# Summary

The Schmidt number is a dimensionless number that describes the ratio of momentum diffusivity to mass diffusivity that is commonly used in analysis of mass transfer systems. This article describes the Schmidt Number and typical formulations.

# Definitions

D | : | Mass diffusivity, |

: | Eddy diffusivity, | |

: | Dynamic viscosity, | |

: | Kinematic viscosity, | |

: | Eddy viscosity, | |

: | Density, |

# Introduction

The Schmidt number is a dimensionless number named after Ernst Heinrich Wilhelm Schmidt and describes the ratio of momentum diffusivity to mass diffusivity. It is used to characterise fluids in which simultaneous momentum and mass diffusion convection processes and occurs.

Quantitatively the Schmidt number determines the thickness of the hydrodynamic layer relative to the mass-transfer boundary layer, and describes whether momentum or diffusion will dominate mass transfer. The Schmidt number is stated as follows:

Where the Schmidt number is small mass diffusion will dominate, whereas for high Schmidt numbers momentum diffusion will dominate. More specifically changes in the three key properties will have the following effects on Schmidt number:

- Increase in dynamic viscosity will increase Schmidt number
- Increase in density will reduce Schmidt number
- Increase in mass diffusivity will reduce Schmidt number

For gas-gas diffusive systems at standard conditions the Sc is typically in the range 0.2 - 4, while for gas-liquid and liquid-liquid systems values are typically 200-1500.

The Schmidt number is the mass transfer analogue of the Prandtl number, and may be used with the Reynolds number to determine the Sherwood number.

# Turbulent Schmidt Number

Similar to the Prandtl number there is a form of the Schmidt number used for turbulent flow which describes the ratio between the turbulent transfer of momentum and the turbulent transfer of mass:

This form of the Schmidt number is used turbulence research to describe the mass transfer of boundary layers flows.

# Further Reading

- Chemical Engineering Volume 1, Sixth Edition: Fluid Flow, Heat Transfer and Mass Transfer
- Perry’s Chemical Engineers’ Handbook, Eighth Edition
- Fundamentals of Heat and Mass Transfer, 7th Edition

Article Tags