Mass Péclet number#

Also known as: Bodenstein number.

Named after: Jean Claude Eugène Péclet (1793-1857).

$$\text{Pe}_m \stackrel{\text{def}}{=} \frac{U L}{D} \sim \frac{\text{advection}}{\text{mass diffusion}}$$

Description#

Measures advective species transport relative to molecular diffusion. It indicates whether concentration fields are carried mainly by flow or smoothed by diffusion.

Quantities#

Name	Symbol	SI units	Dimension
velocity	$U$	$\mathrm{m}\,\mathrm{s}^{-1}$	$\text L\,\text T^{-1}$
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	Molecular diffusion transports species faster than the flow carries them across the characteristic length.
1 – ∞	advection dominated	Bulk motion carries species faster than molecular diffusion can smooth concentration gradients.

Name	Symbol	SI units	Dimension
velocity	\(U\)	\(\mathrm{m}\,\mathrm{s}^{-1}\)	\(\text L\,\text T^{-1}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
diffusivity	\(D\)	\(\mathrm{m}^{2}\,\mathrm{s}^{-1}\)	\(\text L^{2}\,\text T^{-1}\)