Sherwood number#
Named after: Thomas Kilgore Sherwood (1903-1976).
$$\text{Sh} \stackrel{\text{def}}{=} \frac{k_m L}{D} \sim \frac{\text{convective mass transfer}}{\text{molecular diffusion}}$$
Description#
Measures convective mass transfer relative to molecular diffusion. It indicates how much flow enhances species transport above the diffusive reference.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| mass transfer coefficient | \(k_m\) | \(\mathrm{m}\,\mathrm{s}^{-1}\) | \(\text L\,\text T^{-1}\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
| diffusivity | \(D\) | \(\mathrm{m}^{2}\,\mathrm{s}^{-1}\) | \(\text L^{2}\,\text T^{-1}\) |
Regimes#
Mass transfer
| Range | Regime | Description |
|---|---|---|
| 0 – 1 | diffusion dominated | Mass transfer is dominated by molecular diffusion. Sh ≈ 1 corresponds to the purely diffusive limit. |
| 1 – ∞ | convection enhanced | Convection significantly enhances mass transfer above the purely diffusive rate. |