Properties equivalent diameter

Djj. The Grashof number Nq, = Dj pgpAto/p" were is equivalent diameter, g is acceleration due to gravity, p is coefficient of volumetric expansion, p is viscosity, p is density, and Atg is the difference between the temperature at the wall and that in the bulk fluid. Nq, must be calculated from fluid properties at the bulk temperature. 

Tab. 3.3.1 Physical properties of the packed porous particles. The relaxation times were determined at a Larmor frequency of 300 MHz for protons of water adsorbed into saturated catalyst pellets (average error 2%). The equivalent diameter is defined by 6 Vp/Ap where Vp and Ap are volume and external surface of the particles, respectively.

Hence, Ub is a function of UbL, Db, and fluid properties. The equivalent diameter of the vapor blanket, Db, can be obtained from the correlation for the bubble departure diameter (Cole and Rohsenow, 1969). To calculate the liquid velocity, UbL,... 

A fluidized bed reactor contains catalyst particles with a mean diameter of 500 pm and a density of 2.5 g/cm3. The reactor feed has properties equivalent to 35° API distillate at 400°F. Determine the range of superficial velocities over which the bed will be in a fluidized state. 

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 ... 

In this chapter, the basic definitions of the equivalent diameter for an individual particle of irregular shape and its corresponding particle sizing techniques are presented. Typical density functions characterizing the particle size distribution for polydispersed particle systems are introduced. Several formulae expressing the particle size averaging methods are given. Basic characteristics of various material properties are illustrated. 

The book contains two parts each part comprises six chapters. Part I deals with basic relationships and phenomena of gas-solid flows while Part II is concerned with the characteristics of selected gas-solid flow systems. Specifically, the geometric features (size and size distributions) and material properties of particles are presented in Chapter 1. Basic particle sizing techniques associated with various definitions of equivalent diameters of particles are also included in the chapter. In Chapter 2, the collisional mechanics of solids, based primarily on elastic deformation theories, is introduced. The contact time, area, and... 

In the case of fumed powders, the results of particle size analysis depend veiy strongly on the characterization method. Each method measures a different particle property, from which sphere equivalent diameters are calculated. The underlying models assume homogeneous, spherical particles, which does not apply to the porous aggregates and agglomerates of these materials. 

An advantage of equivalent diameters is that they provide a unique characterization of particle size for the given method of measurement. In addition, the diameter gives information about the particle properties. For example, the equivalent surface diameter would give information about the surface area of the particle and the equivalent volume diameter would give information about the volume. Thus, if the density of the particles is known, the mass and properties important to pharmaceutical applications can be calculated. The numerical value for equivalent diameters derived from different geometric properties will only be identical in the case of perfectly spherical particles, and if the particle irregularity increases so will the differences between the different equivalent diameters. 

This example shows that an irregularly shaped particle can have different values for the different equivalent diameters when they are calculated from different geometric properties, i.e., each type of equivalent diameter weights the particle based upon the property that was measured (Fig. 4B). 

In addition to equivalent diameters based on geometric properties there are also equivalent diameters that are based on the physical properties of the particle. For example, the Stokes diameter uses Stoke law to calculate the diameter of a sphere with the same settling velocity as the particle in question. The terminal velocity (VJ of a sphere settling in a fluid can be de.scribed by Stokes law ... 

In summary, not all equivalent diameters are equivalent to each other, unless the particles are perfect spheres this highlights the importance of reporting the type of particle size and method of measurement. Different equivalent diameters emphasize different properties of the particle as shown in Example 1, and these differences become more significant as the particles become more irregular. The choice of diameter is in part determined by the method of measurement, because different methods measure different... 

Prego et al., 1998). The embryo that surrounds the perisperm is dicotyledonous and is part of the bran fraction of the seed it is high in proteins and lipids, and contains most of the ash, fiber, and saponins (Mastebroek et al., 2000 Varriano-Marston and DeFrancisco, 1984). The shape of QS is similar to a flattened sphere their mean equivalent diameter varies from 1.4 to 1.6 mm (Chauhan et al., 1992a,b Vilche et al., 2003). As mentioned previously, carbohydrates, proteins, and lipids are the main component of the seeds, and they are mostly responsible for the functional properties that have made them new ingredients in the development of new products. 

The terms dispersion characteristic and respective or constituent amount need further explanation. The dispersion characteristic, also called particle size, grain size, fineness index, or dispersion parameter, is a physical property which can be measured and defines, in a suitable way, the dispersity or, in a narrower sense, the dimensions of the particles. In the case of spheres, diameter would be the most descriptive dispersion characteristic. If the particles are irregularly shaped, other linear dimensions must be chosen, e.g. the statistical chord lengths according to Martin or Feret (Figure 21), the mesh size of a screen through which the particle just passes, or so-called equivalent diameters. Equivalent diameters are calculated from other dispersion characteristics, which must not necessarily be linear dimensions, using mathematical relationships and/or physical laws. 

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

Diameter of immaginary monosized spherical particles which feature the same property as the particulate mass to be characterized. For example surface equivalent diameter. 

Since industrial plants process large amounts of solids, the forces required to transport these masses and to cause the turbulent, stochastic movement of individual particles, nuclei, and agglomerates are much bigger than those experienced in the smaller developmental systems. Therefore, it is not unusual that additional and/or more effective binder(s) is (are) required or the feed size must be adjusted to feature a smaller surface equivalent diameter of the fresh input, possibly combined with modified recycle properties, such as smaller size obtained by a suitable mill to be installed in the return loop. 

Equivalent diameter The equivalent diameter of an imaginary spherical particle, droplet or bubble that behaves the same with regard to some physical property as the species under consideration. Also termed equivalent spherical diameter... 

In many cases, particularly for very small particles, surface area is a more appropriate characteristic to assess than some size based on an equivalent diameter. Particle surface area is important, for example, in paints and pigments or when chemical reactivity is an important property, as in the setting of cement. Precipitated materials are often characterized in this manner. Amongst the several techniques available, those based on permeability and gas adsorption are probably the most popular. 

The experimental coefficients fci and k2 depend on material properties and bed characteristics such as particle diameter, diffusion coefficient, water concenttation gradient, etc. For example, for the bed of silica gel with equivalent diameter de = 0.22 mm, ki = 5.72 10 , and kz = 0.23 g/(cm s), while... 

Consulting a Tyler Standard Screen Scale Table, it can be read the value of the screen equivalent diameter as 0.208 mm, so the pulverized coal may be considered a fine powder. Since the particles are taken as spherical, the ideal porosity =0.4 can be used for calculation. Finally, from any reference book (or appendix of some engineering textbook) listing physical properties of materials, at approximately 25°C the density of air is of the order of 1.2 kg/m. Substituting directly into Equation 7.5 ... 

However, the term particle size does not describe an unambiguous quantity, but rather a variety of measurands which are related to the outer particle dimensions. Indeed, particle size is always derived from a geometrical or physical property. If the property is not a length, it is usually converted to a diameter of a sphere being equivalent to the particle with regard to this property. The corresponding diameter is called equivalent diameter (e.g. equivalency in volume V leads to volume equivalent diameter xty. Table 2.1 lists some of these properties and the associated equivalent diameters. 

Table 2.1 Partiele properties, in brackets the associated equivalent diameters (if existing)...

Based on the solution of the velocity field, the force and torque acting on the aggregates can be calculated and the hydrodynamic equivalent diameters for translation (xh,t) and rotation (xi -) can be derived. They scale with the aggregate mass via a power law that reflects the stmctural properties of the aggregate. That means, while for hep aggregates the aggregate mass (N) is proportional to the third power of Xh, there is a fractal-tike relationship for DLCA aggregates with a hydrodynamic dimension 4i close to the fiactal dimension (Fig. 4.17, left cf. discussion to Kirkwood-Riseman theory on pp. 164). This fractal relationship... 

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