Advanced Diffusion Flux Calculator

Enter diffusion inputs

Use steady state engineering values for a planar layer. The calculator estimates flux, rate, amount transferred, and mass moved.

Reference diffusivity, D_ref (m^2/s)

Base molecular diffusivity at the reference temperature.

Reference temperature (K)

Temperature that matches the supplied reference diffusivity.

Operating temperature (K)

Actual process temperature for the diffusion estimate.

Activation energy (kJ/mol)

Set to zero if temperature correction is not needed.

Side 1 concentration (mol/m^3)

Higher value usually drives diffusion toward side 2.

Side 2 concentration (mol/m^3)

Lower value creates a stronger concentration gradient.

Diffusion path thickness (m)

Use membrane, film, or layer thickness.

Transfer area (m^2)

Area converts flux into total molar transfer rate.

Porosity

Fraction of open void volume in a porous layer.

Tortuosity

Higher tortuosity lowers the effective diffusivity.

Partition coefficient

Use 1.0 when no interfacial partition adjustment exists.

Elapsed time (s)

Used to estimate total moles and mass transferred.

Molar mass (g/mol)

Mass result becomes zero only if this value is zero.

Example data table

Case	D_ref (m^2/s)	T (K)	C₁ (mol/m^3)	C₂ (mol/m^3)	L (m)	A (m^2)	J (mol/m^2-s)
Membrane transfer example	2.0000e-09	313.15	2.00	0.40	0.0020	0.25	9.3538e-07
Dense film example	1.2000e-09	298.15	1.40	0.30	0.0015	0.12	5.2800e-07

Use the example values to validate your setup before replacing them with measured process data.

Formula used

This calculator is based on steady state planar diffusion. It extends Fick's first law with a temperature correction and porous media adjustment.

D(T) = D_ref x exp[(Ea/R) x (1/T_ref - 1/T)]
D_eff = D(T) x (porosity / tortuosity) x partition coefficient
dC/dx = (C2 - C1) / L
J = -D_eff x dC/dx
Rate = J x A
Transferred amount = Rate x time
Transferred mass = amount x molar mass / 1000

The negative sign preserves physical direction. Positive flux means transport from side 1 toward side 2 when side 1 concentration is higher.

How to use this calculator

Enter the reference diffusivity measured or published for your species.
Provide reference and operating temperatures in kelvin.
Set activation energy to zero when temperature correction is unnecessary.
Enter concentrations on both sides of the diffusion layer.
Add thickness and exposed transfer area for the geometry.
Include porosity, tortuosity, and partition coefficient for porous or composite media.
Provide elapsed time and molar mass if you need total transfer and mass.
Press the calculate button and review the results block above the form.
Use CSV or PDF export when you need documentation or sharing.

Frequently asked questions

1. What does diffusion flux represent?

Diffusion flux measures how many moles pass through each square meter every second. It describes transport intensity, not the total amount transferred through the full area.

2. Why is there a negative sign in Fick's law?

The negative sign ensures diffusion occurs from higher concentration toward lower concentration. It preserves physical direction when the concentration gradient is written from side 1 to side 2.

3. When should I use the activation energy input?

Use activation energy when diffusivity changes meaningfully with temperature. If your diffusivity already matches operating temperature, set activation energy to zero or keep both temperatures identical.

4. What is effective diffusivity?

Effective diffusivity adjusts molecular diffusivity for porosity, tortuosity, and partitioning. It better represents transport in membranes, packed solids, catalysts, and porous engineering materials.

5. Can this calculator handle transient diffusion?

No. This page is built for steady state planar diffusion. Use a transient diffusion model when concentrations or profiles change strongly with time inside the layer.

6. Which units should I keep consistent?

Use SI units throughout: diffusivity in m^2/s, concentration in mol/m^3, thickness in meters, area in m^2, time in seconds, and molar mass in g/mol.

7. What happens if side 2 concentration exceeds side 1?

The flux becomes negative, indicating diffusion reverses direction. That result is valid and shows the species moves from side 2 toward side 1.

8. Why does thickness matter so much?

Thickness appears in the denominator of the gradient. A thinner path creates a stronger concentration gradient, which usually increases flux when all other variables remain constant.