs with a mean pore diameter of 225 A, a specific surface area (Ssp) of 130 m2/g and a pore volume of 0.8 cm3/g were modified by the silane dissolved in dry toluene. After washings and drying, 0.55% by weight of nitrogen and 4.65% of carbon remained on the microballs. Chromatographic tests carried out with a series of proteins have proved the size-exclusion mechanism of their separation. 

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