Want to know if inertia matters in your system? 🤓Compute the transition pressure pt and compare ΔP/pt:
• If <1 → inertia negligible
• If >1 → big efficiency loss
Ex: 💧through a pore of square aspect ratio h/a=1 of radius… 1️⃣ 10 nm pore @30 bar → safe; 2️⃣ 10 µm pore @30 kPa → ~70% lost!

Using a simple U-tube, we measure pressure-driving flow through a single pore. At low Re, viscous drag dominates; but above Re ≈ 10, inertia takes over: resistance rises with pressure, overtaking viscosity. Simulations and model capture this transition from viscous to inertia regime 💻📝

Inertial correction to viscous drag along a pore length (Hagen-Poiseuille) are well studied; but this effect at the pore entrance (Sampson resistance) has received little attention, for example in work on end corrections for long pipes a century ago (Johansen Proc. R. Soc. A 1930)

Even if you reduce viscous drag with optimal geometry or special coatings, you still need to accelerate the fluid through the pore. That acceleration -- fluid inertia -- sets an upper bound on flow efficiency through micropores