Diameter parameter, definition

Clearly, if a B were chosen to be equal to in (4.105), we would have two very similar components. We have made the two components different by choosing different diameters in (4.105). The value of A b computed for this case is about 0.76 hence, the two components are not similar. We can now change the value of EbbI T and follow the dependence of A b on this parameter. Figure 4.5 shows the dependence of A b on ebbI T, where all other parameters are as in (4.105). Note that at about bbI T == 0.70, we get A b = 0. Thus, the two components, which may seem to be quite different in the conventional sense, are considered to be similar according to our definition. This illustrates the idea that the energy and diameter parameters in the Lennard-Jones potential can be adjusted in such a way that the resulting value of Aj b will be zero. In other words, the dissimilarity in the can be compensated by a dissimi-... 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

To characterize a droplet size distribution, at least two parameters are typically necessary, i.e., a representative droplet diameter, (for example, mean droplet size) and a measure of droplet size range (for example, standard deviation or q). Many representative droplet diameters have been used in specifying distribution functions. The definitions of these diameters and the relevant relationships are summarized in Table 4.2. These relationships are derived on the basis of the Rosin-Rammler distribution function (Eq. 14), and the diameters are uniquely related to each other via the distribution parameter q in the Rosin-Rammler distribution function. Lefebvre 1 calculated the values of these diameters for q ranging from 1.2 to 4.0. The calculated results showed that Dpeak is always larger than SMD, and SMD is between 80% and 84% of Dpeak for many droplet generation processes for which 2left-hand side of Dpeak. The ratio MMD/SMD is... 

As mentioned in Section 11.8.4, the parameters that are most important for a qualitative analysis using most GC detectors are retention time, tR adjusted retention time, t R and selectivity, a. Their definitions were graphically presented in Figures 11.16 and 11.17. Under a given set of conditions (the nature of the stationary phase, the column temperature, the carrier flow rate, the column length and diameter, and the instrument dead volume), the retention time is a particular value for each component. It changes... 

CNTs may consist of just one layer (i.e. single-walled carbon nanotubes, SWCNTs), two layers (DWCNTs) or many layers (MWCNTs) and per definition exhibit diameters in the range of 0.7 < d < 2 nm, 1 < d < 3 nm, and 1. 4 < d < 150 nm, respectively. The length of CNTs depends on the synthesis technique used (Section 1.1.4) and can vary from a few microns to a current world record of a few cm [16]. This amounts to aspect ratios (i.e. length/diameter) of up to 107, which are considerably larger than those of high-performance polyethylene (PE, Dyneema). The aspect ratio is a crucial parameter, since it affects, for example, the electrical and mechanical properties of CNT-containing nanocomposites. 

The product selectivity is strongly affected by the flow rate, reactor geometry (i.e., internal diameter and "heated zone) and weight of catalyst. On this account, the space time yield to HCHO - or HCHO productivity -( HCHO Scat h ) appears to be the more definite parameter to evaluate the reactivity of the partial oxi tion catalysts. 

Particles used in practice for gas-solid flows are usually nonspherical and polydispersed. For a nonspherical particle, several equivalent diameters, which are usually based on equivalences either in geometric parameters (e.g., volume) or in flow dynamic characteristics (e.g., terminal velocity), are defined. Thus, for a given nonspherical particle, more than one equivalent diameter can be defined, as exemplified by the particle shown in Fig. 1.2, in which three different equivalent diameters are defined for the given nonspherical particle. The selection of a desired definition is often based on the specific process application intended. 

The major reason why a reduction of the particle size or column diameter is expected to lead to an increase of separation speed (resolution power per time unit) can be found in its effect to decrease r. Separation speed is often expressed in the analytical literature in terms of the number of theoretical plates N per time unit f (for a definition of N in terms of experimental parameters see Sect. 3.1.1). For zone dispersion due to lateral non-equilibrium, the ratio N/t will be in general inversely proportional to r [20] ... 

A more basic difficulty and one not yet adequately resolved is that encountered in the use of artificial models to represent molecules. From a rigorous point of view the entire behavior of a molecular encounter is determined by the force field surrounding each molecule. By representing molecular force fields by artificial models we avoid the impossible mathematical problem involved in the rigorous approach. The result, however, is to introduce an entirely new set of molecular parameters which remain as yet unpredictable from simpler molecular properties. In the case of the hard sphere model we have introduced the molecular diameter additional parameters which were somewhat concealed in the discussion, namely, the two accommodation coefficients, one for velocity transfers between molecules in collision and the other for collision between molecules and surfaces. 

In gas chromatography the analyte partitioning between mobile gas phase and stationary liquid phase is a real retention mechanism also, phase parameters, such as volume, thickness, internal diameter, and so on, are well known and easily determined. In liquid chromatography, however, the correct definition of the mobile-phase volume has been a subject of continuous debate in the last 30 years [13-16]. The assumption that the retardation factor, i /, which is a quantitative ratio, could be considered as the fraction of time that components spend in the mobile phase is not obvious either. 

Before discussing our method for determining particle size, it is necessary to briefly review the definition of size distribution. If all particles of a given system were spherical in shape, the only size parameter would be the diameter. In most real cases of irregular particles, however, the size is usually expressed in terms of a sphere equivalent to the particle with regard to some property. Particles of a dispersed system are never of either perfectly identical size or shape A spread around the mean distribution) is found. Such a spread is often described in terms of standard deviation. However, a frequency function, or its integrated (cumulative) distribution function, more properly defines not only the spread but also the shape of such a spread around the mean value. This is commonly referred to as the particle size distribution (PSD) profile of the dispersed sample. 

Definitions of particle diameters derived by different methods have been described in detail [4]. The aerodynamic diameter is defined as the diameter of a unit-density sphere having the same settling velocity, generally in air, as the particle. This encompasses particle shape, density, and physical size, all of which influence the aerodynamic behavior of the particle. As a dynamic parameter, it can generally be linked with aerosol deposition and specifically with that in the lung [5]. 

Table 7. Mathematical definitions of the average diameters of non-uniform particulate substances in terms of the parameters of the distribution curves by count and by weight (from Hatch, 1933)...

Figure 18. Effect of interparticle distance, A, on plastic deformation of matrix strands between particles (a) definitions of the size parameters D = particle diameter, vP = particle volume content, aQ = applied stress, and aK = stress concentration (b) with a small interparticle distance, a uniaxial stress state is dominant between the particles and microvoids after cracking of the particles, and plastic yielding can be obtained and (c) with a large interparticle distance, thick matrix strands favor a triaxial stress state between the particles and microvoids, and plastic yielding is hindered.

As with most questions on particle size, the answer is very dependent on the definition used and the experimental technique. For a dynamic aerosol cloud, the correct definition is the aerodynamic particle size, which is the diameter of an equivalent sphere of unit density. An equivalent sphere is a conventional assumption in particle sizing, but for the aerodynamic size, the density is included to account for the momentum of the particle, i.e., both mass and velocity are important. The technique chosen for measurement must include these parameters, and impaction is the normally chosen technique, which also reflects the major deposition mechanism in the lung. A schematic of an impaction plate is given in Figure 10.3. 

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