Schmidt number

In fluid dynamics, the Schmidt number (denoted $Sc$ ) of a fluid is a dimensionless number defined as the ratio of momentum diffusivity (kinematic viscosity) and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975).

The Schmidt number is the ratio of the shear component for diffusivity (viscosity divided by density) to the diffusivity for mass transfer $D$ . It physically relates the relative thickness of the hydrodynamic layer and mass-transfer boundary layer.^[1]

It is defined^[2] as:

\mathrm {Sc} ={\frac {\nu }{D}}={\frac {\mu }{\rho D}}={\frac {\mbox{viscous diffusion rate}}{\mbox{molecular (mass) diffusion rate}}}

where (in SI units):

$\nu ={\tfrac {\mu }{\rho }}$ is the kinematic viscosity (m²/s)
$D$ is the mass diffusivity (m²/s).
$μ$ is the dynamic viscosity of the fluid (Pa·s = N·s/m² = kg/m·s)
$ρ$ is the density of the fluid (kg/m³).

The heat transfer analog of the Schmidt number is the Prandtl number ( $Pr$ ). The ratio of thermal diffusivity to mass diffusivity is the Lewis number ( $Le$ ).

^ tec-science (2020-05-10). "Schmidt number". tec-science. Retrieved 2020-06-25.
^ Incropera, Frank P.; DeWitt, David P. (1990), Fundamentals of Heat and Mass Transfer (3rd ed.), John Wiley & Sons, p. 345, ISBN 978-0-471-51729-0 Eq. 6.71.

[1] tec-science (2020-05-10). "Schmidt number". tec-science. Retrieved 2020-06-25.

[2] Incropera, Frank P.; DeWitt, David P. (1990), Fundamentals of Heat and Mass Transfer (3rd ed.), John Wiley & Sons, p. 345, ISBN 978-0-471-51729-0 Eq. 6.71.

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