Knudsen number

About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.

Beyond Navier–Stokes: Burnett equations for flows in the continuum–transition regime

Abstract: In hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices, the local Knudsen number lies in the continuum–transition regime Navier–Stokes equations are not adequate to model these flows since they are based on small deviation from local thermodynamic equilibrium To model these flows, a number of extended hydrodynamics or generalized hydrodynamics models have been proposed over the past fifty years, along with the direct simulation Monte Carlo (DSMC) approach One of these models is the Burnett equations which are obtained from the Chapman–Enskog expansion of the Boltzmann equation [with Knudsen number (Kn) as a small parameter] to O(Kn2) With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with the Burnett model As a result, several improvements to the conventio

Flow of a Rarefied Gas between Two Parallel Plates

Abstract: The Poiseuille flow of a rarefied gas between two parallel plates is analyzed numerically for an inverse Knudsen number ranging from 0 to 10.5. The Bhatnagar, Gross, and Krook model is used and the transport integrodifferential equation is reduced to a purely integral one, which is solved numerically by the discrete ordinate method.The plot of the volume flow rate vs pressure is shown to have the expected minimum; besides, it fits well with experimental results and previous approximate calculations.In particular, the results given by Takao, properly corrected, are in good agreement with ours.

On fluid/wall slippage

Abstract: Certain (non polymeric) fluids show an anomalously low friction when flowing against well chosen solid walls. We discuss here one possible explanation, postulating that a gaseous film of small thickness h is present between fluid and wall. When h is smaller than the mean free path l of the gas (Knudsen regime) the Navier length b is expected to be independent of h and very large (microns).

Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

Abstract: We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan et al. [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.