Knudsen Number

on . Posted in Dimensionless Numbers

Knudsen number, abbreviated as Kn, a dimensionless number, is used in fluid dynamics to describe the relative importance of molecular mean free path to a characteristic length scale in a gas flow.  It's particularly useful for assessing the behavior of gases in rarefied or low pressure conditions, where the continuum assumption breaks down, and the individual gas molecules become important.

Key points about Knudsen number

  • Continuum Flow, Kn < 1  -  In this regime, the mean free path of gas molecules is much smaller than the characteristic length scale of the system.  In continuum flow, fluid dynamics equations like the Navier-Stokes equations are valid, and the gas behaves like a continuous fluid.
  • Transitional Flow, 0.1 < Kn < 10  -  In this regime, the mean free path is comparable to the characteristic length scale.  As a result, gas flow starts to exhibit non-continuum behavior, and the Navier-Stokes equations may not accurately describe the flow.  Specialized methods like the Boltzmann equation or Direct Simulation Monte Carlo (DSMC) methods are used to model these flows.
  • Free Molecular Flow, Kn > 10  -  In this regime, the mean free path is much larger than the characteristic length scale, and gas molecules move independently without frequent collisions.  In free molecular flow, the behavior of individual gas molecules dominates, and continuum fluid dynamics equations are not applicable. Instead, molecular models are used to describe the gas behavior.

The Knudsen number is particularly relevant in fields such as rarefied gas dynamics, microfluidics, and vacuum technology, where gas behavior deviates significantly from the idealized continuous flow assumptions of traditional fluid dynamics.  Understanding the Knudsen number helps engineers and scientists determine the appropriate modeling and analysis techniques for their specific gas flow problems.


Knudsen Number formula

\( Kn \;=\; \lambda \;/\; l \)     (Knudsen Number)

\( \lambda \;=\; Kn  \; l  \)

\( l  \;=\; \lambda \;/\; Kn \)

Symbol English Metric
\( Kn \) = Knudsen number \(dimensionless\)
\( \lambda \) (Greek symbol lambda) = mean free path \(in\) \(mm\)
\( l \) = length \(in\) \(mm\)


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Tags: Fluid