Particle diameter surface-volume mean

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... 

The definition of the surface-volume mean diamefer given by equation 1.11 must be modified for use wifh dafa from a sieve analysis. By assuming that the shape and density of fhe particles are constant for all size fractions, a number distribution can be transformed fo a mass distribution (Smith, 2003) and therefore the surface-volume diameter becomes... 

For non-spherical particles, values of sphericity lie in the range 0 < < 1. Thus, the effective particle diameter for fluidization purposes is the product of the surface-volume mean diameter and the sphericity (Kunii and Levenspiel, 1991). The sphericity of regular-shaped particles can be deduced by geometry whilst the sphericity of irregular-shaped... 

The surface volume mean diameter for a suspension of spherical particles is given by ... 

Specific surface may be e q>ressed on a mass basis using the material density to modify the volume. The diameter of the here having the same equivalent ecific sur ce as the particle is sometimes termed the surface volume mean or the Sauter mean diameter. 

The correct mean particle diameter is therefore the surface-volume mean as defined above. (We saw in Section 1.6 that this may be calculated as the arithmetic mean of the... 

A packed bed of solid particles of density 2500 kg/m occupies a depth of 1 m in a vessel of cross-sectional area 0.04 m. The mass of solids in the bed is 50 kg and the surface-volume mean diameter of the particles is 1mm. A liquid of density 800kg/m and viscosity 0.002Pas flows upwards through the bed, which is restrained at its upper surface. 

A 10 m long vertical standpipe of inside diameter 0.1 m transports solids at a flux of 100 kg/m s from an upper vessel which is held at a pressure 1.0 bar to a lower vessel held at 1.5 bar. The particle density of the solids is 2500 kg/m and the surface-volume mean particle size is 250 gm. Assuming that the voidage is constant along the standpipe and equal to 0.50, and that the effect of pressure change may be ignored, determine the direction and flow rate of gas passing between the vessels. (Properties of gas in the system density, 1 kg/m viscosity, 2 x 10 Pas.)... 

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). 

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... 

A typical feed composition was 1000 g capsul, 2334 g deionized water and 200 g orange oil. The finished powders were stored in amber bottles at -25prior to accelerated storage study and relevant analyses. Particle Size Analysis. To ascertain the effect of atomizer voltage on the particle size, the particle size distributions of three powders were first determined. The Microtrac laser light particle size analyzer (Medallion Laboratories, Minneapolis, MN) was used in this study. The volume percent data over particle diameter ranging 2.8 p. to 176 jii was recorded. Mean value of the volume percent distribution and calculated surface area were also obtained. 

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). 

Specific surface area is dependent on the reciprocal of pore diameter. However, with a given pore diameter the measured specific surface may be different. A silicagel should be defined with mean particle diameter, specific surface area, pore diameter, and pore volume. 

Stainless steel powder with a mean particle diameter of 50 mm has been compacted to a green density of 58% and sintered in pure H2. The resulting shrinkage measurements are given below. Published diffusion data for this stainless steel show that the activation energies are 225 kJ/mol for surface diffusion, 200 kJ/mol for grain boundary diffusion, and 290 kJ/mol for volume diffusion. Use the data below to determine the mechanism. 

Other possible geometrical diameters can be used to determine the mean particle diameter of a polydisperse system. Examples are the surface average, ds, and volume average diameters, dv where ds is defined as the diameter of a sphere having the same surface area as the particle and dw is the diameter of a sphere having the same volume as the particle. These are given by ... 

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) ... 

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