Knudsen number


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Knudsen number

In gas dynamics, the ratio of the molecular mean free path λ to some characteristic length L: Kn = λ/L. The length chosen will depend on the problem under consideration. It may be, for example, the diameter of a pipe or an object immersed in a flow, or the thickness of a boundary layer or a shock wave. See Mean free path

The magnitude of the Knudsen number determines the appropriate gas dynamic regime. When the Knudsen number is small compared to unity, of the order of Kn ≤ 0.1, the fluid can be treated as a continuous medium and described in terms of the macroscopic variables: velocity, density, pressure, and temperature. In the transition flow regime, for Knudsen numbers of the order of unity or greater, a microscopic approach is required, wherein the trajectories of individual representative molecules are considered, and macroscopic variables are obtained from the statistical properties of their motions. In both internal and external flows, for Kn ≥ 10, intermolecular collisions in the region of interest are much less frequent than molecular interactions with solid boundaries, and can be ignored. Flows under such conditions are termed collisionless or free molecular. In the range 0.1 ≤ Kn ≤ 1.0, termed the slip flow regime, it is sometimes possible to obtain useful results by treating the gas as a continuum, but allowing for discontinuities in velocity and temperature at solid boundaries. See Gas dynamics, Kinetic theory of matter, Rarefied gas flow

Knudsen number

[kə′nüd·sən ‚nəm·bər]
(fluid mechanics)
The ratio of the mean free path length of the molecules of a fluid to a characteristic length; used to describe the flow of low-density gases.
References in periodicals archive ?
The importance of slip effect is characterized by the value of the Knudsen number:
The two definitions of the collision diameter give different values (Figure 20) and this adds another layer of uncertainty to the definition of the Knudsen number.
The flow of gas in micro/nanoscale medium is usually a function of the ratio of the molecular mean free path of a gas molecule to characteristic length of the medium; this function is referred to as the Knudsen number. In such mediums, collisions between a molecule and wall dominate over intermolecule collisions, which causes each molecule to act independently and control the gas properties [3], a condition often referred as rarefied gas flow.
Knudsen number is defined as the ratio of the gas mean free path ([lambda]) and the pore diameter (2[r.sub.m]):
Knudsen number (Kn), a ratio of the mean free path of the gas molecules to the characteristic length L of the device, describes the various regimes.
Also, the Knudsen number Kn is usually used to describe low density flow:
where [K.sub.n] is the Knudsen number, [k.sub.d, 0] is the thermal conductivity of air when [K.sub.n] = 0, and [beta] is a gas constant and taken as 1.5 for air.
The slip correction factor has been investigated at reduced pressures and high Knudsen number using polystyrene latex (PSL) particles.
The first category is correcting intrinsic permeability with a function of Knudsen number. Empirical parameters are included in most of the models, and gas flow regimes (viscous flow, slip flow, transition flow, and Knudsen diffusion) in a single capillary are classified based on Knudsen number and viscous flow slip flow and diffusion are mutually exclusive.
Knudsen (1934) introduced the concept of Knudsen number Kn, as is given by
That is, momentum and energy transport and the convergence to equilibrium are based on the collisions between molecules in the bulk fluid, which no longer exist at higher Knudsen number. In such small size domains, even the definitions of macroscopic variables (e.g., density, pressure, and temperature) as a manifestation of the average of the behavior of fluid particles within a representative volume may not be unique and will essentially be size-dependent.