Particle equivalent length

The capacity of a pneumatic-conveying system depends on (1) product bulk density (and particle size and shape to some extent), (2) energy content of the conveying air over the entire system, (3) diameter of conveying line, and (4) equivalent length of conveying line. 

Equivalent) diameter of catalyst particle dp Length of tubes... 

Because of the diversity of filler particle shapes, it is difficult to clearly express particle size values in terms of a particle dimension such as length or diameter. Therefore, the particle size of fillers is usually expressed as a theoretical dimension, the equivalent spherical diameter (esd), ie, the diameter of a sphere having the same volume as the particle. An estimate of regularity may be made by comparing the surface area of the equivalent sphere to the actual measured surface area of the particle. The greater the deviation, the more irregular the particle. 

Several diameter definitions are used in particle image measurements (Fig. 7). Martin diameter, the chord length which divides the projected particle into two equal areas with respect to a fixed dkection (29) Feret diameter, the projected length with respect to a reference dkection (30) and the diameter of equivalent surface area, the diameter of a ckcle the area of which is equivalent to the projected area of the particle in question (3). 

The values of m given above conform to Hemng s scaling law (1950) which states that since the driving force for sintering, the transport length, the area over which uansport occurs and the volume of matter to be transported are proportional to a, and respectively, the times for equivalent change in two powder samples of initial particle size ai q and 2,0 are... 

Thus even if the mean free path is small compared to the cell length, particle (or equivalently grid) shifting will cause particles to collide with molecules in nearby cells, thereby reducing the effects of locally correlated collision events in the same cell. 

The equivalent particle diameter appearing in these dimensionless groups is the diameter of a sphere having the same external surface area as the particle in question. Thus for a cylinder of length Lc and radius rc, the equivalent particle diameter is given by... 

The mean measured activity per unit surface area are shown for airways and bifurcations separately in Table II. These data are for those segments which contained only airway lengths bifurcations. The results are given as the number of particles which deposit per cm2 for 10 particles which enter the trachea. This assumes that the particle and activity distributions are equivalent. For the 0.2 and 0.15 ym particles the surface density at the bifurcations is greater than that along the airway lengths at p <. 01 when the paired data are compared by a one tailed t-test. 

Here z is the ion valency, nQ is the number density of added electrolyte and q is the surface charge density of the particles. Figure 3.21 clearly illustrates the sensitivity at the lower added electrolyte concentrations where the diffuse layer Debye length is equivalent to that which would be estimated for an added electrolyte concentration two orders of magnitude higher, at a volume fraction of 0.5. Clearly higher concentrations of added electrolyte are not as sensitive but the variation is still significant. 

Furthermore, it is possible to increase the efficiency by a factor 3 when changing particle size from 5 to 1.7 pm while maintaining an equivalent column length, and decrease analysis time by a factor 9 while maintaining equivalent efficiencies [21],... 

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