Permeability Methods for Characterizing the Fineness of a Powder System

One measures the permeability of a powder bed by measuring the resistance to flow offered by the bed when a given pressure is applied to drive a fluid through it. To interpret permeability data in terms of the surface area of the powder under test, it is common practice to use an equation originally developed by Kozeny and modified by Carman who considered the packed powder bed to consist of a set of tortuous capillary tubes [6, 7]. 

The Kozeny-Carman equation is usually written in the form 

For the assumptions made in deriving this equation to be valid, the pressure difference across the powder plug is assumed small and the powder compact is presumed to be a uniform cylinder of length i and cross-sectional area A. 

Carman showed that for many materials the constant B, could be taken as 5. However, Carman stated clearly that the universal use of the value 5 will lead to error in certain cases [6, 7]. Because of the lack of alternative values, however, commercially available permeameters such as the Fisher Subsieve Sizer are calibrated for operation on the assumption that the value B = 5 is used in the Kozeny-Carman equation [8]. The unknown value of B for any specific powder is an immediate source of discrepancy between the surface area measured by permeability with that measured by other techniques. The only way to determine B exactly is to use an independent method of analysis to measure the surface area of the powder. B is sometimes called a tortuosity factor but it is my opinion that it is better to call the factor B a correlation factor and in this way firmly state the true nature of the adjustment being made to the equation. 

Fowler and Hertel have investigated the values that the constant has for various powder systems [9]. It can be seen that in reality permeability methods of analysis are secondary methods in that the equation used to calculate surface areas has an empirical constant which has to be measured experimentaUy. It can now be seen that if measured permeability surface areas agree with those values as measured by independent methods this is not a vindication of the method but are an indication that the size distribution and/or the experimental conditions were similar to those used by Carman in his original work. 

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Permeability Methods for Characterizing the Fineness of a Powder System 251... 

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