Mass Fourier number#
Named after: Jean-Baptiste Joseph Fourier (1768-1830).
$$\text{Fo}_m \stackrel{\text{def}}{=} \frac{D t}{L^{2}} \sim \frac{\text{mass diffusion spread}}{\text{length squared}}$$
Description#
Measures elapsed time relative to the mass diffusion time across a length scale. It indicates how far a transient concentration disturbance has penetrated.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| diffusivity | \(D\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-1}\) | \(\text L^{2}\,\text T^{-1}\) |
| time | \(t\) | \(\mathrm{s}\) | \(\text T\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
Regimes#
Transient diffusion
| Range | Regime | Description |
|---|---|---|
| 0 – 0.2 | early transient | Concentration gradients remain localized. The diffusing species has not penetrated the full characteristic length. |
| 0.2 – ∞ | late transient | Diffusion has spread across much of the characteristic length. Concentration gradients are relaxing toward equilibrium. |