I am building an experiment where one has a bed of sand on top of a porous plate. The pores allow air to be blown through the plate from the bottom but the pores must be sufficiently fine to not allow sand to fall back through.
The sand grains will probably have diameters ranging between 20 and 60 $\mu m$ and the permeability of the plate is $3 \times 10^{-13} \: \text{m}^2$. How does one estimate the pore size from this?
I checked online and it seems the relevant relation is the Kozeny equation for absolute permeability:
$\kappa = \Phi_s^2 \frac{\epsilon^3 d_p^2}{180 (1 - \epsilon)^2},$
where $\Phi_s$ is the sphericity of the particles in the sand bed, $\epsilon$ is the porosity, and $d_p$ is the diameter of the volume equivalent spherical particle. $\kappa$ is the absolute permeability. Is this the correct equation for determining the pore size of the plate?
