Knudsen Effect Research Articles

Absolute permeability and Knudsen diffusivity measurements in PEMFC gas diffusion layers and micro porous layers

A novel approach for predicting absolute permeability and effective Knudsen diffusivity values in gas-diffusion-layers/microporous layers (GDLs/MPLs) is proposed. A conventional diffusion bridge setup with modifications is used to obtain the pressure drop across the GDL at several mass flow rates. The experimental results are then fitted to both the Darcy's model and the binary friction model (BFM). Experimental data obtained using different working gases, e.g. O2, N2, He and Ar, are used to validate the two model predictions. Experimental results show that the traditionally used Darcy's law is not able to predict the pressure drop across the GDL, especially in a GDL with an MPL, due to Knudsen effects. The BFM accounts for both viscous and Knudsen transport and it is thereby shown to provide more accurate predictions for any working fluid tested. Permeability and effective Knudsen diffusivities obtained using both Darcy's model and BFM for a SGL (Weisbaden, Germany) SIGRELET 34BA and 34BC are reported.

Experimental measurement of effective diffusion coefficient of gas diffusion layer/microporous layer in PEM fuel cells

Accuracy in the effective diffusion coefficient of the gas diffusion layer (GDL)/microporous layer (MPL) is important to accurately predict the mass transport limitations for high current density operation of polymer electrolyte membrane (PEM) fuel cells. All the previous studies regarding mass transport limitations were limited to pure GDLs, and experimental analysis of the impact of the MPL on the overall diffusion in the porous GDL is still lacking. A modified Loschmidt cell with an oxygen–nitrogen mixture is used in this work to determine the effect of MPL on the effective diffusion coefficients. It is found that Knudsen effects play a dominant role in the diffusion through the MPL where pore diameters are less than 1μm. Experimental results show that the effective diffusion coefficient of the MPL is only about 21% that of its GDL substrate and Knudsen diffusion accounts for 80% of the effective diffusion coefficient of the GDL with MPL measured in this study. No existing correlations can correlate the effective diffusion coefficient with significant Knudsen contribution.

Estimation of Effective Thermal Conductivity of Two-Phase Materials by Considering the Knudsen Effect: An Analytical Approach

In this article, the analytic model has been developed to estimate the effective thermal conductivity (ETC) of two-phase materials based on the unit cell approach by considering the concentration, conductivity ratio, contact resistance, and Knudsen effect. The derivations of algebraic equations for standard geometry, such as hexagon and octagon cylinder models are developed based on parallel isotherm approach. The developed analytic model has been used to predict the thermal conductivity of various two-phase materials (conductivity ratio, α = 3.11-310.86 and concentration, ν = 0.05 and 0.74). The present models are validated using the standard models and compared with the experimental data. Further the comparison is made between the present models and existing models. The results are in good agreement.

Comment on “Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method”

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model "is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to Kn=1 in the transitional regime" made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called "Knudsen effects" described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that 6σKn<-1, where Kn is the Knudsen number σ=(2-σ(v))/σ(v) and σ(v)∈(0,1] is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.

A fractal model for determining oxygen effective diffusivity of gas diffusion layer under the dry and wet conditions

In this paper, we propose a new fractal model to determine the oxygen effective diffusivity of the porous gas diffusion layer (GDL) in proton exchange membrane fuel cell for both the dry and wet conditions. The model considers the GDL structure in terms of tortuosity and area fractal dimensions and also takes the Knudsen effect into account, which has no empirical constant but parameters with physical meanings. The fractal model is verified by the fair agreement with the experimental data and the results obtained from existing models. It is revealed that the Knudsen effect is essential for the understanding of the oxygen transport through the GDL. Under the dry condition, the oxygen effective diffusivity increases with higher area fractal dimension and lower tortuosity fractal dimension. For the wet condition, the water condensation in the GDL of mixed wettability is considered; and it is found that the behavior of oxygen effective diffusivity with liquid saturation depends on the GDL wettability. It is further revealed that for a given liquid saturation, the oxygen effective diffusivity increases with greater area fractal dimension; with the decrease of tortuosity fractal dimension, it also increases, except for the hydrophilic case at high liquid saturation.

Pore network modeling: Application to multiphase transport inside the cathode catalyst layer of proton exchange membrane fuel cell

A pore network modeling (PNM) approach is developed to study multiphase transport phenomena inside a porous structure representative of the Cathode Catalyst Layer (CCL) of Proton Exchange Membrane Fuel Cells. Two algorithms for predicting the invasion of the CCL by liquid water are proposed and compared. The effect of wetting is studied and a change in wettability, from hydrophilic to hydrophobic, is shown to have a significant influence. The total liquid saturation at the end of invasion is lower when the network is hydrophilic whereas the number of breakthrough points is greater. The simulations fully support the idea that water exits the CCL through a series of independent outlet points. Diffusion processes in the gas phase are also analyzed within the framework of the PNM. The results indicate that the Knudsen effect, and to a lesser extent the diffusion-slip effect must be taken into account. These results open up the route for the development of a full coupled PN model of transport phenomena occurring in the CCL.

Measurement of effective gas diffusion coefficients of catalyst layers of PEM fuel cells with a Loschmidt diffusion cell

In this work, using an in-house made Loschmidt diffusion cell, we measure the effective coefficient of dry gas (O 2–N 2) diffusion in cathode catalyst layers of PEM fuel cells at 25 °C and 1 atmosphere. The thicknesses of the catalyst layers under investigation are from 6 to 29 μm. Each catalyst layer is deposited on an Al 2O 3 membrane substrate by an automated spray coater. Diffusion signal processing procedure is developed to deduce the effective diffusion coefficient, which is found to be (1.47 ± 0.05) × 10 −7 m 2 s −1 for the catalyst layers. Porosity and pore size distribution of the catalyst layers are also measured using Hg porosimetry. The diffusion resistance of the interface between the catalyst layer and the substrate is found to be negligible. The experimental results show that the O 2–N 2 diffusion in the catalyst layers is dominated by the Knudsen effect.

Extraction of Transport Coefficients from Molecular Dynamics Simulations of Granular Flows: A Perspective

Molecular dynamics (MD) simulations of solids flows provide a useful tool for extracting transport coefficients needed for the closure of continuum models. This “empirical” approach is particularly powerful for systems with complex interactions—nonspherical particles, cohesive particles, etc.—that are difficult to handle with first-principles (e.g., kinetic-theory-based) approaches. Nonetheless, the extraction of such quantities is characterized by several subtleties which may lead to inaccuracies if ignored. In this work, four such complexities are illustrated: (i) the presence of clustering instabilities, (ii) the a priori need for the general form of the flux law, (iii) the presence of more than one transport coefficient in a given flux law, and (iv) the presence of Knudsen (higher-order) effects.

Nanoparticles Modeling in Axially Injection Suspension Plasma Spray of Zirconia and Alumina Ceramics

Suspension plasma spray (SPS) is a thermal spray method in which nanoparticles are injected into the plasma jet with the help of suspension droplets to achieve thin and finely structured nanocoatings. The nanoparticles experience three in-flight stages: injection within the suspension droplets, discharge of the nanoparticle agglomerates after the evaporation of the suspension solvent, and tracking of the nanoparticle or agglomerates during the momentum and heat transfer with the plasma jet before coating. A numerical model is proposed in this paper for nanoparticle injection, discharge, acceleration, heating, melting, and evaporation. Initial values of suspension droplet size and agglomerate size are selected according to typical experimental data. Noncontinuum effects on particle acceleration and heating, known as Knudsen effects, are considered, as well as the influence of evaporation on the heat transfer. After a comparison with the experimental data, this nanoparticle model is applied for zirconia and alumina axially injected into the suspension plasma spray. Trajectory, velocity, and temperature of the in-flight nanoparticles are predicted for different initial sizes ranging from 30 nm to 1.5 μm; the distributions of the particle characteristics for multiple particles in the spray are also presented. The effects of powder size and material, power input, plasma gas flow rate, and standoff distance on the nanoparticle characteristics have been investigated and discussed.

Modeling of Influence of Gas Atmosphere and Pore-Size Distribution on the Effective Thermal Conductivity of Knudsen and Non-Knudsen Porous Materials

Application of porous insulation materials in various gas atmospheres changes their effective thermal conductivity due to many structural and thermal influences. One of those is the pore-size distribution of the material. In this paper a study of the influence and modeling of the modification of the effective thermal conductivity of various materials is presented by exchanging the gas atmosphere. For this purpose 11 different materials with various pore-size distributions are investigated. The experimental work included thermal conductivity measurements along with an analysis of the porous structure. Two additional important effects of thermal accommodation and radiation will be clearly identified as caused by the exchange of the filling gas. Modeling the gas thermal conductivity for different polydisperse systems is carried out based on kinetic theory and the Knudsen effect of rarefaction of the gas in a wide range of the Knudsen number. Development of the single pore model of the gas thermal conductivity to a new predictive model with an exponential parameter gives good agreement with the experimental results.

Microstructural characterization of porous thermal barrier coatings by laser flash technique

An inversion procedure has been developed to obtain microstructural parameters describing the porosity morphology of porous thermal barrier coatings (TBCs) from the thermal diffusivity measured in different environments by a laser flash technique. The model base for the inversion procedure combines the Knudsen effect (i.e. the thermal conductivity variation of gases within a pore as a function of pore size and shape) with the asymmetric Bruggeman model that describes the effect of porosity on the thermal conductivity of a porous medium in terms of pore shape, orientation and content. A simplified approach in the inversion procedure has been proposed, and the reliability has been checked by simulating different microstructures within the TBC. The inversion procedure has been also applied to experimental thermal diffusivity values of a TBC which were obtained by filling pores with He, N 2, Ar and in vacuo.

Experimental Study of Gas Transport Parameters in Unsaturated Silica Flour

An experimental study was conducted to assess the relative contributions of molecular and Knudsen diffusions for gas‐phase transport in unsaturated silica flour with an intrinsic permeability of 1 ∼ 2 × 10−14 m2 Single‐gas phase flow and binary diffusion experiments were performed on the same soils to determine the Knudsen diffusion and the effective gas‐phase diffusion coefficients, respectively. These results were further used to assess the diffusibility factor for Fick's law of diffusion and the obstruction factor for the Dusty Gas Model theory. These factors were used to account for impedance to gas diffusion caused by the tortuous nature of soil pores. The Knudsen diffusion coefficient was found to be one to two orders of magnitude greater than the effective diffusion coefficient for silica flour at water saturations ranging from 53 to 75% (v/v), which suggested that the Knudsen effect has negligible impact on the effective diffusion coefficient for the unsaturated silica‐flour system at water saturations lower than 75%. For unsaturated silica flour with air‐filled porosity &lt;0.2, the diffusibility factor (or the obstruction factor) value can be more than 10 times smaller than the values estimated by other diffusibility correlations published in the literature.

Determination of the effective diffusion coefficient in porous media including Knudsen effects

A 3-D bond pore network model is presented and used to evaluate the effect of pore size and connectivity on the effective diffusion coefficient in random porous media. The control equations of the system are set up and the simulation method is discussed. The simulation results show that when the average pore size dm < 1 μm, the effective diffusion coefficient is strongly dependent on pore size. The analysis shows that Knudsen and bulk diffusion effects can be decoupled, and for any given diffusion conditions, the effect coefficient accounting for Knudsen diffusion can be obtained. Thus, the effect of pore size can been readily accounted for by correcting the bulk effective diffusivity with the Knudsen effect coefficient. The simulations also show that the percolation threshold in random porous materials decreases with increased pore network connectivity.

Templated cross-linking reactions for designing nanoporous materials

Nanoporous materials are potentially useful for their permeation, dielectric, thermal and optical properties. These materials could be a future alternative for the insulating foams currently used in different industries. In order to realize such performance, highly nanoporous materials (pore size∼100–150 nm and porosity≥85%) that take advantage of the Knudsen effect and low solids contribution to heat conduction are required. The potential for designing such materials by carrying out templated cross-linking reactions using microemulsions and colloidal dispersions was investigated. It was found that these templates helped in imposing some fine pore structures (<200 nm) characteristic of them but the coarser pores (>1 μm) that are formed due to phase separation and aggregation effects upon cross-linking could not be avoided. As a result the thermal performance of these materials was in between the conventional macroporous foam (dpore∼40–100 μm) and sol-gel based nanoporous materials (dpore∼150 nm).

On phase transition in compressible flows: modelling and validation

A physical model for compressible flows with phase transition is described, in which all the processes of phase transition, i.e. nucleation, droplet growth, droplet evaporation and de-nucleation, are incorporated. The model is focused on dilute mixtures of vapour and droplets in a carrier gas with typical maximum liquid mass fraction smaller than 0.02. The new model is based on a reinterpretation of Hill's method of moments of the droplet size distribution function. Starting from the general dynamic equation, it is emphasized that nucleation or de-nucleation correspond to the rates at which droplets enter or leave droplet size space, respectively. Nucleation and de-nucleation have to be treated differently in agreement with their differences in physical nature. Attention is given to the droplet growth model that takes into account Knudsen effects and temperature differences between droplets and gas. The new phase transition model is then combined with the Euler equations and results in a new numerical method: ASCE2D. The numerical method is first applied to the problem of shock/expansion wave formation in a closed shock tube with humid nitrogen as a driver gas. Nucleation and droplet growth are induced by the expansion wave, and in turn affect the structure of the expansion wave. When the main shock, reflected from the end wall of the low-pressure section, passes the condensation zone, evaporation and de-nucleation occur. As a second example, the problem of the flow of humid nitrogen in a pulse-expansion wave tube, designed to study nucleation and droplet growth in monodisperse clouds, is investigated experimentally and numerically.

Knudsen Effect in a Nonequilibrium Gas

From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in the boundary layer is obtained. The agreement between the theoretical result and the numerical result is fairly good.

Numerical Calculation of the Hypersonic Rarefied Transverse Flow Past a Cold Flat Plate

The hypersonic rarefied transverse flow past a flat plate is considered over a wide Knudsen number range. The problem is formulated for a model kinetic equation and solved using an implicit finite-difference second-order method. The results presented demonstrate the Knudsen and Mach number effect on the aerodynamic characteristics of the plate and the flow pattern.

Supersonic dusty-gas flows with Knudsen effect in interphase momentum exchange

On the basis of the two-continuum model of dilute gas-solid suspensions, the dynamic behavior of inertial particles in supersonic dusty-gas flows past a blunt body is studied for moderate Reynolds numbers, when the Knudsen effect in the interphase momentum exchange is significant. The limits of the inertial particle deposition regime in the space of governing parameters are found numerically under the assumption of the slip and free-molecule flow regimes around particles. As a model problem, the flow structure is obtained for a supersonic dusty-gas point-source flow colliding with a hypersonic flow of pure gas. The calculations performed using the full Lagrangian approach for the near-symmetry-axis region and the free-molecular flow regime around the particles reveal a multi-layer structure of the dispersed-phase density with a sharp accumulation of the particles in some thin regions between the bow and termination shock waves.

Effect of thermal variations on the Knudsen forces in the transitional regime

When objects are maintained at different temperatures and separated by distances of the order of the mean free path of the surrounding host gas molecules, gas kinetic forces called Knudsen forces may be involved. The understanding of this effect may result in some improvements in microelectromechanical devices and measurement systems. We present the thermal dependence of these forces in the transitional regime for different gases. In this mode, the Knudsen effect can be significant and, therefore, become a problem in microscale devices. For this study, a silicon microcantilever, mounted close to a substrate, is used and changes in temperature are observed by measuring bending of the microcantilever.

Observation of Knudsen effect with microcantilevers

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.