Porosity Variability In Random Paper

We estimate: variance of local porosity $\tilde{\epsilon},$ in paper of thickness $\bar{z},$ mean grammage $\bar{\beta},$ and fluid flow.

Local contacts per fibre, $\tilde{n}_{contacts},$ is related to $\tilde{\epsilon}$ via fibre aspect ratio A:

$$\tilde{n}_{contacts} = \frac{2 A \tilde{c}}{\rho} = \frac{2A \tilde{\beta}}{\tilde{z}\rho} = 2A(1-\tilde{\epsilon})$$ (48)

Number fibres is ratio: mass of zone to mass of one fibre: $N=\bar{\beta} x^2/\delta\lambda.$