Knudsen number

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

An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances

Abstract: : The experimental investigation discussed here gives experimental confirmation of the slip-flow theory for modeling hydrodynamic gas bearings with clearances below 025 microns An interferometric technique employing two CW lasers is used to measure the small clearances with an accuracy of 0025 microns The effects of molecular rarefaction are studied by operating the slider bearing in different gas media of different mean free paths Bearings operating at extremely high local Knudsen numbers are studied without approaching excessively high bearing numbers Experimentally measured trailing edge clearances and pitch angles are compared with theoretical predictions using the modified Reynolds equation with velocity slip boundary conditions Excellent agreement between experiment and theory is found for clearances as high as 160 microns to as low as 0075 microns with corresponding ambient Knudsen numbers of 004 and 251, respectively

Hydrodynamic electron flow in high-mobility wires.

Abstract: Hydrodynamic electron flow is experimentally observed in the differential resistance of electrostatically defined wires in the two-dimensional electron gas in (Al,Ga)As heterostructures. In these experiments current heating is used to induce a controlled increase in the number of electron-electron collisions in the wire. The interplay between the partly diffusive wire-boundary scattering and the electron-electron scattering leads first to an increase and then to a decrease of the resistance of the wire with increasing current. These effects are the electronic analog of Knudsen and Poiseuille flow in gas transport, respectively. The electron flow is studied theoretically through a Boltzmann transport equation, which includes impurity, electron-electron, and boundary scattering. A solution is obtained for arbitrary scattering parameters. By calculation of flow profiles inside the wire it is demonstrated how normal flow evolves into Poiseuille flow. The boundary-scattering parameters for the gate-defined wires can be deduced from the magnitude of the Knudsen effect. Good agreement between experiment and theory is obtained.

Boundary conditions for the lattice Boltzmann method

Abstract: When the Lattice Boltzmann Method (LBM) is used for simulating continuum fluid flow, the discrete mass distribution must satisfy imposed constraints for density and momentum along the boundaries of the lattice. These constraints uniquely determine the three‐dimensional (3‐D) mass distribution for boundary nodes only when the number of external (inward‐pointing) lattice links does not exceed four. We propose supplementary rules for computing the boundary distribution where the number of external links does exceed four, which is the case for all except simple rectangular lattices. Results obtained with 3‐D body‐centered‐cubic lattices are presented for Poiseuille flow, porous‐plate Couette flow, pipe flow, and rectangular duct flow. The accuracy of the two‐dimensional (2‐D) Poiseuille and Couette flows persists even when the mean free path between collisions is large, but that of the 3‐D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3‐D low‐Reynolds‐number flow.

A review on slip models for gas microflows

Abstract: Accurate modeling of gas microflow is crucial for the microfluidic devices in MEMS. Gas microflows through these devices are often in the slip and transition flow regimes, characterized by the Knudsen number of the order of 10−2~100. An increasing number of researchers now dedicate great attention to the developments in the modeling of non-equilibrium boundary conditions in the gas microflows, concentrating on the slip model. In this review, we present various slip models obtained from different theoretical, computational and experimental studies for gas microflows. Correct descriptions of the Knudsen layer effect are of critical importance in modeling and designing of gas microflow systems and in predicting their performances. Theoretical descriptions of the gas-surface interaction and gas-surface molecular interaction models are introduced to describe the boundary conditions. Various methods and techniques for determination of the slip coefficients are reviewed. The review presents the considerable success in the implementation of various slip boundary conditions to extend the Navier–Stokes (N–S) equations into the slip and transition flow regimes. Comparisons of different values and formulations of the first- and second-order slip coefficients and models reveal the discrepancies arising from different definitions in the first-order slip coefficient and various approaches to determine the second-order slip coefficient. In addition, no consensus has been reached on the correct and generalized form of higher-order slip expression. The influences of specific effects, such as effective mean free path of the gas molecules and viscosity, surface roughness, gas composition and tangential momentum accommodation coefficient, on the hybrid slip models for gas microflows are analyzed and discussed. It shows that although the various hybrid slip models are proposed from different viewpoints, they can contribute to N–S equations for capturing the high Knudsen number effects in the slip and transition flow regimes. Future studies are also discussed for improving the understanding of gas microflows and enabling us to exactly predict and actively control gas slip.