## History and Theory

The original study of fluid flow through compacted particulate matter is attributed to D'Arcy (Ref 15), who examined water flow rates from the public fountains of Dijon, France, through sand beds of varying thicknesses in 1856. He formulated the basic principle behind permeability, showing that the average flow rate is proportional to the pressure gradient and inversely proportional to the thickness of the bed.

In 1927, Kozeny (Ref 16) published the first derivation showing correlation among porosity, permeability, and particle surface area. Following the lead of Blake (Ref 17), Kozeny treated the flow of fluid through a particulate bed as being equivalent to the flow of fluid through a comparable volume of parallel pipe channels of circular cross section. This simplification resulted in determining an equivalent diameter of pipe channel to characterize flow rate through the powder bed.

In 1938, Carman (Ref 18) and Dallavalle (Ref 19) independently proposed the determination of specific surface area for powders using permeability methods. Carman published related experimental work in 1941 (Ref 20). He developed a liquid flow technique to determine surface area for coarse materials by taking into consideration (1) the dependence of permeability on the number of permeable pores of the particle bed, (2) the pore or void volume fraction contribution to total bed volume, (3) the friction of the gas or liquid flowing through the bed, and (4) the adsorption of immobile liquid layers that effectively reduce the capillary diameter, thus causing less permeability and therefore a greater apparent surface area.

The Kozeny-Carman equation, given below, has served as the most widely used basis for all permeability variations:

where S is surface area per unit weight of the powder, AP is the pressure drop across the powder bed, /, is void fraction of packed sample, v is velocity of fluid flow, /■'is density of the powder material, '/is viscosity of the fluid, L is length of the powder bed, and Le is average path length through the powder bed.

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