Diffusion & mixingMVP
Diffusion time
Estimate how long a species takes to spread a given distance by diffusion.
Inputs
Result
Enter distance and diffusion coefficient to estimate the time.
Interpretation
Diffusion time grows with the square of distance (t ∝ L²), so shrinking the mixing distance is the most effective way to mix faster.
Formula
t ≈ L² / (2D)
1-D scaling law — an order-of-magnitude estimate.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| t | Diffusion time | s |
| L | Diffusion distance | m |
| D | Diffusion coefficient | m²/s |
Assumptions & validity
This tool assumes:
- 1-D diffusion; t ≈ L²/2D is an ESTIMATE (characteristic scaling), not an exact concentration profile.
- Constant diffusion coefficient D.
- No advection or reaction — pure diffusion.
Worked example
A small molecule (D ≈ 1000 µm²/s = 1×10⁻⁹ m²/s) diffuses across a 100 µm channel.
t ≈ (100×10⁻⁶)² / (2 × 1×10⁻⁹) = 1×10⁻⁸ / 2×10⁻⁹ = 5 s