What is knudsen number?

The Knudsen number, named after the Danish physicist Martin Knudsen, is a dimensionless number used in fluid mechanics to characterize the relative importance of molecular mean free path length to a characteristic length scale of a flow. It is defined as the ratio of the molecular mean free path length to a characteristic length scale of the flow.

The Knudsen number is used to determine whether the flow is in the continuum regime (Kn << 1) or in the rarefied gas regime (Kn > 1). In the continuum regime, the effects of viscosity dominate and the flow can be described by the Navier-Stokes equations. In the rarefied gas regime, on the other hand, the mean free path length is comparable to or larger than the characteristic length scale of the flow, leading to non-negligible molecular interactions and collisions.

The Knudsen number is a crucial parameter in the study of microfluidics, gas dynamics, and hypersonic flows, where the effects of rarefaction become significant. It is also important in the design of various engineering systems, such as MEMS devices, gas sensors, and vacuum systems.