Knudsen number

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

Vertically-aligned carbon nanotube membranes for hydrogen separation

Abstract: Vertically-aligned carbon nanotube membranes have been fabricated and characterized and the corresponding gas permeability and hydrogen separation were measured. The carbon nanotube diameter and areal density were adjusted by varying the catalyst vapour concentration (Fe/C ratio) in the mixed precursor. The permeances are one to two magnitudes higher than the Knudsen prediction, while the gas selectivities are still in the Knudsen range. The diameter and areal density effects were studied and compared, the temperature dependence of permeation is also discussed. The results confirm the existence of non-Knudsen transport and that surface adsorption diffusion may affect the total permeance at relative low temperature. The permeance of aligned carbon nanotube membranes can be improved by increasing areal density and operating at an optimum temperature.

Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory

Abstract: The steady behavior of a multicomponent mixture of vapors and noncondensable gases between two parallel plane condensed phases for small Knudsen numbers, especially for the continuum limit (i.e., the limit as the Knudsen number vanishes), is investigated in the light of kinetic theory. By a systematic asymptotic analysis of the Boltzmann equation with kinetic boundary conditions, the flow due to evaporation and condensation on the condensed phases is shown to vanish in the continuum limit, and then the system of fluid-dynamic-type equations and their boundary conditions which describes the behavior in the limit is derived. On the basis of the system, it is shown that the vanishingly weak evaporation and condensation give a finite effect on the behavior of the mixture in the continuum limit. This is an example of the ghost effect discovered recently by Sone and co-workers [e.g., Y. Sone et al., Phys. Fluids 8, 628 and 3403 (1996); Y. Sone, in Rarefied Gas Dynamics, edited by C. Shen (Peking U.P., Beijing, 1997), p. 3]. Finally, for the case of a binary mixture of a vapor and a noncondensable gas, two typical problems, the simultaneous mass and heat transfer and the plane Couette flow, are considered to demonstrate the effect more concretely. The result is also compared with that obtained by the numerical analysis of the Boltzmann equation by the direct simulation Monte Carlo method.

Rarefied gas flow in a rectangular enclosure induced by non-isothermal walls

Abstract: The flow of a rarefied gas in a rectangular enclosure due to the non-isothermal walls with no synergetic contributions from external force fields is investigated. The top and bottom walls are maintained at constant but different temperatures and along the lateral walls a linear temperature profile is assumed. Modeling is based on the direct numerical solution of the Shakhov kinetic equation and the Direct Simulation Monte Carlo (DSMC) method. Solving the problem both deterministically and stochastically allows a systematic comparison and verification of the results as well as the exploitation of the numerical advantages of each approach in the investigation of the involved flow and heat transfer phenomena. The thermally induced flow is simulated in terms of three dimensionless parameters characterizing the problem, namely, the reference Knudsen number, the temperature ratio of the bottom over the top plates, and the enclosure aspect ratio. Their effect on the flow configuration and bulk quantities is thoroughly examined. Along the side walls, the gas flows at small Knudsen numbers from cold-to-hot, while as the Knudsen number is increased the gas flows from hot-to-cold and the thermally induced flow configuration becomes more complex. These flow patterns with the hot-to-cold flow to be extended to the whole length of the non-isothermal side walls may exist even at small temperature differences and then, they are enhanced as the temperature difference between the top and bottom plates is increased. The cavity aspect ratio also influences this flow configuration and the hot-to-cold flow is becoming more dominant as the depth compared to the width of the cavity is increased. To further analyze the flow patterns a novel solution decomposition into ballistic and collision parts is introduced. This is achieved by accordingly modifying the indexing process of the typical DSMC algorithm. The contribution of each part of the solution is separately examined and a physical interpretation of the flow configuration, including the hot-to-cold flow close to the side walls, in the whole range of the Knudsen number is provided.

From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight

Abstract: We study the Boltzmann equation on the d-dimensional torus in a perturbative setting around a global equilibrium under the Navier-Stokes lineari- sation. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a C0-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently on the Knudsen number. Finally we show a Cauchy theory and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal and furthermore, this result only requires derivatives in the space variable and allows to connect to solutions to the incompressible Navier-Stokes equations in these spaces.