Darcys Law for Viscous Flow

In the simplest situation of a flow through a straight cylindrical pore, Darcy s law, based on the Hagen-Poiseuille equation, describes the process with the expression [73] 

Darcy s law for laminar flow in a real macroporous membrane is described by the following equation [16] 

The Physical Chemistry of Materials Energy and Environmental Applications 

For the description of this flow, the Carman-Kozeny expression [16] can be applied, since the Hagen-Poiseuille equation is not valid, given that usually inorganic macroporous and mesoporous membranes are prepared by the sinterization of packed quasispherical particles, which develop a random pore structure [19]. In this case, the Carman-Kozeny factor for a membrane formulated with pressed spherical particles is [74] 

3 is the Carman-Kozeny constant d, is the membrane pore diameter e is the membrane porosity pA is the apparent membrane density [g/cm3] pR is the real membrane density [g/cm3] [18,19] 

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