The Knudsen number (Kn) is a dimensionless quantity used in fluid mechanics and gas dynamics to determine whether a gas flow can be accurately modeled as a continuous fluid or if molecular effects must be considered.
It is defined as the ratio of the mean free path of gas molecules (the average distance a molecule travels before colliding with another) to a characteristic physical length scale of the system (like the size of a container or a pipe diameter).
Interpretation:
- Low Knudsen number (Kn << 1): The gas behaves like a continuum, and classical fluid dynamics equations (like Navier–Stokes) apply.
- High Knudsen number (Kn > 0.1): Molecular effects become significant; the continuum assumption breaks down, and methods like molecular dynamics or kinetic theory are needed.
Examples:
- Atmospheric air at normal pressure: Low Kn, treated as a continuum.
- Gas flow in micro- or nano-scale devices: High Kn, requires molecular-level modeling.
- Space vacuum conditions: Very high Kn, free molecular flow dominates.
The Knudsen number helps engineers and scientists decide the right modeling approach for gases in applications ranging from aerospace engineering to microfluidics.