Equivalent diameter spherical particles

Thus we see that the adhesion of irregular particles can be characterized by means of the average force of adhesion, which is determined from the distribution of the irregular adherent particles with respect to adhesive force, on the basis of equivalent size (diameter). The relationship between the average adhesive force and particle size is more complex for the irregular particles than for the equivalent-size spherical particles. For a certain size range of the irregular particles, there will be a maximum in adhesion. 

Eor randomly packed spherical particles, the constants M and B have been deterrnined experimentally to be 150 and 1.75, respectively. Eor nonspherical particles, equivalent spherical diameters are employed and additional corrections for shape are introduced. 

As an additional guide, the values are correlated with the equivalent spherical particle diameter by Stokes law, as in equation 1. A density... 

Equivalent diameter of a particle The diameter of a standard-density sphere whose motion would be similar to a given real particle, which may not be. spherical. 

Diameter for light phase, ft Diameter of particle, ft or equivalent diameter of spherical particle, ft Minimum diameter of particle that is completely collected, ft Diameter of particle, in. or mm Droplet diameter, ft... 

As mentioned, the data obtained by this method are expressed as cumulative size distribution curves. Since the computations assume Stokes law for spherical particles, the plotted curves give the distribution of spherical particles which would behave like the actual sample with respect to this experiment. For this reason, the sizes on the distribution curves should be labelled Stokes Equivalent Diameter . Because of the underlying assumptions and the above interpretation of the results, it is clear that the repeatability of this method has more meaning than accuracy of comparison with results of other methods... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Many particles are not spherical and so will not have the same drag properties as spherical particles. The effective diameter for such particles is often characterized by the equivalent Stokes diameter, which is the diameter of the sphere that has the same terminal velocity as the particle. This can be determined from a direct measurement of the settling rate of the... 

Mitochondria (45-56) are organelles possessing a double membrane, the inner of which is invaginated as cristae. An intermembrane space exists between the inner and outer membranes. The inner membrane consists of an unusually high amount of protein and possesses spherically shaped particles approx 9 nm in diameter. These particles appear to be equivalent to F0, Fb and adenosine triphosphatase. In contrast to the inner membrane, the outer membrane is smooth and appears to be connected to the smooth er. This membrane is permeable to all molecules of 10,000 Dalton or less. A mitochondrial matrix is enclosed by the inner membrane and consists of a ground substance of particles, nucleoids, ribosomes, and electron-transparent regions containing DNA. 

Indeed, it is easy to define the size (sizes) of simple particles (e.g., in the case of spherical globules or cylinders). But, for many real PSs, the form of particles and pores is complicated. The sizes of complicated particles or pores are expressed with equivalent diameters (sizes). The particular choice of an equivalent is directed by measuring the technique or other reasons. Following are some frequently used expressions for equivalent diameters [52] ... 

Particle size will always be expressed in terms of diameter rather than radius in this chapter. In all developments in this chapter, the particles will be assumed to be spherical. Consequently, when applying the results to other than spherical particles, that equivalent spherical diameter must be used which would correspond to the phenomenon involved. 

Relatively little appears to be known about the influence of shape on the behaviour of particulate solids and it is notoriously difficult to measure. Whilst a sphere may be characterised uniquely by its diameter and a cube by the length of a side, few natural or manufactured food particles are truly spherical or cubic. For irregular particles, or for regular but non-spherical particles, an equivalent spherical diameter de can be defined as the diameter of a sphere with the same volume V as the original particle. Thus... 

As an additional guide, the Q0/Z values are correlated with the equivalent spherical particle diameter by Stokes law, as in equation 1. A density difference A8 of 1.0 g/cm3 and a viscosity of 1 mPa-sf =cP) are assumed, thus conversion to other physical characteristics of the system requires that the particle size scale be adjusted to equate a particle of 1.0 pm diameter to its j20/ - i 1 cm/s, according to the relationship Q0 /E = 10 7 x 1.09 AS/p, for A8 in g/cm3, and viscosity p in Pas. For interpretation of the particle sizes, the scale refers to the 50% cutoff particle size, and under actual centrifugation conditions the value of Z, determined from Figure 8, must be increased by efficiency factors to give the theoretical value of Z. 

An equivalent diameter of a particle is usually defined in relation to a specific sizing method developed on the basis of a certain equivalency criterion. Several equivalent diameters of a spherical particle commonly employed are discussed in the following sections. 

Table 6.8 presents the details of calculations for spherical particles with an equivalent diameter of 2.4mm. It may be observed that the pore diffusion considerably affects the process rate, particularly at higher temperatures. The external mass transfer plays a minor role. Their combination leads to a global effectiveness that drops from 75% to 35% when the temperature varies from 160 to 220°C. Based on the above elements the apparent reaction constant may be expressed by the following Arrhenius law ... 

The alloy is failed during some cycles of hydrogen sorption - desorption and turns into powder with particles 3-4 microns. The specific surface of such powder can be estimated with assumption of their spherical shape a (1.5-2.0 microns) with equivalent diameter of a particle ded=4s/[ 0(l- )]=1.3-1.6 microns. These values can be used in calculations of gas dynamics of hydrogen flow and heat exchange in a layer. 

Darton and Harrison20 studied the hydrodynamics of a single gas bubble with equivalent diameters in the range 5 through 25 mm in water-fluidized beds of 500-/imand l-mmsand particles in a 22.9-cm-diameter column. The rising velocity of spherical cap bubbles was correlated by a relation... 

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