Search results for "Knudsen number"
showing 10 items of 13 documents
Evaluation of permeability applicability based on continuum mechanics law in fluid flow through graphene membrane
2019
AbstractGraphene is expected to be used in separation applications such as desalination. However, it is difficult to predict the flow phenomena at the nanoscale using the conventional continuum law. Particularly at a Knudsen number (Kn) of >0.1, which is applied in filtration, it has been reported that not even slip boundary conditions can be applied. In this study, to identify the parameters that affect the applicability of the continuum law, we conducted a fluid permeation simulation using graphene. The deviation of the permeability from that of the continuum model was calculated by changing the channel width, fluid temperature, and fluid type. The result showed that the channel width …
Effects of temperature and pressure on microcantilever resonance response.
2003
Abstract The variation in resonance response of microcantilevers was investigated as a function of pressure (10 −2 –10 6 Pa) and temperature (290–390 K) in atmospheres of helium (He) and dry nitrogen (N 2 ). Our results for a silicon cantilever under vacuum show that the frequency varies in direct proportion to the temperature. The linear response is explained by the decrease in Young's modulus with increasing the temperature. However, when the cantilever is bimaterial, the response is nonlinear due to differential thermal expansion. Resonance response as a function of pressure shows three different regions, which correspond to molecular flow regime, transition regime, and viscous regime. …
Diffusion of Oxygen through Cork Stopper: Is It a Knudsen or a Fickian Mechanism?
2014
International audience; The aim of this work is to identify which law governs oxygen transfer through cork: Knudsen or Fickian mechanism. This is important to better understand wine oxidation during post-bottling aging. Oxygen transfer through cork wafers is measured at 298 K using a manometric permeation technique. Depending on the mechanism, we can extract the transport coefficients. Increasing the initial pressure of oxygen from 50 to 800 hPa leads to a change in the values of the transport coefficients. This implies that oxygen transport through cork does not obey the Knudsen law. From these results, we conclude that the limiting step of oxygen transport through cork occurs in the cell …
Trapping of laser-vaporized alkali metal atoms in rare-gas matrices
1999
Abstract Alkali metal atoms prepared by laser ablation of solid Li and Na are trapped in Ar, Kr, and Xe matrices and studied by electron paramagnetic resonance spectroscopy (EPR) at 15 K. Evidence for tight trapping sites, not observed for atoms generated by conventional Knudsen oven techniques, is presented. The novel tight trapping sites are characterized by a large increase in the isotropic hyperfine coupling constant and a simultaneous decrease in the isotropic g -value. Based on the EPR data, it is suggested that the observed tight trapping corresponds to single substitution of lattice atoms in Ar, Kr, and Xe matrices.
Observation of Knudsen effect with microcantilevers
2003
The Knudsen effect is estimated theoretically and observed experimentally using a U-shaped silicon microcantilever. Though Knudsen forces are extremely small in most cases involving microcantilevers, there exist situations where these forces can be significant and may be important in atomic force microscopy and in microelectromechanical systems (MEMS). The criteria for the presence of Knudsen forces are outlined and an analytical expression in the form of a linear function of the pressure is given for the force in the free molecular regime. The experimental results display peaks in the transitional regime while varying linearly in the molecular regime.
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
2011
In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a…
Exploring the applicability of dissipative fluid dynamics to small systems by comparison to the Boltzmann equation
2018
[Background] Experimental data from heavy-ion experiments at RHIC-BNL and LHC-CERN are quantitatively described using relativistic fluid dynamics. Even p+A and p+p collisions show signs of collective behavior describable in the same manner. Nevertheless, small system sizes and large gradients strain the limits of applicability of fluid-dynamical methods. [Purpose] The range of applicability of fluid dynamics for the description of the collective behavior, and in particular of the elliptic flow, of small systems needs to be explored. [Method] Results of relativistic fluid-dynamical simulations are compared with solutions of the Boltzmann equation in a longitudinally boost-invariant picture. …
Latest results from the EbyE NLO EKRT model
2017
We review the results from the event-by-event next-to-leading order perturbative QCD + saturation + viscous hydrodynamics (EbyE NLO EKRT) model. With a simultaneous analysis of LHC and RHIC bulk observables we systematically constrain the QCD matter shear viscosity-to-entropy ratio eta/s(T), and test the initial state computation. In particular, we study the centrality dependences of hadronic multiplicities, pT spectra, flow coefficients, relative elliptic flow fluctuations, and various flow-correlations in 2.76 and 5.02 TeV Pb+Pb collisions at the LHC and 200 GeV Au+Au collisions at RHIC. Overall, our results match remarkably well with the LHC and RHIC measurements, and predictions for the…
Derivation of transient relativistic fluid dynamics from the Boltzmann equation
2012
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inve…
Does interferometry probe thermalization?
2009
We carry out a systematic study of interferometry radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii R_o and R_s as a function of p_t for various values of the Knudsen number, which measures the degree of thermalization in the system. They converge to the hydrodynamical limit much more slowly (by a factor 3) than elliptic flow. This solves most of the HBT puzzle for central collisions: R_o/R_s is in the range 1.1-1.2 for realistic values of the Knudsen number, much closer to experimental data ($\simeq 1$) than the value 1.5 from hydrodynamical calculations. The p_t dependence of R_o and R_s, which is usually said to refl…