Fick's Law of Diffusion Calculator

How it works

Fick's first law: J = −D · dC/dx ≈ D · ΔC ÷ Δx · rate = J × A = D · A · ΔC ÷ Δx · typical diffusion time t ≈ Δx² ÷ 2D · units: D in m²/s, A in m², ΔC in mol/m³ (= mmol/L), Δx in m

Fick's first law (Adolf Fick, 1855) says that the net rate of diffusion is proportional to the surface area and the concentration difference, and inversely proportional to the distance travelled. It is why lungs, gills, villi and root hairs have huge surface areas and very thin walls, and why breathing and blood flow keep the concentration gradient steep. Diffusion coefficients are typical values at about 25 °C; D rises with temperature and falls for larger molecules. Diffusion time grows with the square of the distance, so it is fast across a cell but far too slow over centimetres.

Worked example

Oxygen (D = 2.10 × 10⁻⁹ m²/s in water) crosses 1 cm² (10⁻⁴ m²) of a 1 µm barrier with a 0.1 mmol/L (0.1 mol/m³) difference. Rate = 2.1 × 10⁻⁹ × 10⁻⁴ × 0.1 ÷ 10⁻⁶ = 2.100 × 10⁻⁸ mol/s, or 21.00 nmol/s. A molecule takes on the order of (10⁻⁶)² ÷ (2 × 2.1 × 10⁻⁹) = 2.381 × 10⁻⁴ s to cross.

Sources: Wikipedia — Fick's laws of diffusion · Wikipedia — Mass diffusivity (typical coefficients)

Frequently asked questions