\[Q = \frac{\kappa }{\eta }\frac{{\Delta P}}{{\Delta x}}\]

Q  : Flux through filter (m³ m^-2 s^-1)
κ   : Filter permeability (m²)
η   : Fluid viscosity (Pa s)
Δp : Pressure difference across filter (Pa)
Δx : Filter thickness (m)

Darcy's law states that the flux of fluid through a filter is proportional to the pressure gradient across it. It is also dependent on the fluid viscosity and filter permeability. Initially there is a transient state where the fluid travles at a slower speed in the filter than either side of it. Eventually the fluid flows faster through the filter as there is less free volume in the filter and the flux is constant everywhere (in and outside the filter).

\[\kappa = \frac{{{P^3}}}{{\lambda \left( {1 - P} \right){}^2{S^2}}}\]

κ   : Filter permeability (m²)
P   : Filter porosity (dimensionless fraction)
λ   : Constant (usually = 5)
S: Filter specific surface area (m² m^-3)

Porosity is the volume fraction of free space in the filter. Specific surface area is the surface area of particles or fibers the filter is made of per unit volume. Specific surface area can be expressed as the total surface area of the solid constituents - for example, 2πRL for fibres - divided by the total volume, which is the volume of solid over the solid fraction - for example, LπR²/(1–P) for fibres. Particles can be modelled as randomly packed spheres, fibers are modelled as cylinders; touching at single points so their full surface area is assumed.