Particle mean size

The mean partide size measured by these various methods is different depending on the method used. The mathematical definition of the various mean sizes, with their mathematical definitions, follow [1]. Number, length mean diameter or arithimatic diameter  

Volume, moment mean diameter and weight (or mass), moment mean diameter  

Particle size interval (/xm) Middle size (fjLm), d Frequency of occurrence n Count frequency of n (%) nd n log d nd nd Mass frequency of nd (%) nd  

As you can see from this set of data, many different mean sizes can be calculated. Therefore, reporting a mean size without reference to the statistical method used is utterly useless. 

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One of the most important uses of specific surface determination is for the estimation of the particles size of finely divided solids the inverse relationship between these two properties has already been dealt with at some length. The adsorption method is particularly relevant to powders having particle sizes below about 1 pm, where methods based on the optical microscope are inapplicable. If, as is usually the case, the powder has a raiige of particle sizes, the specific surface will lead to a mean particle size directly, whereas in any microscopic method, whether optical or electron-optical, a large number of particles, constituting a representative sample, would have to be examined and the mean size then calculated. 

Another technique is to change the particle size distribution. There are, however, disadvantages. If segregation is occurring by the sifting mechanism, the particles must be almost identical in size before sifting is prevented. Alternatively, the mean particle size can be reduced below 100 p.m, but this size reduction (qv) increases the probabiUty of segregation by the too fine powder mechanisms. 

Experimental exponents for cake thickness vary from 0.5 to as much as 3.0. The theoretical value of //2 may be approached only by incompressible cakes of a narrow range of sizes. The proper and characteristic value for the mean particle size, d, is difficult to ascertain. In practice, the most finely divided particles, eg, 10—15 wt % of soHds, almost whoUy determine the Hquid content of a cake, regardless of the rest of the size distribution. It seems reasonable to use a d closely related to Hquid content, eg, the 10% point on a cumulative weight-distribution curve. 

Following carbonation, the product can be further purified by screening. This screening, also used to control the maximum size of the product, is followed by dewatering (qv). Rotary vacuum filters, pressure filters, or centrifuges are used in the mechanical removal of water. Final drying is accompHshed as with natural calcium carbonate in either a rotary, spray, or flash dryer. Products having mean particle sizes from submicrometers (- O-OS fiTo) to several micrometers are available. 

Circulating fluidized-beds do not contain any in-bed tube bundle heating surface. The furnace enclosure and internal division wall-type surfaces provide the required heat removal. This is possible because of the large quantity of soflds that are recycled internally and externally around the furnace. The bed temperature remains uniform, because the mass flow rate of the recycled soflds is many times the mass flow rate of the combustion gas. Operating temperatures for circulating beds are in the range of 816 to 871°C. Superficial gas velocities in some commercially available beds are about 6 m/s at full loads. The size of the soflds in the bed is usually smaller than 590 p.m, with the mean particle size in the 150—200 p.m range (81). 

Types of Solids Geldart [Fowder TechnoL, 7, 285-292 (1973)] has characterized four groups of solids that exhibit different properties when fluidized with a gas. Figure 17-j shows the division oi the classes as a function of mean particle size, d,, Im, and densitv difference, (p, — P/ ), g/cm, where p, = particle density and p = fluid density... 

As long as the largest particle separated by the fines-destruction baffle is small compared with the mean particle size of the product, the seed for the product may be thought of as the particle-size distribution corresponding to the fine material which ranges in length from zero to Lj, the largest size separated by the baffle. 

Type of centrifuge G/g Minimum feed sclids ccncentraticn by wt. Minimum mean particle size, im Minimum Vy, m/s... 

The structure of the cake formed and, consequently, its resistance to liquid flow depends on the properties of the solid particles and the liquid phase suspension, as well as on the conditions of filtration. Cake structure is first established by hydrodynamic factors (cake porosity, mean particle size, size distribution, and particle specific surface area and sphericity). It is also strongly influenced by some factors that can conditionally be denoted as physicochemical. These factors are ... 

The ratio of p JPmin be as high as 1.52 depending on the material. Consequently, when bulk densities are reported it is important to note whether the value was determined under loose or tapped conditions, along with the mean particle size. Most literature values report an average bulk density that is representative of the material most often handled. Loose solids may be broadly characterized according to their bulk densities ... 

The complete mathematical definition of a particle size distribution is often cumbersome and it is more convenient to use one or two single numbers representing say the mean and spread of the distribution. The mean particle size thus enables a distribution to be represented by a single dimension while its standard deviation indicates its spread about the mean. There are two classes of means ... 

Figure 8.7 Mean particle size versus specific energy input for different feed point positions if.p.p.) (CaOx, Rushton turbine, 40 min feed time, total concentration 0.008 M.) After Zauner and Jones, 2000b)...

Figure 8.14 Predicted (a) concentration profiles in the film region, and (h) mean particle sizes during gas-liquid precipitation of CaC03 (Wachi and Jones, 1991a). Ga.s-liquid precipitation cell...

A common starting point is that the process engineer is given a brief from which to determine a crystallization plant design viz. some specification of the product and process (e.g. mean particle size, production rate) and characteristics of the feed solution (e.g. composition, temperature etc.). Figure 9.1. 

At the crystallization stage, the rates of generation and growth of particles together with their residence times are all important for the formal accounting of particle numbers in each size range. Use of the mass and population balances facilitates calculation of the particle size distribution and its statistics i.e. mean particle size, etc. 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

Nozzle Size, In. Operating Pressure, Psig Approx. Mean Particle Size, Microns... 

The final polymer particles have a narrow particle size distribution. Figure 2 (] ), and the mean particle size is a strong function of the agitation in the prepolymerizer. 

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