Knudsen Number Calculator

The Knudsen number (Kn) is a dimensionless parameter defined as the ratio of the molecular mean free path to a representative physical length scale. The governing equation is expressed as Kn = lambda / L, where lambda represents the mean free path of the molecules and L is the characteristic linear dimension of the flow geometry, such as a pipe diameter or object width. If Kn is much smaller than 0.01, standard continuum fluid dynamics applies. As Kn increases, slip flow, transition flow, and eventually free molecular flow regimes emerge.

Consider a microfluidic channel with a characteristic linear dimension (L) of 5 micrometers (5 x 10^-6 meters) through which nitrogen gas flows at standard conditions. At this pressure, the molecular mean free path (lambda) is approximately 68 nanometers (6.8 x 10^-8 meters). To find the Knudsen number, divide the mean free path by the linear dimension: Kn = (6.8 x 10^-8) / (5 x 10^-6) = 0.0136. Because this value falls between 0.001 and 0.1, the flow operates in the slip flow regime, meaning velocity slip at the channel walls must be accounted for in accurate simulations.

Always ensure your input units are consistent before performing the division; mixing nanometers and meters will yield incorrect orders of magnitude. When analyzing complex geometries, choose a representative length scale that accurately reflects the narrowest constriction or boundary layer where molecular collisions matter most. Keep in mind that changes in pressure and temperature directly alter the mean free path, shifting the system into an entirely different Knudsen regime.