Particles concentration distribution

Fig. 3 Particle concentration distribution in a turbulent flowing fluid in a pipe.

The application of CFD in the modeling of solid-liquid mixing is fairly recent. In 1994, Bakker et al. developed a two-dimensional computational approach to predict the particle concentration distribution in stirred vessels. In their model, the velocity field of the liquid phase is first simulated taking into account the flow turbulence. Then, using a finite volume approach, the diffusion-sedimentation equation along with the convective terms is solved, which includes Ds, a... 

Dilute transport fluidization The gas velocity is so large that all the particles are carried out of the bed with the gas. This solid transport by gas blowing through a pipe is named pneumatic conveying. In vertical pneumatic transport, particles are always suspended in the gas stream mainly because the direction of gravity is in line with that of the gas flow. The radial particle concentration distribution is almost uniform. No axial variation of solids concentration except i the bottom acceleration section [58]. 

In vertical pneumatic transport the radial particle concentration distribution is almost uniform, but some particle strands may still be identified near the wall. Little or no axial variation of solids concentration except in the bottom acceleration section is observed [58]. The flow associated with transport bed reactors tends to be dilute (typically 1 to 5 % by volume solids) and uniform. By virtue of the smaller reflux and density of the suspension within the dilute pneumatic conveying regime, there might be larger temperature gradients than within the fast fluidization regime [56]. 

Figure 1 shows the microelements filled with melt of reinforcement particles and alloy liquid in the cenrifugal force field. The initial concentration of this microelement is C and the densities of particles and alloy are Pp and pi, respectively. The gravity is omitted because it is far smaller than the centrifugal force. Thus, the reinforcement particles can only move in radius direction. If the particle concentration distribution is axisymmetrical, it can be considered as the function of radius r and time t. At any time t, in a mieroelement At, the volume concentration of particles is C, and the sedimentary velocity is Uc. The unit volume flux J of reinforcement particles in unit time is... 

Fig.2 shows the changes of particle concentration distribution with time. All the results are normalized. The reinforcement particles is SiC with the density of 3.2g/cm, and the base alloy is A1 alloy. The viscosity of liquid is 1.19 X I0 g/(mm.sec), and the centrifugal accelerate is SOOg. The average concentration Co of reinforcement particles is 20%, and the initial concentration is uniform. Other parameters are selected from reference. ... 

Following the approach introduced by Ya. Frenkel, let us apply the concepts of particle size distribution to the analysis of the kinetics of the formation of new phase nuclei during phase transitions. Equation (IV. 13), describing the particle size distribution, yields the particle concentration distribution curve with respect to particle radii, n(r) when applied to metastable system (Ap = p. -pr<0 also assuming that the interfacial tension is independent of particle size distribution). The particle radii distribution curve contains a minimum (Fig. IV-8). The shape of the curve indicates that the formation of large particles only occurs in a... 

Coupling CFD with one of the much simpler zone models is potentially particularly valuable. It is difficult and time consuming to add the additional complexity of mixing, heat and mass transfer, and dynamic population balance modeling to the CFD model, plus it makes the CFD model very slow. Sufficient accuracy may be achievable for many applications from applying the population balance modeling to the simpler zone models, although accuracy will be limited because the effects of the particle concentration, distribution and PSD will not be fed back to the transport models. Alternately, comprehensive CFD models can be used to understand the flow and its variation for a limited number of conditions, but simpler zone models may be used for application of the model where speed and convenience are important and detailed accuracy is not, e.g., process control. 

FIG. 3—Particle concentration distribution profile across the exposure chamber at the middle height of the test rack for particles within the approximate size range 0.018-0.032 m. 

N. Huber and M. Sommerfeld, Characterisation of the Cross-Sectional Particle Concentration Distribution in Pneumatic Conveying Systems, Powder Technology, 79 (1994) 191-210. 

Of the three worldwide manufacturers of poly(ethylene oxide) resins. Union Carbide Corp. offers the broadest range of products. The primary quaUty control measure for these resins is the concentrated aqueous solution viscosity, which is related to molecular weight. Specifications for Polyox are summarized in Table 4. Additional product specifications frequendy include moisture content, particle size distribution, and residual catalyst by-product level. 

In the second process, a small particle-size latex is prepared and treated so that a limited and controlled degree of particle agglomeration occurs. The agglomerated latex is then concentrated as before but, because of the particle-size distribution obtained, the soHds may be raised to ca 70 wt %. Two methods exist for agglomeration of latices, ie, chemical and freeze agglomeration (45,46). 

In particle-size measurement, gravity sedimentation at low soHds concentrations (<0.5% by vol) is used to determine particle-size distributions of equivalent Stokes diameters ia the range from 2 to 80 pm. Particle size is deduced from the height and time of fall usiag Stokes law, whereas the corresponding fractions are measured gravimetrically, by light, or by x-rays. Some commercial instmments measure particles coarser than 80 pm by sedimentation when Stokes law cannot be appHed. 

Several properties of the filler are important to the compounder (279). Properties that are frequentiy reported by fumed sihca manufacturers include the acidity of the filler, nitrogen adsorption, oil absorption, and particle size distribution (280,281). The adsorption techniques provide a measure of the surface area of the filler, whereas oil absorption is an indication of the stmcture of the filler (282). Measurement of the sdanol concentration is critical, and some techniques that are commonly used in the industry to estimate this parameter are the methyl red absorption and methanol wettabihty (273,274,277) tests. Other techniques include various spectroscopies, such as diffuse reflectance infrared spectroscopy (drift), inverse gas chromatography (igc), photoacoustic ir, nmr, Raman, and surface forces apparatus (277,283—290). 

Some concerns directly related to a tomizer operation include inadequate mixing of Hquid and gas, incomplete droplet evaporation, hydrodynamic instabiHty, formation of nonuniform sprays, uneven deposition of Hquid particles on soHd surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

The two steps in the removal of a particle from the Hquid phase by the filter medium are the transport of the suspended particle to the surface of the medium and interaction with the surface to form a bond strong enough to withstand the hydraulic stresses imposed on it by the passage of water over the surface. The transport step is influenced by such physical factors as concentration of the suspension, medium particle size, medium particle-size distribution, temperature, flow rate, and flow time. These parameters have been considered in various empirical relationships that help predict filter performance based on physical factors only (8,9). Attention has also been placed on the interaction between the particles and the filter surface. The mechanisms postulated are based on adsorption (qv) or specific chemical interactions (10). 

Aerosol Dynamics. Inclusion of a description of aerosol dynamics within air quaUty models is of primary importance because of the health effects associated with fine particles in the atmosphere, visibiUty deterioration, and the acid deposition problem. Aerosol dynamics differ markedly from gaseous pollutant dynamics in that particles come in a continuous distribution of sizes and can coagulate, evaporate, grow in size by condensation, be formed by nucleation, or be deposited by sedimentation. Furthermore, the species mass concentration alone does not fliUy characterize the aerosol. The particle size distribution, which changes as a function of time, and size-dependent composition determine the fate of particulate air pollutants and their... 

The shiny should always be defined as completely as possible by noting suspended solids concentration, particle size distribution, viscosity, density of solids and liquid, temperature, chemical composition, and so on. 

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