The Carman-Kozeny Equation
This is an empirical relationship, usually expressed as
\[\kappa = \frac{{{P^3}}}{{\lambda \left( {1 - P} \right){}^2{S^2}}}\]
where P is the porosity level, S is the specific surface area (m2 m-3) and λ is a dimensionless constant (typically having a value of ~5). Fine filters tend to have large values of S, leading to low permeabilities. The equation takes no account of the pore architecture (beyond its influence on S). The connectivity of the pores is in practice a key issue. (A material with a high volume fraction of coarse, isolated pores would have a relatively large value of Κ according to the above equation, but would in fact be impermeable - ie Κ = 0.) Nevertheless, the equation is often a useful guide, at least for materials with good pore connectivity, such as fibrous membranes. This is illustrated by the figure below, which is a plot of dimensionless permeability, allowing values to be plotted for membranes of fibres with a wide diameter range.
