How the Diffusion Rate Calculator Works
This Diffusion Rate Calculator estimates how quickly a substance moves through a material due to a concentration difference. It is based on Fick's First Law of Diffusion, which describes steady diffusion from high concentration to low concentration.
The calculator returns both diffusive flux, measured in mol/(m²·s), and total diffusion rate, measured in mol/s.
Fick's First Law Formula
In one-dimensional form, Fick's First Law is:
For a flat layer of thickness d, this is commonly approximated as:
The total diffusion rate through area A is:
where:
- D = diffusion coefficient (m²/s)
- A = diffusion surface area (m²)
- ΔC = concentration difference (mol/m³)
- d = diffusion distance or layer thickness (m)
- J = diffusive flux (mol/(m²·s))
Sign Convention
Fick's Law includes a negative sign because diffusion moves from high concentration to low concentration. If ΔC is entered as C₂ - C₁, the flux may be negative. For practical rate calculations, this calculator reports the absolute magnitude of the diffusion rate.
Typical Diffusion Coefficients
| Medium / Example | Approximate D (m²/s) |
|---|---|
| Gases in air | ~10⁻⁵ |
| Small molecules in water | ~10⁻⁹ |
| Polymers and membranes | ~10⁻¹² to 10⁻⁹ |
| Dense solids / glass | ~10⁻¹⁴ to 10⁻¹² |
| Metals, low-temperature diffusion | can be extremely small |
How to Use the Calculator
- Select a rough example diffusion coefficient or choose custom input.
- Enter the surface area where diffusion occurs.
- Enter the concentration difference across the layer.
- Enter the diffusion distance or material thickness.
- Click calculate to get flux and total diffusion rate.
Example Calculation
Suppose diffusion occurs through a membrane with:
- D = 1×10⁻⁹ m²/s
- A = 0.05 m²
- ΔC = 50 mol/m³
- d = 0.002 m
The total diffusion rate is:
Important Assumptions
- The calculation assumes steady-state one-dimensional diffusion.
- The diffusion coefficient is constant.
- The concentration gradient is approximated as linear.
- The surface area is uniform.
- No chemical reaction, convection, swelling, or phase change is included.
- For gases at high pressure gradients, porous media, or biological membranes, more detailed models may be required.
Frequently Asked Questions
What is diffusion?
Diffusion is the movement of particles from regions of higher concentration to regions of lower concentration due to random molecular motion.
What is diffusive flux?
Diffusive flux is the amount of substance passing through a unit area per unit time. It is usually measured in mol/(m²·s).
What is diffusion rate?
Diffusion rate is the total amount of substance passing through the entire surface area per unit time, usually measured in mol/s.
Does temperature affect diffusion?
Yes. Temperature strongly affects the diffusion coefficient. Higher temperature often increases diffusion, especially in liquids and solids.
Can this calculator be used for gases and liquids?
Yes, as long as the correct diffusion coefficient and assumptions are appropriate for the system.