Schmidt number

Physical key figure
Surname	Schmidt number
Formula symbol	${\displaystyle {\mathit {Sc}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Sc}}={\frac {\nu }{D}}}$
${\displaystyle \nu }$ kinematic viscosity ${\displaystyle D}$ Diffusion coefficient
Named after	Ernst Schmidt
scope of application	diffusion

The Schmidt number (after Ernst Schmidt ) is a dimensionless number in physics. It describes the ratio of diffusive momentum transport to diffusive substance transport as the quotient of the kinematic viscosity of a fluid and the diffusion coefficient of a chemical substance contained in it: ${\displaystyle {\mathit {Sc}}}$ ${\displaystyle {\nu }}$ ${\displaystyle D}$

${\displaystyle {\mathit {Sc}}={\frac {\nu }{D}}={\frac {\eta }{\rho \cdot D}}}$

With

• dynamic viscosity ${\displaystyle \eta }$
• density ${\displaystyle \rho .}$

The Schmidt number is a clear measure of the ratio of the boundary layer thickness between the hydrodynamic boundary layer and the concentration boundary layer.

At high values ​​( ) the impulse transport is more pronounced than the mass transport. This applies e.g. B. for liquids ( ), but not for gases ( ). ${\displaystyle {\mathit {Sc}}\gg 1}$ ${\displaystyle {\mathit {Sc}}\approx 1000}$ ${\displaystyle Sc\approx 1}$

The Schmidt number is the quotient of the Péclet number , which compares advective with diffusive mass transport, and the Reynolds number , which compares advective with diffusive momentum transport: ${\displaystyle Pe}$ ${\displaystyle Re}$

${\displaystyle {\mathit {Sc}}={\frac {\mathit {Pe}}{\mathit {Re}}}={\frac {L\cdot v}{D}}\cdot {\frac {\nu }{d\cdot v}}}$

With

• the speed ${\displaystyle v}$
• the characteristic length ${\displaystyle L}$
• the characteristic diameter ${\displaystyle d.}$

In addition, the Schmidt number is the analogue of the Prandtl number used in heat transfer and is linked to this via the Lewis number : ${\displaystyle {\mathit {Pr}}}$ ${\displaystyle {\mathit {Le}}}$

${\displaystyle {\mathit {Sc}}={\mathit {Pr}}\cdot {\mathit {Le}}={\frac {\nu }{a}}\cdot {\frac {a}{D}}}$

with the thermal diffusivity . ${\displaystyle a}$

Individual evidence

1. ^ Josef Kunes: Dimensionless Physical Quantities in Science and Engineering . Elsevier, 2012, ISBN 0-12-391458-2 , pp. 263 ( limited preview in Google Book search).
2. ↑ tec-science: Schmidt number. In: tec-science. May 9, 2020, accessed on June 25, 2020 (German).