Knudsen Minimum

Model ID: 11775


When a constant pressure difference drives flow through a narrow constriction between parallel plates (or through a cylindrical tube), the flow rate exhibits a characteristic minimum as the absolute pressure at the inlet is reduced. This phenomenon is commonly referred to as Knudsen’s minimum, and occurs as a result of the rarefaction of the gas. The observation of a minimum in flow rate for this type of flow is a common benchmark employed in the simulation of rarefied gas flows.

In this model, the pressure driven flow of gas through a channel between parallel plates is modeled using the Laminar Flow, Slip Flow, Transitional Flow, and Free Molecular Flow interfaces. The flow rate is computed as a function of the Knudsen number (Kn), which is the ratio of the mean free path of the gas to the characteristic dimension of the geometry (in this case the separation of the plates), for each interface. The Transitional Flow interface is shown to agree well with the Free Molecular Flow and Slip Flow/Laminar Flow interfaces within their respective ranges of validity. In the transition region, the absence of an appropriate pressure boundary condition limits the validity of the solution. Nonetheless, solutions obtained with the Navier-Stokes limit and molecular-flow limit boundary conditions provide interesting insights when compared with experimental data.