Mixing particle concentration

Due to turbulent mixing, particle concentration is uniform across the duct cross-sectional area 2bW. 

Typically it took about 160 to 200 seconds to inject a pulse of about 455 kg coarse tracer particles into the bed pneumatically from the coaxial solid feed tube. It can be clearly seen from Figs. 38 to 42 that the tracer particle concentration increases from essentially zero to a final equilibrium value, depending on the location of the sampling port. The steady state was usually reached within about 5 minutes. There is considerable scatter in the data in some cases. This is to be expected because the tracer concentration to be detected is small, on the order of 4%, and absolute uniformity of mixing inside a heterogeneous fluidized bed is difficult to obtain. 

On the reverse, how does the presence of particles affect local and global flow features in the vessel such as the vortex structure in the vicinity of the impeller, power consumption, circulation and mixing times, and the spatial distribution of turbulence quantities more specifically colliding particles have an impact on the liquid s turbulence (Ten Cate et al., 2004) while local particle concentrations affect the effective (slurry) viscosity which may be useful in the macroflow simulations ... 

Simple steady-state models may be used in order to relate quantitatively the mean concentration in the lake water column and the residence time of metal ions to the removal rate by sedimentation (for a detailed treatment of lake models see Imboden and Schwarzenbach, 1985). In a simple steady-state model, the inputs to the lake equal the removal by sedimentation and by outflow the water column is considered as fully mixed mean concentrations and residence times in the water column can be derived from the measured sedimentation fluxes. The binding of metals to the particles is fast in comparison to the settling. 

Equation 5.113 gives the rate of fall of the interface between zones (b) and (c) that is the apparent rate of settling of the zone of mixed particles. The velocity of fall // of the interface between zones (a) and (b) is the sedimentation rate of the suspension composed only of fine particles, and will therefore depend on the free-falling velocity u<)S and the concentration Cf of this zone. ... 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

These equations have been solved for rigid (Nl) and circulating spheres (Jl, K6, W3, W4) in creeping flow. Since the dimensionless velocities within the particle are proportional to (1 + k) (see Eq. (3-8)), F is a function only of Tp and PCp/(l + k). In presenting the results, it is instructive to consider the instantaneous overall Sherwood number, Shp, as well as F. The driving force is taken as the difference between the concentration inside the interface, and the mixed mean particle concentration, Cp, giving... 

If a fluid particle oscillates violently enough to mix its contents in each oscillation cycle, the average internal resistance is constant if the driving force is based upon the mixed mean concentration within the drop. The fractional approach to equilibrium is then given by Eq. (7-40) or (7-41). 

Figure 3.1.3 shows a TEM image of mixed particles of CdS xZnS (jc = 21.5) (upper) and an SEM image of mixes particles of CdSctPbS (jc = 2.1) (lower). In the preparation of the ZnS and PbS seed sols used for the preparation of these mixed sulfide particles, only —4% of the original concentration of Zn2+ and —6% of Pb2+ were used up, repectively. For CdS xZnS prepared in the presence of ZnS seeds,... 

Mixing equal concentrations of two separately prepared solutions of colloidal lead and silver particles (each degassed by repeated freeze-pump-thaw cycles on a high-vacuum line and mixed under vacuum) resulted in a slow blue shift of the silver plasmon band from 390 nm to 337 nm and a concomitant broadening... 

One of the simplest methods to generalize formal kinetics is to treat reactant concentrations as continuous stochastic functions of time, which results in a transformation of deterministic equations (2.1.1), (2.1.40) into stochastic differential equations. In a system with completely mixed particles the macroscopic concentration n (t) turns out to be the average of the stochastic function Cj(<)... 

Until the geminate pairs start to mix, i.e., at relatively short times r relative diffusion coefficient, the monomolecular kinetics reads n(t) = n(0)u>(t), with n(0) = nA(0) = ne(0) being initial particle concentration. The distinctive feature of this stage is the linearity of the recombination kinetics n(t) with respect to the irradiation dose n(0). 

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

Figure 4 shows that higher concentrations of seed latex decrease the reaction rate, at constant mixed emulsifier concentrations, while Figure 5 shows that the smallest latex particle gave the lowest reaction rate. This effect is explained by the decreased availability of emulsifier to create micelles, since the small seed latex particle or high seed latex concentrations adsorb more of the surfactant, thus removing it from the water phase. 

In addition, a model derived by Meredith and Tobias [51] applies to a cubic array of spheres inside a matrix. Consequently, it cannot be used for volumetric concentration above 52% since the spheres will touch at that point. However, their model predicts the thermal conductivity very well up to 40% by volume of particle concentration. When mixing several materials the following variation of Knappe s model applies... 

The collection efficiency of the wire-plate-type of electrostatic precipitator can be estimated by the widely used Deutsch theory [Deutsch, 1922]. To obtain the Deutsch equation, the following assumptions are made (1) because of the turbulent mixing effect, particle concentration at any cross section of the precipitator is uniformly distributed ... 

Determination of the maximum particle concentration is also of interest since it no longer constitutes a purely kinematical problem. Rather, the suspension contained within the unit cell is now a mixed object possessing both solid-like and liquid-like features. In particular, it behaves like a solid insofar as mutual impenetrability demands are concerned, whereas it behaves like a liquid in its ability to change its configuration (i.e., it can flow ). 

It is obvious that a consistent system for the description of concentrations in the gas phase is necessary. Usually, fractional or percentage concentrations are used. Mixing ratios of low concentrated volatile compounds and gases are based on the parts per... unit system. This unit is obsolete but is still used in the current literature. It cannot be utihzed for particle concentrations. Therefore, the WHO (1999) has adopted a mass per volume system with concentrations [C] in mgm . Other units frequently employed to express the concentration of gases include moles per volume or molecules per volume (vanLoon and Duffy, 2000, Kurzweil, 1999). 

The slurry distribution and mixing system operates in the background of the actual wafer processing. However, a slurry with consistent physical and chemical properties is critical for maintaining a repeatable W CMP process with steady yield. Two of the most important parameters to monitor are etchant (oxidizer) and solid (abrasive particle) concentrations. 

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