Schmidt number#

Named after: Ernst Heinrich Wilhelm Schmidt (1892-1975).

$$\text{Sc} \stackrel{\text{def}}{=} \frac{\nu}{D} \sim \frac{\text{momentum diffusion}}{\text{mass diffusion}}$$

Measures momentum diffusivity relative to mass diffusivity. It indicates the relative thickness of velocity and concentration boundary layers.

Name	Symbol	SI units	Dimension
kinematic viscosity	$\nu$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$
diffusivity	$D$	$\mathrm{m}^{2}\,\mathrm{s}^{-1}$	$\text L^{2}\,\text T^{-1}$

Molecular diffusion

Range	Regime	Description
0 – 0.2	liquid metal	Mass diffusivity dominates over momentum diffusivity. Occurs in liquid metals and dilute gases.
0.2 – 4	gas	Momentum and mass diffusivities are comparable. Common in many gases.
4 – ∞	liquid	Typical for liquids, e.g. 600 to 700 for water.

Name	Symbol	SI units	Dimension
kinematic viscosity	\(\nu\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)
diffusivity	\(D\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)