Knudsen number

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

Molecular Simulations of Knudsen Wall-slip: Effect of Wall Morphology

Abstract: This work involves a molecular simulation study of the phenomena of wall slip occurring in rarefied gases flowing through micro- and nano-channels. A simulation strategy that mimics a scattering experiment is developed in order to compute the tangential momentum accommodation coefficient (f) which governs the degree of slip at the wall surface. Noninteracting gas molecules are bombarded at an atomic wall composed of rigid atoms with suitably distributed velocities and a tangential drift velocity that simulates flow. The accommodation coefficient is computed from the loss in the tangential momentum of these molecules. The accommodation coefficient is observed to be strongly dependent on the physical roughness of the wall, as characterized by the parameter sgr wg/L, and the attractiveness of the wall to the fluid, as characterized by the parameter e wg/k B T, where sgr wg and e wg are the Lennard–Jones interaction parameters of the wall and gas atoms while L is the lattice unit length. The accommodation coe...

A lattice Boltzmann BGK model for simulation of micro flows

Abstract: We propose a lattice Boltzmann BGK model for simulation of micro flows. This model is based on the kinetic theory and the entropic lattice Boltzmann method (S. Ansumali and I. V. Karlin, J. Stat. Phys. 107 (2002) 291) but the relaxation time is re-defined in terms of the Knudsen number, and a diffuse-scattering boundary condition (DSBC) is adopted to consider the velocity slip at the wall. Simple theoretical analysis and numerical validation show that the proposed model gives good predictions of the micro fluidic behaviors.

Kinetics of hydrocarbon adsorption on activated carbon and silica gel

Abstract: Experimental breakthrough results of methane, ethane and propane in activated carbon and silica gel obtained over a wide range of gas compositions, bed pressures, interstitial velocities, and column temperatures were analyzed using a dynamic, nonisothermal, nontrace column breakthrough model. A linear driving force (LDF) approximation is used for particle uptake, and the Langmuir-Freundlich isotherm represents adsorption equilibrium. The LDF mass-transfer-rate coefficient (and, hence, effective particle diffusivity) and column-wall heat-transfer coefficient were determined. The results show that hydrocarbon transport in the activated carbon particles used is essentially by Knudsen and surface flow, while for the silica gel used the transport is primarily by Knudsen flow. For activated carbon, the experimentally derived LDF coefficients for all three sorbates are well correlated using an average effective diffusivity value. With regard to heat transfer, the column-wall Nusselt number is approximately constant for the range of Reynolds numbers considered. Simulations of multicomponent breakthrough in the activated-carbon bed based on independently measured single-component kinetic parameters and the extended Langmuir-Freundlich isotherm agree very well with experimental results. The computational efficiency gained by adopting the simpler extended Langmuir isotherm model is also investigated.

Fokker–Planck model for computational studies of monatomic rarefied gas flows

Abstract: In this study, we propose a non-linear continuous stochastic velocity process for simulations of monatomic gas flows. The model equation is derived from a Fokker–Planck approximation of the Boltzmann equation. By introducing a cubic non-linear drift term, the model leads to the correct Prandtl number of 2/3 for monatomic gas, which is crucial to study heat transport phenomena. Moreover, a highly accurate scheme to evolve the computational particles in velocity- and physical space is devised. An important property of this integration scheme is that it ensures energy conservation and honours the tortuosity of particle trajectories. Especially in situations with small to moderate Knudsen numbers, this allows to proceed with much larger time steps than with direct simulation Monte Carlo (DSMC), i.e. the mean collision time not necessarily has to be resolved, and thus leads to more efficient simulations. Another computational advantage is that no direct collisions have to be calculated in the proposed algorithm. For validation, different micro-channel flow test cases in the near continuum and transitional regimes were considered. Detailed comparisons with DSMC for Knudsen numbers between 0.07 and 2 reveal that the new solution algorithm based on the Fokker–Planck approximation for the collision operator can accurately predict molecular stresses and heat flux and thus also gas velocity and temperature profiles. Moreover, for the Knudsen Paradox, it is shown that good agreement with DSMC is achieved up to a Knudsen number of about 5.