🧫 Membrane Diffusion Calculator
Estimate gas or vapor transport through dense or porous membranes using solution-diffusion, Knudsen diffusion, or mixed resistance models. Outputs permeance, selectivity, and transmembrane flux.
🧬 Membrane Transport Schematic
📝 Configuration
Solution-diffusion: P = D S, J = (P/δ) Δp
Permeance: Π = P/δ
Knudsen diffusion: DK = (2/3) rp √(8RT/πMW)
Porous flux: J = (ε/τ) DK ΔC/δ
Selectivity: αA/B = ΠA/ΠB
📊 Results & Visualization
Configure inputs and click Calculate to view results.
This calculator estimates membrane transport from a pressure or concentration driving force. Dense polymer membranes use solution-diffusion; porous membranes use Knudsen diffusion when molecule-wall collisions dominate.
📘 Calculation Methodology
Mathematical Model & Theory
The solution-diffusion model treats permeability as the product of diffusivity and solubility. Knudsen diffusion estimates pore transport when pore size is small enough that wall collisions dominate. The mixed model combines dense and pore resistances in series.
Worked Engineering Example
CO₂/N₂ membrane: feed gas at 5 bar and permeate at 1 bar gives partial-pressure driving forces for each component. The calculator computes permeance, flux, selectivity, permeate flow and an approximate stage cut from the specified membrane area.
Assumptions & Notes
- Steady isothermal membrane transport.
- Ideal gas partial pressures.
- No concentration polarization, plasticization, competitive sorption, or pressure drop included.
- For porous membranes, Knudsen selectivity scales approximately with √(MWB/MWA).
- Use experimental permeance for final design when available.