Modeling of the particle

In its most elementary aspects, kinetic theory is developed on the basis of a hard sphere model of the particles (atoms or molecules) making up the gas.1 The assumption is made that the particles are uniformly distributed in space and that all have the same speed, but that there are equal numbers of particles moving parallel to each coordinate axis. This last assumption allows one to take averages over... 

A.T. Harris, R.B. Thorpe, J.F. Davidson, Stochastic modelling of the particle residence time distribution in circulating fluidised bed risers, Chem. Eng. Sci. 57 (2002) 4779-4796. 

In the interpretation of these spectra it is assumed that the geometry (i.e., the layer statistics in the NMR layer model) of the particles does not change as a result of chemisorption but that the surface LDOS and the healing length are affected. In principle, this suggestion can be tested experimentally by comparing the lineshape in a double-resonance experiment on... 

The properties of the above system at modest particle concentrations are relatively simple to model, because the grafted octadecyl layer is thin compared to the particle radius and because the particle-particle interactions are weak enough that the properties of the dispersion are not sensitive to the detailed shape of the particle-particle interaction potential. These considerations have motivated the use of a simple square-well potential as a model of the particle-particle interactions (Woutersen and de Kruif 1991) (see Fig. 7-3). This potential consists of an infinite repulsion at particle-particle contact (where D — 0), bounded by an attractive well of width A and depth e. There are no interactions at particle-particle gaps greater than A. Near the theta point, the well depth s depends on temperature as follows (Hory and Krigbaum 1950) ... 

A model of the particle ensemble, with gas streamlining particular elements (particles) of the layer. 

The terminal velocity that particles reach when in free fall is an important particle characteristic. It is also fairly straightforward to measure and was therefore used to check the accuracy and validity of the particle tracking model. The measurement technique is entrainment of a small sample of a particular size class in a narrow tube taking the average of the band within which 90% of the small sample are entrained. In the computational modelling of the particle tracks the upper end of the class size is used as the particle diameter and the particles are started from rest and from a falling velocity greater than their terminal velocity. 

Problem 9.11 Relate the additional stabilization associated with delocalized m.o.s with the model of the particle in the box studied in Chapter 2. 

Werther J, Hartge E-U (2004) A population balance model of the particle inventory in a fluidized-bed reactor/regenerator system. Powder Technology 148 113-122... 

Fisher, R. R. 1987. Protein precipitation with acids and polyelectrolytes The effects of reactor conditions and models of the particle size distribution. Ph.D. Thesis. Iowa State University, 165 pp. 

Dalton s atomic theory gave chemists a model of the particle nature of matter. However, it also raised new questions. If all elements are made up of atoms, why are there so many different elements What makes one atom different from another atom Experiments in the late 19th century began to suggest that atoms are made up of even smaller particles. Present-day chemistry explains the properties and behavior of substances in terms of three of these smaller particles. You will learn more about each of these particles in Section 2.2. 

Since its discovery the existence of the stratospheric aerosol layer has been proved by many investigators (e.g. Mossop, 1965 Friend, 1966 Kondratyev et ai, 1969). A mathematical model of the particles in the aerosol layer, constructed by Friend (1966), led to a size distribution with a maximum in the vicinity of 0.3 fim particle radius. However, according to the results of more recent measurements by Bigg (1976) the actual distribution has its maximum at smaller sizes. The observations of Kondratiev et al. (1974) show that the stratospheric concentration of aerosol particles with radii larger than 0.2 /an may be as great as 1 cm-3. However, this concentration is strongly time dependent (Bigg, 1976) as we shall discuss in Subsection 4.4.3. 

Some photobleaching experiments have been carried out with QDQWs [58]. They reveal that the photobleaching spectrally follows the newly evolving Is-Is electronic transition of the composite particles, thus pointing also in the direction that the electronic structure of QDQWs is not simply a superposition of the electronic properties of the segments of the particles. This is also concluded from theoretical modeling of the particles in the framework of the effective mass approximation [57]. This calculation fits the Is-Is optical transition of the QDQWs of various compositions very well. A further description of the model goes beyond the scope of this chapter. 

Figure 3.115 Powder XRD patterns for cobalt nanoparticles (circles) and their corresponding simulations (solids lines) using atomic-level models of the particles, (a) e -Co (b) multiply-...

Descriptions of pore development and stracture require microscopic models of the particle. These models include intrinsic kinetics and pore stractural changes during bumoff. Three of the most popular mieroscopic models are a random eapillaiy pore model, one in which the pores are considered spherical vesicles connected by cyhndri-cal micropores, and one in which the pores have a treelike structure. These models allow for pore growth and coalescence in their respective fashions and provide estimates of reactive smface area. Parameters required for these models are obtained from experimental measurements of the various chars. 

Figure 10.8. Three-dimensional model of the particle shown in Figure 10.7, showing an 82-particle aggregate. Model constructed by Medalia (1970) and Sambrook (1970, 1971).

A simple geometric model of the particle described in terms of measurable physical properties is devised. 

Figure 3 A model of the particles in the ionic solution of copper chloride, drawn...

Similarly, in chemistry, you have to learn to think about both the number of particles, grouped in moles, and the mass of those particles. Considering moles of particles is useful when you are thinking about models of the particles and their reactivity. On the other hand, when you want a certain number of particles for a chemistry experiment, you will often weigh a specified amount of the macroscopic solid. So thinking about mass is important, too. You have to understand both methods for expressing amount of a substance. 

Most models currently available for blood filtration are based on empirical models/ Bruil proposed a mathematical model for leucocyte filtration process and could explain the filtration law in the plain membrane filter. However, the effect of direct interception in blood filtration is not clearly understood, and the particle capture efficiency may be modelled based on an empirical model proposed by Khilar and Fogler"" for Newtonian liquid flow. With the consideration of the further particle capture due to the reduction of the pore sizes and the porosity of filter fabric by particle bridging, pore blockage, and pore closure, a modified Khilar—Fogler model of the particle capture efficiency by Gruesbeck and Collins" may be applied in blood filtration. 

A blue shift in the absorption spectrum of a solution of colloidal CdS was first observed in 1982 by Henglein. The cause was attributed to the quantum-confinement effect (quantum-size effect). It is responsible for the blue shift of the photoabsorption spectrum with decreasing particle size compared to the bulk band gap of the material. As a first approximation the model of the particle in a box ean be used to explain this behaviour with deereasing system size, the spacing between the energy levels and, thus, also the excitation energies increases. In the particle-in-a-box model the energies... 

In some theoretical works by Theocaris, adhesion was taken into account. The interlayer between the filler particle and matrix, called mesophase by Theocaris, is considered as a homogeneous independent phase. It is convenient for calculation but not correct from the thermodynamic point of view. Theocaris used the model of the particle separated by the mesophase (interlayer) from the matrix. The analysis of the mechanical behavior of the system is done for a three or N-layer model. In the latter case, the mesophase is considered to be formed by N layers with various properties. 

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