Definition of Schmidt Number
Definition
The kinematic viscosity $\nu$ divided by the mass diffusivity $D$ — a dimensionless quantity — is called the Schmidt number. $$ \mathrm{Sc} := \frac{ \nu }{ D } $$
Description
The Schmidt number is, in fluid mechanics, the ratio of momentum diffusivity to mass diffusivity and plays a role analogous to the Prandtl number in heat transfer. Intuitively, a large Schmidt number means the fluid is relatively viscous and the substance tends to retain its form, while a small Schmidt number means the substance spreads more easily.
Relation to other dimensionless numbers
The Schmidt number and the Prandtl number both contain the kinematic viscosity $\nu$, which cancels when forming their ratio; this ratio expresses the Lewis number. $$ \begin{align*} \mathrm{Sc} =& {\frac{ \nu }{ D }} \\ \mathrm{Pr} =& {\frac{ \nu }{ \alpha }} \\ \implies \mathrm{Le} =& = {\frac{ \nu }{ D }} \left( {\frac{ \nu }{ \alpha }} \right)^{-1} = \frac{ \mathrm{Sc} }{ \mathrm{Pr} } \end{align*} $$