Powders with granular distributions

All the models that we described assume that the initial powders all have grains with the same shape and same sizes, for example, the same radius for the spherical powders. How should the behavior of a powder, which would consist of grains, all of the same form, but of different sizes, be modeled  

The powder will now be characterized by a frequency of distribution, (ro), of the number of grains whose radius lies between - dro and ro + dro, that is to say, if Nq is the total number of grains of the powder, this frequency of distribution is given as  

Let us indicate by a(r ) the fractional extent for the eollection of grains with the size ro, it is possible to calculate the expression of the rate for any size by the preceding models and to deduce the expression of the rate for the powder with granular distribution by expressing it in the form  

It is noted that considering the granular distribution led to the curves with a best fit with the experiment, especially at the end of the reaction, as shown by Perrin [PER 02]. 

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In summary, as it happens with granular and powder carbons, a proper selection of the CF and the activation method and experimental conditions permits the preparation of ACFs with a tailored pore size distribution, with the additional advantage of their fiber shape and small diameters that allow faster mass transfer rates when compared with conventional ACs. 

The term particle (or grain) size refers to the structural make-up of such substances as granulates, powders, dusts, granular mixes, and suspensions. Knowledge of the particle size, in conjunction with the comminution process, determines such details as grinding efficiency and ultimate product fineness. To establish particle sizes and their distribution within powdered systems, the user can have recourse to a number of different measuring processes designed to indicate, with appropriate particle definition, details of the probable equivalent diameter of a particle. 

In addition to surface area, pore size distribution, and surface chemistry, other important properties of commercial activated carbon products include pore volume, particle size distribution, apparent or bulk density, particle density, abrasion resistance, hardness, and ash content. The range of these and other properties is illustrated in Table 1 together with specific values for selected commercial grades of powdered, granular, and shaped activated carbon products used in Hquid- or gas-phase appHcations (19). 

Properties Off-white granular powder. Den 47-53 Ib/f3, pH of 0.5% solution at 77F 6.5-8.5. TM for a dry polyacrylamide cationic, flocculated with controlled molecular weight distribution and varying charge densities. 

From the point of view of gas adsorption, which is the main objective of this chapter, there are no differences in the results obtained between the ACFs and the granular and powder ACs, except for the kinetics of gas adsorption due to the special pore structure of the ACF [2, 40, 41] and for the higher packing density that can be obtained with them due to their fiber shape [3]. In this way, although there are important differences in the pore structure and distribution of porosity among the ACFs and the conventional ACs (this aspect will be described in a next section), the adsorption isotherms are not sensitive to them and do not allow to distinguish the shape of the porous carbons (i.e., fiber, granular, powder, monohth). 

Activated carbon, in powdered (PAC) or granular (GAC) form, has many applications in drinking water treatment. It can be used for removing taste and odor (T O) compoimds, synthetic organic chemicals (SOCs), and dissolved natural ot] nic matter (DOM) from water. PAC typically has a diameter less than 0.15 mm, and can be applied at various locations in a treatment system (Fig. 1). GAC, with diameters ranging from 0.5 to 2.5 mm, is employed in fixed-bed adsorbers such as granular media filters or post filters. Despite difference in particle size, the adsorption properties of PAC and GAC are fundamentally the same because the characteristics of activated carbon (pore size distribution, internal surface area and smface chemistry) controlling the equilibrium aspects of adsorption are independent of particle size. However, particle size impacts adsorption kinetics. 

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