Equivalent Particle Diameters

For irregular (nonspherical) solid particles, the usual method of particle characterization is to introduce an equivalent dituneter —that is, the diameter of a spherical particle that would give the same behavior in the experimental system of interest. 

The aerodynamic diameter is one of the most common equivalent diameters. It can be defined as the diameter of a unit den.sity sphere with the same terminal settling velocity as the particle being measured. The aerodynamic diameter is commonly used to describe the mt)lioii of particles in collection devices such as cyclone separators and impactors. However, in shear flows, the motion of irregular particles may not be characterized accurately by the equivalent diameter alone because of the complex rotational and translational motion of inegular particles compared with spheres. That is, the path of the irregular particle may not follow that of a particle of the same aerodynamic diameter. It is of course possible that there may be a. sphere of a certain diameter and unit density that deposits at the same point this could be an average point of deposition because of the effects of turbulence or the. stochastic behavior of irregular particles. 

In addition to particle motion, other properties can be characterized by an equivalent diameter. For example, lighi-scattcring instniments are often calibrated using spherical 

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In the previous section we determined the equivalent particle diameter of a set of particles of different sizes, with the aid of which we can treat the mixture as composed of one size of particles, namely The mean free-falling velocity of the mixture is the same. 

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 catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Figure 2. Distribution of selected minerals in Upper Freeport coal as a function of area-equivalent particle diameter (ym).

A represent a case in which the ice bed rides with 10 feet of its height out of the water. The particle diameters refer to equivalent diameters as defined by the Carmen-Kozeney equation which equates particle diameter to the filter properties of a bed. Because small particles give poor filterability, there will be less piston leakage for beds made up of fine particles than for those of coarse particles. Likewise, the drainage properties of the bed from the top to the screen are affected by particle diameter. If it is assumed that the minimum pressure at the screen were to be the same as the pressure above the bed—in other words, full gravity drainage—then the maximum lineal ice rate is established for each equivalent particle diameter. Calculations based on the filtration behavior of the bed and on calorimetric determinations of porosity indicate the approximate relationship ... 

Vmax = maximum lineal ice rate, feet per hour Dp = equivalent particle diameter, inches... 

Single-particle optical analyzers are especially useful for continuous measurement of particles of uniform physical properties. However, as discussed earlier, uncertainties develop in the measurement of particle clouds that are heterogeneous in composition because the refractive index may vary from particle to particle. Thus, in making atmospheric aerosol measurements, workers have assumed an average refractive index characteristic of the mixture to estimate a calibration curve or have reported data in terms of the equivalent particle diameter for a standard aerosol, such as suspended polystyrene latex spheres. 

The relationship between the catalyst size classification, the equivalent particle diameter and the percentage saving in catalyst or converter volume is summarized in Table 6.174. 

Particle Size. The equivalent radius R0 may also be reported out as the equivalent particle diameter 2R0. The size may be reported out as mean and standard deviation as shown in Table II or as a histogram as shown in Figure la,b. The size template in Figure 2 illustrates the principle underlying the RQ term. 

Re = Reynolds number based on the equivalent particle diameter r = radial reactor coordinate [ mr]... 

The soil material used for the experiments was taken from the field of a former paint factory, a clayey loam with an equivalent particle diameter of 10 pm. It was weathered for more than 20 years and contained 19 wt% hydrocarbons (37 % long alcanes, 34 % monoaromatic, 16% diaromatic, 12% polyaromatic hydrocarbons). Only the agglomerate fraction (hydrocarbons and sand) smaller than 355 pm was employed. As supercritical solvent demineralized water was used. 

Catalyst size classification, mm Approximate equivalent particle diameter, mm Relative ratal) si ohmic. %... 

Hydraulic channel diameter d, was assumed to be a defining parameter for the first model, while equivalent particle diameter 4 was chosen for the second model. The conventional equation for computing hydraulic resistance is known to be ... 

The above factors are well explained by Maiti et al. Under the structure of the packed bed, the liquid distribution is dependent on 1) porosity distribution 2) Z)/dp ratio D is the diameter of reactor and dp is the equivalent particle diameter) 3) H/d ratio (orientation problem) H is the height of the catalyst bed) and 4) method of loading—convex, concave, and random (sock and dense loading). 

The equivalent particle diameter. Jpg is the diameter of a sphere of equal volume as the particle. 

The following initial conditions are often used a.t z = 0, ps -Pt = Pt,o- In this model dp is the equivalent particle diameter. 

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