Glossary term
Knudsen Number
A dimensionless number comparing molecular mean free path with a characteristic length scale.
Definition
quantityThe Knudsen number is the ratio of molecular mean free path to a characteristic physical length scale.
The Knudsen number indicates whether a gas can be treated as a continuum or whether molecular effects must be modeled explicitly. It is written as Kn = lambda / L, where lambda is mean free path and L is a representative length such as channel diameter, pore size, body length, or boundary-layer thickness. It is important in rarefied gas dynamics, vacuum systems, microfluidics, high-altitude flight, porous media, MEMS, and heat transfer at small scales.
The Knudsen number compares a gas molecule’s average travel distance between collisions with the size of the system being analysed:
where \lambda is molecular mean free path and L is a characteristic length. If molecules collide many times over the length scale of interest, the gas behaves like a continuum. If molecules travel distances comparable to the geometry before colliding, molecular effects become important.
Flow regimes
For very small Kn, usually below about 0.01, continuum assumptions are generally valid and the Navier-Stokes equations with no-slip boundary conditions are often appropriate. In the slip-flow regime, roughly 0.01 < Kn < 0.1, continuum equations may still be used with modified boundary conditions that allow velocity slip and temperature jump at walls.
For transitional flow, roughly 0.1 < Kn < 10, continuum models become unreliable. Molecular methods or specialized rarefied-flow models are needed. At high Knudsen number, above about 10, free molecular flow dominates and molecule-wall interactions are more important than molecule-molecule collisions.
Applications
Knudsen number is important in high-altitude aerodynamics, spacecraft re-entry, vacuum chambers, gas flow through microchannels, MEMS devices, nanopores, porous catalysts, thin-film deposition, leak testing, and thermal transport at small scales. The same physical device can move between regimes if pressure changes because mean free path increases as gas density decreases.
In heat transfer, high Knudsen number can reduce effective gas conduction because molecules interact less frequently with each other. In microfluidic gas flows, pressure drop and mass flow may deviate from continuum predictions. In aerospace, rarefaction affects drag, heating, and attitude dynamics at very high altitudes.
Common mistakes
A common mistake is using a continuum CFD model only because the geometry is macroscopic. At low pressure, the mean free path may be large enough for rarefaction to matter. Another mistake is choosing an arbitrary characteristic length. For external flow, body length may be appropriate; near a wall, boundary-layer thickness or local feature size may be more relevant. Good analysis states gas species, pressure, temperature, mean free path model, characteristic length, and the flow regime implied by Kn.