Tangential Momentum Accommodation Coefficient Research Articles

Influence of the pairwise potential on the tangential momentum accommodation coefficient: a multi-scale study applied to the argon on Pt(111) system

The tangential momentum accommodation coefficient (TMAC) of argon atoms on a Pt(111) surface has been investigated using a multi-scale computational approach in order to emphasize the effect of the Pt-Ar pairwise potential on this parameter. For the different Pt-Ar pairwise potentials available in the literature, the TMAC has been determined by Molecular Dynamics simulations from the difference of the incident and reflected velocities of projected Ar atoms on the atomistic Pt surface. Temperature and incident angle dependencies of this parameter are also explored. A new Pt-Ar potential has also been calculated using periodic density functional theory computations. The resulting potential successfully reproduced the available experimental data and is compared with the previous empirical potentials. The TMAC deduced from our pairwise potential is 0.42 at T = 300 K.

Gas Flows near Solids Coated with Thin Water Films

We determined the tangential momentum accommodation coefficient (TMAC) of nitrogen gas at glass surfaces that were coated in thin water films produced by controlling the humidity. The accommodation coefficients were determined by measuring the damping of a spherical particle which was separated from a flat plate by a distance of 10 nm to 10 μm. We examined two solids: hydrophilic glass terminated in hydroxyl groups and hydrophobic glass terminated in methyl groups. At the same relative humidity, thicker films of water form on the hydroxyl-terminated films than on the methyl-terminated films, consistent with formation of hydrogen bonds on the hydroxyl-terminated solid and not on the methyl-terminated solid. The TMACs are surprisingly interesting functions of the humidity. For the hydroxyl-terminated silica, the TMAC is 0.5 at 0% relative humidity and increases almost to 1 when the humidity increases to a few percent. The TMAC decreases to 0.25 at around 87% humidity before rising to 0.9 at 100% humidity. W...

Erratum to: Experimental measurement on tangential momentum accommodation coefficient in a single microtube

The online version of the original article can be found underdoi:10.1007/s10404-011-0773-x.H. Yamaguchi (&) T. Hanawa O. Yamamoto Y. Matsuda T. NiimiDepartment of Micro-Nano Systems Engineering,Nagoya University, B3-1(641) Furo-cho,Chikusa, Nagoya, Aichi 464-8603, Japane-mail: hiroki@nagoya-u.jpY. EgamiDepartment of Mechanical Engineering,Aichi Institute of Technology, 1247 Yachigusa,Yakusa-Cho, Toyota 470-0392, Japan

Seepage Mechanism and Transient Pressure Analysis of Shale Gas

The current research of nonlinear seepage theory of shale-gas reservoir is still in its infancy. According to the characteristics of shale gas in adsorption-desorption, diffusion, slippage and seepage during accumulation, migration and production, a mathematical model of unstable seepage in dual-porosity sealed shale-gas reservoir was developed while considering Knudsen diffusion, slip-flow effect and Langmuir desorption effect. By solving the model utilizing the Stehfest numerical inversion and computer programming in Laplace space, several typical curves of bottomhole pressure were obtained. In this paper, we discussed the effects of several parameters on the pressure dynamics, i.e. storativity ratio, Langmuir volume, Langmuir pressure, adsorption-desorption, tangential momentum accommodation coefficient, flow coefficient, boundary. The results show that the desorbed gas extends the time for fluid to flow from matrix system to fracture system; the changes of Langmuir volume and Langmuir pressure associated with desorption and adsorption effect are the internal causes of the storativity ratio change; when the tangential momentum accommodation coefficient decreases, the time for pressure wave to spread to the border reduces; interporosity flow coefficient determines the occurrence time of the transition stage; boundary range restricts the time for pressure wave to spread to the border.

Calculation of thermo-physical properties of Poiseuille flow in a nano-channel

In this article, flow of Lennard–Jones fluid through a nano-channel is studied with molecular dynamics (MD). The present study examines the thermo-physical properties of a gaseous flow between parallel walls at various rarefaction levels. The walls of the channel are maintained at a constant temperature while the rarefaction levels of the fluid are in the transition regime. The properties of gravity driven Poieuille flow, such as the density profiles across the channel, collision frequency on the walls and velocity profiles are investigated using MD. The amount of slip and tangential momentum accommodation coefficient (TMAC) are investigated, and the amount of slip is predicted using calculated values of TMAC. Using MD data, viscosity of the Poiseuille flow is investigated using the model based on kinetic theory. Subsequently, from the calculated values of TMAC, the dimensionless friction constant is calculated for different flow conditions. The value of the friction constant predicted using the Maxwell slip model is compared with the value obtained using a second order slip model. The second order model, which employ calculated values of TMAC, gives promising results on friction constant at moderately rarefied conditions.

Effects of surface morphology and anisotropy on the tangential-momentum accommodation coefficient between Pt(100) and Ar

In this paper, we study the influence of platinum (100) surface morphology on the tangential-momentum accommodation coefficient with argon using a molecular dynamics method. The coefficient is computed directly by beaming Ar atoms onto the surfaces and measuring the relative momentum changes. The wall is maintained at a constant temperature and its interaction with the gas atoms is governed by the Kulginov potential. To capture correctly the surface effect of the walls and the atoms' trajectories, the quantum Sutton-Chen multibody potential is employed between the Pt atoms. The effects of wall surface morphology, incident direction, and temperature are considered in this work and provide full information on the gas-wall interaction.

The contribution of diffusion to gas microflow: An experimental study

Moderately rarefied gas flows are clearly distinguished from viscous flow in the continuum regime and from molecular diffusion at high rarefaction. They are an intermediate of the two border cases referred to as slip flow and transition regime flow. Here, we present a new pencil-and-paper approach for modeling flows in these regimes by a superposition of convection and Fickian diffusion. It allows us to predict mass flows for helium, argon, nitrogen, and carbon dioxide in microducts with parallel walls and with slightly varying cross section. The model was validated by measurement series taken from literature and by own permeation experiments on tapered microchannels. Analytical investigation of the approach showed that the diffusive flow is proportional to the cross-sectional area at the channel entrance. Hence, the mass flow in a tapered channel is unequal in both directions when diffusion dominates due to increased rarefaction. In contrary to the common Maxwellian slip approach the superposition model describes the data reliably. From this we conclude that deviations from continuum behavior in the intermediate cannot be explained by slip flow at the walls and tangential momentum accommodation, but by Fickian diffusion. Now predictions are possible without any usage of fitted parameters such as the tangential momentum accommodation coefficient.

A review on slip models for gas microflows

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.

Surface–gas interaction effects on nanoscale gas flows

Molecular dynamics (MD) method is used to simulate shear driven argon gas flows in the early transition and free molecular flow regimes to investigate surface effects as a function of the surface–gas potential strength ratio (ewf/eff). Results show a bulk flow region and a near wall region that extends three molecular diameters away from the surfaces. Within the near wall region the velocity, density, and shear stress distributions exhibit deviations from the kinetic theory predictions. Increased ewf/eff results in increased gas density, leading toward monolayer adsorption on surfaces. The near wall velocity profile shows reduced gas slip, and eventually velocity stick with increased ewf/eff. Using MD predicted shear stress values and kinetic theory, tangential momentum accommodation coefficients (TMAC) are calculated as a function of ewf/eff, and TMAC values are shown to be independent of the Knudsen number. Presence of this near wall region breaks down the dynamic similarity between rarefied and nanoscale gas flows.

Tangential Momentum Accommodation Coefficient measurements for various materials and gas species

The tangential momentum accommodation coefficient was measured from the gaseous flow through a single microtube. The mass flow rate was measured by the constant volume technique, where the rate is related to time rate of pressure variation in a fixed volume tank. The measured mass flow rate was fitted by the theoretical mass flow rate expressed by the slip velocity at the surface to deduce the slip coefficient, which can be related to the tangential accommodation coefficient. The mean Knudsen number, which is determined as the mean pressure of the inlet and the outlet, was set to be below 0.32, where the second-order slip boundary condition was suggested to be valid. The measurement system was designed to allow using a microtube with large diameter of several hundred micrometers. Since low pressure environment was essential for large Knudsen number condition for the flow through such large microtube, a low leakage measurement system realized by applying the UHV technology is needed. Applicability of sub millimeters size microtubes allowed us to measure the tangential momentum accommodation coefficients on various materials. In this study, we measured the tangential momentum accommodation coefficients on an engineering metal surface for various gas species.

Experimental study of the gas flows through channels with circular cross sections

The experimental setup based on the constant volume technique is developed to measure the mass flow rate through the microtubes under the isothermal flow conditions. Four different gases: Helium, Nitrogen, Argon and Carbon dioxide, and two surface materials (Stainless stainless Steel steel and Sulfinert) are considered. In this study the Knudsen number varies from ~ 10−4 to 0.3. In this range the approach based on the analytical solution of the Stokes equation subjected to the first and second order velocity slip boundary conditions is used. The tangential momentum accommodation coefficient (TMAC) is extracted from the experimental data on the mass flow rate using its analytical expression. The results are summarized in the tables representing the accommodation coefficients for the couples corresponding gas-surface material combinations. The influence of the molecular mass on the tangential momentum accommodation is discussed.

An analytically predictive model for moderately rarefied gas flow

AbstractIn microducts deviation from continuum flow behaviour of a gas increases with rarefaction. When using Navier–Stokes equations to calculate a flow under slightly and moderately rarefied conditions, slip boundary conditions are used which in turn refer to the tangential momentum accommodation coefficient (TMAC). Here we demonstrate that, in the so-called slip and transition regime, the flow in microducts can be reliably described by a consistently non-empirical model without considering the TMAC. We obtain this equation by superposition of convective transport and Fickian diffusion using two-dimensional solutions of Navier–Stokes equations and a description for the Knudsen diffusion coefficient as derived from kinetic theory respectively. For a wide variety of measurement series found in the literature the calculation predicts the data accurately. Surprisingly only size of the duct, temperature, gas properties and inlet and outlet pressure are necessary to calculate the resulting mass flow by means of a single algebraic equation. From this, and taking the discrepancies of the TMAC concerning surface roughness and nature of the gases into account, we could conclude that neither the diffusive proportions nor the total mass flow rates are influenced by surface topology and chemistry at Knudsen numbers below unity. Compared to the tube geometry, the model slightly underestimates the flow rate in rectangular channels when rarefaction increases. Likewise, the dimensionless mass flow rate and the diffusive proportion of the total flow are distinctly higher in a tube. Thus the cross-sectional geometry has a significant influence on the transport mechanisms under rarefied conditions.

J053025 分子動力学解析に基づく気体分子の固体表面での反射境界条件の考察

The scattering properties of argon (Ar) molecules reflected at a platinum (Pt) wall surface are investigated by the molecular dynamics (MD) method for the gas-surface interaction. The platinum surface is assumed to physically adsorbed water (H20) molecule. Molecular velocity distributions after reflection and the partial tangential momentum accommodation coefficients are obtained for the impinging molecules with specified velocities with in a small range. The scattering distribution indicates a bimodal behavior consisting of diffuse reflection and distribution shifting to the velocity distribution of the impinging molecules. It is seen that the partial tangential momentum accommodation coefficient depends on the tangential velocity of the incident molecule and generally decreases with increasing incident tangential velocity. Comparison between the present scattering distribution based on the MD method for the gas-surface interaction and Cercingani-Lamphis-Lord (CLL) scattering kernel shows large differences. The proposed bimodal scattering kernel for velocity component parallel to the surface is found to favorably represent the scattering distribution of the present simulation.

Second-order gaseous slip flow models in long circular and noncircular microchannels and nanochannels

This paper significantly extends previous studies to the transition regime by employing the second-order slip boundary conditions. A simple analytical model with second-order slip boundary conditions for a normalized Poiseuille number is proposed. The model can be applied to either rarefied gas flows or apparent liquid slip flows. The developed simple models can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels and nanochannels by the research community for the practical engineering design of microchannels and nanochannels. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier–Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as the Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given.

Incompressible Criterion and Pressure Drop for Gaseous Slip Flow in Circular and Noncircular Microchannels

Slip flow in various noncircular microchannels has been further examined, and a simple model for a normalized Poiseuille number is proposed. As for slip flow, no solutions or graphical and tabulated data exist for most geometries; the developed simple model fills this void and can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution, and pressure drop of slip flow in noncircular microchannels by the research community for the practical engineering design of microchannels. The incompressible flow criterion for gas flow in microchannels is given. A Mach number less than 0.3 is not sufficient to ensure that the flow is incompressible. Compressibility depends on the product of two dimensionless parameters: L/L(DRe)(DRe) and Ma (Arkilic et al., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178). Some flows where Ma < 0.3 are low speed compressible flows. A fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels is proposed. If the pressure drop is less than 10% of the outlet pressure, the flow can be considered as incompressible for practical engineering applications. This paper improves and extends previous studies on slip flow in noncircular microchannels.

Molecular dynamics simulations of shear-driven gas flows in nano-channels

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.

Tangential momentum and thermal accommodation coefficients for hydrogen molecules on graphite surface

The scattering of hydrogen molecules from graphite surface was studied through molecular dynamics simulation. The trajectories of the hydrogen molecules and surface atoms were calculated. The distributions of velocity and energy after reflection were obtained depending on direction and quantity of the initial velocity. The energy and tangential momentum accommodation coefficients were calculated for cases where incident velocity distribution can be approximated by Maxwellian function and mean velocity is negligible. Obtained coefficients are in satisfactory agreement with experimental data.

Three-Dimensional Molecular Dynamic Study on Accommodation Coefficients in Rough Nanochannels

The tangential momentum and energy accommodation coefficients (TMAC and EAC) are parameters to characterize the velocity slip and temperature jump in the gas–solid interface. To understand the wall effects on fluid flow and heat transfer in nanochannels, the accommodation coefficients for argon gas molecules and platinum wall atoms were calculated according to a proper statistical algorithm using a three-dimensional molecular dynamic method. Isothermal flows and thermal conductions were simulated in smooth and rough nanochannels, in which the roughness ranged from 0.2 nm to 1.4 nm. From the atomic viewpoint, different lattice arrangements of smooth walls would induce atomic roughness to different extents on the surface, which affected the momentum and energy exchange in gas–wall interactions and resulted in different accommodation coefficients. In channels with nanoscale roughness, the possibility of multiple gas–wall interactions were further increased so that the TMAC and EAC became much larger with more roughness.

A Critical Assessment of the Maxwell Slip Boundary Condition for Rarified Wall Bounded Flows

The Maxwell slip boundary condition is widely used to compute the slip velocity at the wall under rarefied flow condition. In this paper, we apply the Direct Simulation Monte Carlo (DSMC) method on a Couette flow problem in order to evaluate this boundary condition. The computations are performed at different values of tangential momentum accommodation coefficient (between 0.1 and 1) and Knudsen numbers (Kn between 0.001 and 3), at 500 K for Argon, with the aim of comparing the ensuing slip length to that predicted by Maxwell's formula. It is found that the boundary condition is accurate up to a Kn = 0.1 but not at higher Knudsen numbers. Although it has been known that the slip boundary condition is valid only for small Knudsen numbers, the critical Knudsen number from where the deviation begins is not well documented. The present results indicate that such deviations occur at Kn = 0.1 in flows that are bounded by opposing walls. At higher Knudsen numbers, the Knudsen layers overlap and the collisions of...

Viscous micropump simulation by particle/continuum methods

A novel viscous micropump consisting of a cylindrical rotor eccentrically placed inside a microchannel is simulated by the two Volume-CAD (V-CAD) framework-based flow solvers, i.e., the direct simulation Monte Carlo (DSMC) package (named as V-DSMC) and the Navier-Stoke solver (named as V-Flow). V-DSMC is used in the case of the pump applied to gas, while V-Flow is applied to model the pump in the case of liquid working medium. The pumping performance curves under different liquid media with the variation of Reynolds number, as well as under different eccentricity factors are obtained. The performance and the flow filed characteristics are very sensitive to the tangential momentum accommodation coefficient in the case of gas medium. Three recirculations exist in the flow field, and the sizes of recirculation are different at the different operating points in a performance curve.