Topic
Knudsen number
About: Knudsen number is a research topic. Over the lifetime, 5052 publications have been published within this topic receiving 104278 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors studied the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion, and proved the existence of local solutions to the Boltzman equation that are nearby the local relativism Maxwellians, which are constructed from a class of solutions of the Euler equations that includes a large subclass of nearconstant, non-vacuum fluid states.
Abstract: We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellians. The Maxwellians are constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.
50 citations
TL;DR: In this article, the effect of rarefaction on the porosity of granular and fibrous porous media has been investigated using the lattice Boltzmann method and a new correlation between porosity and the Knudsen number has been proposed.
Abstract: The micro flows through two-dimensional and three-dimensional granular and fibrous porous media at various Knudsen numbers are studied by using the lattice Boltzmann method. For the granular materials, the results for the medium of rounded inclusions agree well with the existing empirical and numerical correlations between the permeability and the Reynolds number. However, the agreement becomes poor for the medium of sharp-cornered inclusions. A new correlation for the Darcy–Forchheimer drag for various inclusion shapes and arrangements is then proposed. For the fibrous materials, the current results are also compared with existing experimental and numerical data. They are in good agreement. The calculations are further carried out for these porous media in the slip-flow regime. The effect of rarefaction on the permeability in different porous media is discussed. A new correlation between the permeability, the porosity and the Knudsen number for both granular and fibrous porous media is presented.
50 citations
TL;DR: In this article, a generalize Reynolds-type lubrication equation valid for both arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, and arbitrary accommodation coefficients at boundaries, is derived form a linearized Boltzmann equation.
Abstract: A generalize Reynolds-type lubrication equation valid for both arbitrary Knudsen numbers, defined as the ratio of the molecular mean free path to the film thickness, and arbitrary accommodation coefficients at boundaries, is derived form a linearized Boltzmann equation. Numerical analyses of lubrication characteristics through the equation for high Knudsen numbers reveal that, if the accommodation coefficient is less than 1, that is, if not all the molecules reflect diffusely as is the case with real gases, load carrying capacities are smaller than those for diffuse reflection.
50 citations
TL;DR: In this article, the authors used direct simulation Monte Carlo method to simulate subsonic flow in nanochannels and micro/nanoscale backward-facing (BF) step considering a wide range of Knudsen number regimes.
50 citations
TL;DR: The construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.
Abstract: We introduce a scheme which gives rise to additional degree of freedom for the same number of discrete velocities in the context of the lattice Boltzmann model. We show that an off-lattice D3Q27 model exists with correct equilibrium to recover Galilean-invariant form of Navier-Stokes equation (without any cubic error). In the first part of this work, we show that the present model can capture two important features of the microflow in a single component gas: Knudsen boundary layer and Knudsen Paradox. Finally, we present numerical results corresponding to Couette flow for two representative Knudsen numbers. We show that the off-lattice D3Q27 model exhibits better accuracy as compared to more widely used on-lattice D3Q19 or D3Q27 model. Finally, our construction of discrete velocity model shows that there is no contradiction between entropic construction and quadrature-based procedure for the construction of the lattice Boltzmann model.
50 citations