Particle collision mechanism

The model as formulated in this section cannot be used to predict a priori the solids entrainment rate into the jet because of the two empirical constants in Eq. (61). Lefroy and Davidson (1969) have developed a theoretical model based on a particle collision mechanism for entrainment of solid particles into a jet. The resulting equation for particle entrainment velocity is... 

FIG. 1 Particle collision mechanisms (a) Brownian motion, (b) fluid shear. 

FIG. 1 Continued. Particle collision mechanisms (c) differential sedimentation. 

Three particle collision mechanisms can occur in an agitated vessel. These are (a) particle-vessel, (b) particle-impeller and (c) particle-particle. Most of the work on collisions has been related to secondary nucleation, but there are other systems where mechanical abrasion following impact may occur and may be undesirable, e.g. breakdown of friable catalysts, or in mammalian cell culture on microcarriers or desirable, e.g. removal of an impervious outer skin which forms on ore particles during some leaching processes. 

Particle collision is important in simulating bubble behavior in liquid-solid suspensions, especially for high solids holdup conditions. A simulation without considering particle collision leads to inappropriate nonuniformity of particle distribution in the flow field and hence false flow field information. Numerical instability may also occur as a result of inappropriate particle accumulation in a computational cell. In the collision model discussed above, only the binary-particle collision mechanism is considered, which limits the model to low solids holdup conditions (less than 30-40% by volume). For higher solids holdup cases, the multiparticle collision mechanism needs to be considered. 

Although reduction or elimination of the repulsion barrier is a necessary prerequisite of successful flocculation, the actual flocculation in such a destabilized suspension is effected by particle—particle collisions. Depending on the mechanism that induces the collisions, the flocculation process may be either perikinetic or orthokinetic. 

There are two features of this example that are rather common. First, none of the steps in the reaction mechanism requires the collision of more than two particles. Most chemical reactions proceed by sequences of steps, each involving only two-particle collisions. Second, the overall or net reaction does not show the mechanism. In general, the mechanism of a reaction cannot be deduced from the net equation for the reaction , the various steps by which atoms are rearranged and recombined must be determined through experiment. 

Two-Particle Collisions.—One of the basic assumptions in the derivation of the Boltzmann equation is that the gas being described is sufficiently dilute so that only two-particle collisions are of importance. The mechanics of a two-body encounter will thus be described in order... 

With a simulation technique Peng et al. (1994) have studied the particle-particle collisions with rotational and floating mechanisms of coarse particles in horizontal flow for higher concentrations of particles. Figure 20 gives the distribution of particles across the pipe cross-section. One notes that higher concentrations are seen at the bottom of the pipe. 

Peng, X., Tomita, Y., and Tashiro, H., Effect of Particle-Particle Collision and Particle Rotation upon Floating Mechanism of Coarse Particles in Horizontal Pneumatic Pipe, JSME Inti. J., Series B, 37(3) 485-490 (1994)... 

It should be noted, however, that gaining a deeper insight into the problem of ionization phenomena is not the only reason for steady interest in the problem. Data on charged particle impact ionization is used both for industrial applications and for fundamental scientific research. For applications it is the collisions rates and total cross sections which are usually the most relevant. But in studies focused on the understanding of collision mechanisms of ionization processes, most of the information is lost in the total cross sections due to the integration over the momenta of the ejected electrons in the exit channel. Therefore it is the singly and doubly differential cross sections which are of... 

Decreasing particle size means increased effort required to remove it. This rule arises from the smaller interaction cross sections for collision and momentum transfer. Furthermore, the electrostatic forces are stronger for smaller particles, and they diminish in proportion to 1/r as opposed to 1/r. Both of these factors lead to redeposition being a major source of small particles. Since mechanical action requires increasing amounts of work, chemical dissolution is more effective at removing small particles than is mechanical action. 

The extension of the shock tube to the plasma region where particle collision s become infrequent and other dissipative mechanisms must be explored, opens an exciting area for study... 

Besides the already mentioned techniques, a low-temperature plasma has been adopted to enhance the reaction in CVC. Through the synthesis of AIN UFPs by an RF-plasma-enhanced CVC using trimethylaluminum [A1(CH3)3] and NH3 as reactants, the effect of experimental parameters on the rate of powder formation, particle size, and structure was examined (60). A high RF current was primarily connected to a high electron density, which activated the gas-phase reaction to promote the powder formation rate. The increase of both susceptor temperature and A1(CH3)3 concentration also increased the powder formation rate and enhanced the grain growth, where both mechanisms—coalescence by particle collision and vapor deposition on to particle surfaces—were believed to occur. 

Unvulcanized Latex and Latex Compounds. A prime consideration has to be the fluid-state stability of the raw latex concentrate and liquid compound made from it. For many years, the mechanical stability of latex has been the fundamental test of this aspect. In testing, the raw latex mbber content is adjusted to 55% and an 80 g sample placed in the test vessel. The sample is then mechanically stirred at ultrahigh speed (ca 14,000 rpm) by a rotating disk, causing shear and particle collision. The time taken to cause creation of mbber particle agglomerates is measured, and expressed as the mechanical stability time (MSI). 

Collins and Jameson11 found that for small air bubbles (20 to 100 jzm), varying the particle zeta potential from +30 mV to +60 mV resulted in an order of magnitude change in the observed rate constants for each drop size. Table 9 shows the values of the calculated and observed first-order rate constants for the data of Collins and Jameson obtained when their particles (polystyrene) had the minimum stability (zeta potential + 30 mV). The observed rate constants are much smaller than those calculated from collision theory. Their data indicate that between 1 in 40 to I in 100 collisions results in the particles sticking to bubbles. This is consistent with the particle-collision removal mechanism. 

The internal standard ratio method for quench correction is tedious and time-consuming and it destroys the sample, so it is not an ideal method. Scintillation counters are equipped with a standard radiation source inside the instrument but outside the scintillation solution. The radiation source, usually a gamma emitter, is mechanically moved into a position next to the vial containing the sample, and the combined system of standard and sample is counted. Gamma rays from the standard excite solvent molecules in the sample, and the scintillation process occurs as previously described. However, the instrument is adjusted to register only scintillations due to y particle collisions with solvent molecules. This method for quench correction, called the external standard method, is fast and precise. 

According to the different collision mechanisms in these modes, a distinction between them can be made with the help of the Knudsen number K which compares the mean-free-path length A of the particles with a characteristic dimension d of the tube ... 

The effect of the collisional force due to the impact of particles should be included when accounting for the motion of a particle except in a very dilute gas-solid flow situation. Basic mechanisms of collision between two particles or between a particle and a solid wall are discussed in Chapter 2. The collisional force between a particle and a group of neighboring particles in a shear suspension is discussed in 5.3.4.3. In a very dense system where particle collisions dominate the flow behavior, collisional forces can be described by using kinetic theory, as detailed in 5.5. The key equations derived in other chapters pertaining to the collisional forces can be summarized in the following. 

In a collision between two spheres of different temperatures, heat conduction occurs at the interface. The contact area is usually negligibly small compared to the cross-sectional area of the spheres. Since the duration of the impact is also very short, the temperature change of the colliding particles is confined to a small region around the contact area. Therefore, the heat conduction between the two particles can be treated as that between two semiinfinite media. It is also assumed that there is no thermal resistance between the contact surfaces. Hence, the temperature and heat flux distributions are continuous across the contact area. The surfaces outside the contact area are assumed to be flat and insulated. For general information on collision mechanisms of solids, readers may refer to Chapter 2. 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

The book is arranged in two parts Part I deals with basic relationships and phenomena, including particle size and properties, collision mechanics of solids, momentum transfer and charge transfer, heat and mass transfer, basic equations, and intrinsic phenomena in gas-solid flows. Part II discusses the characteristics of selected gas-solid flow systems such as gas-solid separators, hopper and standpipe flows, dense-phase fluidized beds, circulating fluidized beds, pneumatic conveying systems, and heat and mass transfer in fluidization systems. 

Deposition by diffusion is the main mechanism for particles smaller than 0.5 pm, and is important in bronchioles, alveoli, and bronchial bifurcations. Aerosol particles are displaced by a random collision of gas molecules this results in particle collision with the airway walls [24]. Deposition by diffusion increases with the decrease in particle size, and breath-holding following inhalation was also found to increase this deposition [25]. 

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