Kozeny-Carmen equation

The starting point for deriving a formula to calculate the filtration area is the Kozeny-Carmen equation for flow through porous media. The flow, which is laminar, follows a tortuous path through the cake. The Kozeny-Carmen equation, for a differential cake thickness, is... 

In Equation 6.17, P is flie pressure at any point in the cake shown schematically in Figure 6.11, s, the specific surface (surface area per unit volume of particle), p, the hquid viscosity, vs, the superficial liquid velocity, and 8, the porosity of the cake. The Kozeny-Carmen equation is derived in a number of texts. See, for example. Bird et al. [26], who have called the equation the Blake-Kozeny equation. 

As discussed in the previous chapter, the network of the inter-connected membrane pores formed during preparation and fabrication may be tortuous or nearly straight depending on the synthesis and subsequent heat treatment methods and conditions. The microstructure of a membrane, particularly the type with tortuous pores, is too complicated to be described by a single parameter or a simple model. Due to the relatively poor knowledge of flow through porous media, an empirical term called " tortuosity" has been introduced and used by many researchers to reflect the relative random orientation of a pore network and is based on the Kozeny-Carmen equation for the membrane flux, J ... 

The fineness of a powder can be studied with the help of permeability techniques, in which the resistance to fluid flow of a powder plug is measured and the fineness of the powder deduced from this measured resistance using various equations such as the Kozeny-Carmen equation. The interpretive equations used to calculate the surface area from permeability measurements make several assumptions concerning the pore structure of the packed powder bed, and the... 

The Kozeny-Carmen equation can be rearranged to give the pressure drop through the bed as a function of liquid flow rate and the liquid flow rate as a function of pressure drop through the bed ... 

Xkc = Kozeny-Carmen equation, factor tfin = filtration time Vq = specific cake volume = viscosity filtrate Ap = filtration pressure... 

The Kozeny-Carmen equation for deriving the coefficient of permeability also takes the porosity, n, into account as well as the specific surface area of the porous medium, Sa. that is defined per unit volume of solid... 

Liu and Civan propose that absolute permeability reduction can be attained through the modification of the Carmen-Kozeny equation. 

The permeability of swollen gel layers of superabsorbent polymers can be expressed by the Carmen-Kozeny equation, which is based on the Darcy equation when the porosity and surface area are to be considered ... 

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