How this calculator works
The Knudsen number compares the average distance between molecular collisions with a macroscopic length scale. Use a channel height, particle diameter or other dimension relevant to the flow gradients. A small value supports a continuum approximation. Boundaries between regimes are approximate and depend on the accuracy required.
Formula
Kn = lambda/L; lambda = Kn L; L = lambda/Kn. Common ranges: continuum below 0.01, slip 0.01 to 0.1, transition 0.1 to 10, free molecular at 10 or above.
Worked example
A 68 nm mean free path across a 1 mm channel gives Kn = 0.000068. Across a 1 micrometre channel it gives Kn = 0.068, where wall slip can matter.
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Frequently asked questions
Which length is characteristic?
Choose the smallest flow dimension relevant to molecular transport, rather than automatically using the entire apparatus length.
Does Kn alone specify a flow solution?
No. It helps select a modelling regime; boundary conditions and other dimensionless groups are still needed.
Can I enter zero mean free path?
Zero gives the continuum limit. Recovering a length from zero Kn is indeterminate and is rejected.