Mixed Particles

If the particles treated are not of the same size, some kind of an average particle diameter dp could be adopted, so that the procedure outlined for uniform particles might be followed. 

According to this so-called two-d method, it can be shown that the following expressions for cross-sectional area, height and volume ensue  

Comparison of the above three equations with their corresponding parent equations for uniform particles, reveals that AZ and V calculated from the larger particles of dpI need to be corrected, due to the presence of the smaller particles, by factors shown in the large braces of these equations, all involving the factor MeA in which M=ut2/utI and A =n2-nl. Variation 

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Three different types of furnaces are generally in use for calcination. The shaft furnace is considered to be the most suited for calcining coarse limestone. Furnaces of the rotary kiln type are used for handling materials of mixed particle sizes and lumps which disintegrate during the process. Calcination can be carried out in a fluidized bed-reactor for materials of small and uniform particle size. These furnaces are usually fired with gas, oil or coke in some cases electric heating is resorted to. 

Air blast fluidisation Air blast lifts and mixes particles Dry powders and granules Milk powder detergents, chemicals... 

Biyikli, S., and Chen, J. C., Effect of Mixed Particle Sizes on Local Heat Transfer Coefficients Around a Horizontal Tube in Fluidized Beds, 7th Int. Heat Transfer Conf, Munich, Germany (1982)... 

Figure 4. Fluidized leaching or washing of mixed particles—values of correction factors. (Kwauk, 1973, 1979 Kwauk and Wang, 1981.)...

Particle size reduction makes dissolving procedures more efficient and extracting procedures more accurate because of the improved contact of the solvent with the sample. If accompanied by thorough mixing, particle size reduction also results in more homogeneous samples, which are more representative. 

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. ... 

Figure 6.10. Bed densities as a function of fluidising velocity, showing the mixed particle region9399...

Mullin(3) has used this procedure for the design of a unit for the crystallisation of potassium sulphate at 293 K. The data are given in Table 15.5 from which it will be noted that the cross-sectional area depends linearly on the relative degree of de-supersaturation and the production rate depends linearly on the area but is independent of the height. If the production rate is fixed, then the crystalliser height may be adjusted by altering the sizes of the seed or product crystals. Mullin and Nyvlt(75) have proposed a similar procedure for mixed particle-size in a crystalliser fitted with a classifier at the product outlet which controls the minimum size of product crystals. 

Differential centrifugation is the simplest form of centrifugation A mixed particle population is subjected to centrifugations with... 

Two peaks in the accumulation mode may also result if the particles are externally mixed rather than internally mixed (the latter meaning that all particles have the same composition corresponding to a mixture of the various components). That is, the composition of individual particles may not be the same as the overall bulk particle composition, with some having more hygroscopic components than others. These are referred to as externally mixed particles indeed single-particle analyses suggest that externally mixed particles are common (see Chapter 11.B.4). In this case, a... 

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,... 

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(<)... 

For completely mixed particles in large enough volume, the square of the fluctuation of the number of particles 5N = N — N obeys the ordinary statistical relationship... 

Yang, W. C. (1987). Pneumatic Transport in a 10cm Pipe Horizontal Loop. Powder Tech., 49, 207. Zenz, F. A. (1964). Conveyability of Materials of Mixed Particle Size. I EC Fund., 3,65. 

Many operations treat particle-liquid mixing in chemical industry. The first aim of solid-liquid mixing is to make a solid particle float. However, mixing performance of operations/equipment is not clear. Additionally, when many kinds of particles are involved, it is not known whether there is any difference in the mixedness between the following two cases the case where all particles are treated as a particle (two-phase mixing—particle and continuous liquid phase) and the case where every particle is treated individually (multiple-phase mixing—each particle and continuous liquid phase). Therefore, a solution to this unsolved problem is not imperative. 

To clarify the difference in mixedness M defined by Eq. (2.44) between the following two cases—the case where the two kinds of particles are treated as a particle (two phase mixing particle and continuous liquid phase) and... 

Figure 3. The two limiting cases for mixing earliness. Left, Min. Mix. particles having the same age are close together (on the same vertical) right, Max. Mix. particles having the same life expectancy are close together (on the same vertical).

If the desorption rate is sufficiently large, chromatographic separation and analyses of mixed suspensions become possible. Dependence of adsorption and desorption rates upon particle properties causes some components of a pulse of mixed particles carried through a packed bed to be eluted more quickly than others. This mechanism is analogous to conventional gas chromatography, and all the formalisms developed for the latter may be applied. 

Fluidized leaching and washing belong to counter-down, or mode III, operation for simultaneous particle-fluid motion. A basic case for uniform particle size will be established, and it will then be extended to mixed particle sizes. 

Finkelstein, E., Letan, R., and Elgin, J. C., Mechanics of Vertical Moving Fluidized Systems with Mixed Particle Sizes, AJ.Ch.EJ. 17, 867 (1971). 

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