Analytical solution of inertia effect in high-speed flows through disordered porous media

This work presents an analytical solution of flow through disordered porous media with inertia effects at a finite Reynolds number (Re), and consequently a truncated quadratic formula for easy use without any fitting parameters. The derivation is based on an effective capillary model in which the effective radius of capillaries varies with Re. Inspired by the asymptotic solution of flow in curved capillaries, the Oseen-form equation is derived to capture the flow behavior in each capillary. The analytical formula has been validated by comparisons with numerous available experimental data.