Momentum Accommodation Coefficient Research Articles

Molecular Dynamics Study of Gas–Surface Interactions in a Force-Driven Flow of Argon through a Rectangular Nanochannel

ABSTRACTIn recent times, flows through micro- and nanochannels have gained prominence due to their applicability to the fast growing fields of micro- and nanotechnology among others. Understanding gas–surface interactions in such flows is crucial, because the size of the micro/nanoscale devices is typically comparable to boundary layer thickness near a wall and the surface starts playing a significant role. An attempt is made to understand these interactions by modeling simple force-driven argon gas flow between two parallel platinum plates by the molecular dynamics method. One of the most important parameters that describes gas–surface interactions—that is, the tangential momentum accommodation coefficient, along with flow properties such as velocity and density—is calculated for a range of Knudsen numbers in the early transitional flow regime. A deeper insight into the flow physics is obtained by considering various case studies for the variation of aforesaid properties with respect to external driving forces and gas–wall interaction strengths.

Experimental analysis of velocity slip at the wall for gas flows of nitrogen, R134a, and R600a through a metallic microtube

This paper reports measurements of mass flow rate of nitrogen, R134a, and R600a through a commercially available stainless steel microtube, which closely reproduces the case of gas leakage through micrometric clearances found in compressor valves. The accuracy of the measurements in the whole rarefaction range considered was verified through comparisons with predictions from the BGK kinetic model and results from the Navier–Stokes equations with modified boundary conditions. Furthermore, values of the tangential momentum accommodation coefficient (TMAC) were obtained by using an analytical approach derived from the solution of the Navier–Stokes equations with modified second-order boundary conditions. An incomplete accommodation is observed for all gases, with α = 0.933 ± 0.004 for nitrogen, 0.956 ± 0.004 for R134a, and 0.974 ± 0.008 for R600a. The results for all gases were very similar, indicating that the gas chemical composition does not significantly affect the flow through microtubes with rough internal surfaces, even when heavy polyatomic molecules are considered.

Disk spin-down measurements in the free-molecular flow regime: A new method for measurement of tangential momentum accommodation coefficients

An experimental technique using spin-down of a disk approaching the free-molecular flow limit is developed to measure the tangential momentum accommodation coefficient σt. The new technique uses a disk mounted on a shaft supported by gas bearings in vacuum. A differential scavenging system allows disk spin-down experiments in different gases. Representative test results with two different materials in two different gases are shown, demonstrating the method is capable of handling a range of gases, as well as any material that is available as, or can be formed into, a planar disk.

Slip flow in porous media

The dynamics of fluids and their interaction with surfaces in Unconventional Gas Reservoirs (UGRs) are very different from those in conventional systems. The physics of flow through the matrices of these reservoirs are not well understood. The small size of flow conduits which is comparable to the gas mean free path results in a deviation from Darcy to slip, transition and free molecular flow regimes. Solving Navier–Stokes (N–S) equations with modified boundary conditions has so far been the best practical approach to describe these flow behaviours.In this paper, a study of slip flow in shale gas reservoirs is presented. Several permeability measurements were performed using three shale rock samples to study the slip permeability. The Maxwellian type slip boundary conditions were used in N–S equations to obtain the slip coefficients and tangential momentum accommodation coefficient (TMAC) in porous media from the experimental data. Our results show that slip coefficients in porous media are higher than those in non-porous systems. In addition, it is found that the TMAC is smaller in porous media in comparison to flow in non-porous materials. These observations, which are attributed to greater surface area and roughness, are in agreement with literature data, which are limited to flow through individual micro conduits. The outcomes of this study will be useful for accurate prediction of gas flow rate in shale/tight gas reservoirs when using slip boundary conditions.

Simulation of diatomic gas-wall interaction and accommodation coefficients for negative ion sources and accelerators.

Particle-wall interactions determine in different ways the operating conditions of plasma sources, ion accelerators, and beams operating in vacuum. For instance, a contribution to gas heating is given by ion neutralization at walls; beam losses and stray particle production-detrimental for high current negative ion systems such as beam sources for fusion-are caused by collisional processes with residual gas, with the gas density profile that is determined by the scattering of neutral particles at the walls. This paper shows that Molecular Dynamics (MD) studies at the nano-scale can provide accommodation parameters for gas-wall interactions, such as the momentum accommodation coefficient and energy accommodation coefficient: in non-isothermal flows (such as the neutral gas in the accelerator, coming from the plasma source), these affect the gas density gradients and influence efficiency and losses in particular of negative ion accelerators. For ideal surfaces, the computation also provides the angular distribution of scattered particles. Classical MD method has been applied to the case of diatomic hydrogen molecules. Single collision events, against a frozen wall or a fully thermal lattice, have been simulated by using probe molecules. Different modelling approximations are compared.

Science of Water Leaks: Validated Theory for Moisture Flow in Microchannels and Nanochannels.

Water is ubiquitous; the science of its transport in micro- and nanochannels has applications in electronics, medicine, filtration, packaging, and earth and planetary science. Validated theory for water vapor and two-phase water flows is a "missing link"; completing it enables us to define and quantify flow in a set of four standard leak configurations with dimensions from the nanoscale to the microscale. Here we report the first measurements of water vapor flow rates through four silica microchannels as a function of humidity, including under conditions when air is present as a background gas. An important finding is that the tangential momentum accommodation coefficient (TMAC) is strongly modified by surface layers of adsorbed water molecules, in agreement with previous work on the TMAC for nitrogen molecules impacting a silica surface in the presence of moisture. We measure enhanced flow rates for two-phase flows in silica microchannels driven by capillary filling. For the measurement of flows in nanochannels we use heavy water mass spectrometry. We construct the theory for the flow rates of the dominant modes of water transport through each of the four standard configurations and benchmark it against our new measurements in silica and against previously reported measurements for nanochannels in carbon nanotubes, carbon nanopipes, and porous alumina. The findings show that all behavior can be described by the four standard leak configurations and that measurements of leak behavior made using other molecules, such as helium, are not reliable. Single-phase water vapor flow is overestimated by a helium measurement, while two-phase flows are greatly underestimated for channels larger than 100 nm or for all channels when boundary slip applies, to an extent that depends on the slip length for the liquid-phase flows.

Enhanced Water Vapor Flow in Silica Microchannels: The Effect of Adsorbed Water on Tangential Momentum Accommodation

Maxwell introduced the tangential momentum accommodation coefficient (TMAC) in 1879 to describe boundary conditions in fluid flow. Recent findings of anomalously high gas flow rates in carbon nanotubes have been attributed to smooth hydrophobic walls that reduce TMAC. Here we report the first measurements of water vapor flows in microchannels over a wide humidity range and show that for silica there is a range of humidity over which an adsorbed water layer reduces the TMAC in a way that depends on the surface conditions. We develop a model that unifies Maxwell’s ideas on TMAC with Langmuir’s ideas on adsorption. We fit TMAC data with the model using two stages of Langmuir adsorption and derive total adsorption isotherms for water on silica. The first adsorption stage reduces TMAC by smoothing the surface. The second stage is bulk liquid that imparts large TMAC. We find that leak testing of moisture barriers with an ideal gas such as helium may not be accurate for critical applications and recommend direct...

Modeling wall effects in a micro-scale shock tube using hybrid MD–DSMC algorithm

Wall effects in a micro-scale shock tube are investigated using the Direct Simulation Monte Carlo method as well as a hybrid Molecular Dynamics–Direct Simulation Monte Carlo algorithm. In the Direct Simulation Monte Carlo simulations, the Cercignani–Lampis–Lord model of gas–surface interactions is employed to incorporate the wall effects, and it is shown that the shock attenuation is significantly affected by the choice of the values of tangential momentum accommodation coefficient. A loosely coupled Molecular Dynamics–Direct Simulation Monte Carlo approach is then employed to demonstrate incomplete accommodation in micro-scale shock tube flows. This approach uses fixed values of the accommodation coefficients in the gas–surface interaction model, with their values determined from a separate dynamically similar Molecular Dynamics simulation. Finally, a completely coupled Molecular Dynamics–Direct Simulation Monte Carlo algorithm is used, wherein the bulk of the flow is modeled using Direct Simulation Monte Carlo, while the interaction of gas molecules with the shock tube walls is modeled using Molecular Dynamics. The two regions are separate and coupled both ways using buffer zones and a bootstrap coupling algorithm that accounts for the mismatch of the number of molecules in both regions. It is shown that the hybrid method captures the effect of local properties that cannot be captured using a single value of accommodation coefficient for the entire domain.

Torque data on non-isothermal rarefied Cylindrical Couette flow

The torque exerted on the walls of a micro cylindrical Couette gas flow is studied using Direct Simulation Monte Carlo (DSMC) method and analytical solutions. An analytical solution for temperature filed under specified wall heat flux condition is proposed using a previously introduced power-law (PL) wall-scaling approach. The results of cylindrical Couette flow under specified wall heat flux condition are compared with those of isothermal flow. The effects of rarefaction, compressibility, tangential momentum accommodation coefficient (TMAC) and gas-surface heat exchange on the torque values are investigated for slip to free molecular flow regimes. The results indicate that the torque coefficient has a maximum value at the transitional flow regime for TMAC values less than unity. Lower TMAC values and higher Knudsen numbers lead to reduction and deviation of torque magnitudes from those of continuum limit. Thermal simulations of cylindrical Couette flow show that heating and cooling have significant effects on the torque values. Velocity profiles and normalized torque values demonstrate mixed increasing/decreasing behavior under heating/cooling processes for rarefied gas flow.

An analytical model for shale gas permeability

Based on the kinetic theory of gases and using the regularized 13-moment method, the analytical R13 AP model is introduced for predicting gas apparent permeability of nanoporous shale samples. These samples are characterized by ultratight pores and may introduce significant rarefaction effects, especially under the laboratory conditions, which cannot be accounted for in the classical hydrodynamic equations. Due to the significance of the rarefaction effects, measured values of the gas apparent permeability depend on the operating parameters, such as pressure and temperature, and gas type in addition to pore size. The R13 AP model incorporates these parameters and can predict the apparent permeability for Knudsen numbers up to unity. This model is compared with the other models and experimental results. The results of the R13 AP model match the published experimental data of flow in nanochannels. It is shown that the gas molecular weight and temperature have a significant effect on apparent permeability of the nanochannels, and the Tangential Momentum Accommodation Coefficient (TMAC) has a minimal effect for its experimental range (0.8–1). The effect of adsorption on apparent permeability of nanochannels is studied by employing the experimental Langmuir isotherms of different shale samples. It is shown that the apparent permeability does not change linearly with surface coverage and, change of permeability with surface coverage becomes more pronounced as the surface coverage increases. R13 AP model results for apparent permeability of Carbon Dioxide and Nitrogen agree with the experimental measurements performed on a Marcellus shale sample. The absolute permeability values are calculated and compared with the ones estimated by the double slippage model for both gases. Unlike the double slippage model, the R13 AP model honors the values of apparent permeability at high pressure and estimates lower absolute permeability values. For Carbon Dioxide, the value is slightly lower due to the presence of an adsorbed layer.

Numerical study of effects of accommodation coefficients on slip phenomena

An unstructured mesh Navier-Stokes solver employing a Maxwell slip boundary condition was developed. The present flow solver was applied to the simulation of flows around an axisymmetric hollow cylinder in a Mach 10.4 freestream, known as Calspan-UB Research Center (CUBRC) Run 14 case, and the velocity slip and the temperature jump on the cylinder surface were investigated. The effect of tangential momentum and thermal accommodation coefficients used in the Maxwell condition was also investigated by adjusting their values. The results show that the reverse flow region is developed on the body surface due to the interaction between the shock and the boundary layer. Also, the shock impingement makes pressure high. The flow properties on the surface agree well with the experimental data, and the velocity slip and the temperature jump vary consistently with the local Knudsen number change. The accommodation coefficients affect the slip phenomena and the size of the flow region. The slip phenomena become larger when both tangential momentum and thermal accommodation coefficients are decreased. However, the range of the reverse flow region decreases when the momentum accommodation coefficient is decreased. The characteristics of the momentum and thermal accommodation coefficients also are overlapped when they are altered together.

Accommodative dependence of thermophoresis in gases in the Knudsen regime

The role of accommodation coefficients of energy, as well as tangential and normal momenta, in the phenomenon of thermophoresis of a spherical aerosol particle in the free molecule (Knudsen) regime is studied. The feature of this work is that it does not involve any assumptions about the distribution function of gas molecules reflected from the molecule’s surface. The accommodation coefficients are introduced in equations directly via momentum and energy flows. Expressions for the thermophoresis force and velocity, as well as for the thermal polarization of a particle (difference of temperatures in the direction of the incoming gas flow) have been obtained. It is shown that, in the Knudsen regime, the thermophoresis force and velocity depend only on the accommodation coefficients of momentum and do not depend on the accommodation coefficient of energy. The magnitude of thermal polarization, on the contrary, is directly proportional to the accommodation coefficient of energy and does not depend on the accommodation coefficients of momentum.

Measurement of Continuum Breakdown During Disk Spindown in Low-Pressure Air

The deceleration torque during spindown of a disk is measured across a range of air pressures on three aluminum disks. The diameters of the disk are 0.15, 0.17, and 0.21 m; the range of pressures is 0.71 Pa to atmospheric pressure; and the angular velocities range approximately from 400 to 3300 rpm. The results are compared to computational fluid dynamics for the continuum flow regime and analytical results for the free molecular flow regime. The torque is nondimensionalized using dynamic viscosity of air, instantaneous angular velocity, and the disk diameter and is plotted against Reynolds number. Results show that the nondimensional curves from atmospheric pressure through 100 Pa collapse on each other for all disk diameters and agree with computational-fluid-dynamics results. At low pressures, the nondimensional torque does not change with Reynolds number. The analytically obtained free molecular flow torque is compared with the experimental results at the lowest ambient pressures, and the value of momentum accommodation coefficient is computed to be . The value is consistent for all disk sizes. The scale used for nondimensionalization suggests self-similarity, and therefore continuity, in the spindown experiments between pressures of 100 Pa and atmospheric pressure. The deviation of the nondimensional curves below this pressure suggests continuum breakdown.

Rarefied gas flow simulations with TMAC in the slip and the transition flow regime using the lattice Boltzmann method

The lattice Boltzmann (LB) method has been used to simulate rarefied gas flows in micro-systems as an alternative tool, and shown its application possibility. For the rarefied gas flows, the surface roughness plays an important role for the slip phenomenon at the wall. If the wall surface is sufficiently rough, the reflection of the molecules will be diffuse and the tangential momentum accommodation coefficient (TMAC) is equal to unity. However, it has been known that the reflections are not always fully diffuse. In this study, rarefied gas flows are simulated in the slip and the transition flow regime including the effect of the TMAC. For the simulations, new non-fully diffuse wall boundary treatments of the LB method are proposed. The results of 2D and 3D simulations are in excellent agreement with the analytical solutions for the slip flow regime. The solutions of the linearized Boltzmann equation and DSMC for the transition flow regime are compared with those of high order LB method with present boundary conditions, and they are in excellent agreement. The tangential momentum accommodation coefficient effect is also investigated.

Applicability of molecular dynamics method to the pressure-driven gas flow in finite length nano-scale slit pores

This study investigates the applicability of the molecular dynamics (MD) method to the pressure-driven gas flow in finite length nano-scale slit pores. The reflecting particle membrane is introduced to induce a pressure difference between the inlet and outlet. The flow properties are compared with those of the Burnett equations. The inlet and outlet pressures, as well as the mass flow rate in these two simulations are maintained the same by adjusting the tangential momentum accommodation coefficient in the Burnett simulation, which is found to be between 0.4 and 0.5. Qualitative and quantitative agreements are observed between the MD and Burnett simulation results in the bulk of the pore for both streamwise distributions and cross-section profiles. The MD simulation shows an advantage in the near-wall region, in which the wall force field dominates flow behaviour. This study indicates that MD simulation can be used to describe the pressure-driven gas flow characteristics in finite length nano-scale slit pores.

Revisiting Maxwell’s accommodation coefficient: A study of nitrogen flow in a silica microtube across all flow regimes

Gas flows have been studied quantitatively for more than a hundred years and have relevance in modern fields such as the control of gas inputs to processes, the measurement of leak rates and the separation of gaseous species. Cha and McCoy have derived a convenient formula for the flow of an ideal gas applicable across a wide range of Knudsen numbers (Kn) that approaches the Navier–Stokes equations at small Kn and the Smoluchowski extension of the Knudsen flow equation at large Kn. Smoluchowski’s result relies on the Maxwell definition of the tangential momentum accommodation coefficient α, recently challenged by Arya et al. We measure the flow rate of nitrogen gas in a smooth walled silica tube across a wide range of Knudsen numbers from 0.0048 to 12.4583. We find that the nitrogen flow obeys the Cha and McCoy equation with a large value of α, unlike carbon nanotubes which show flows consistent with a small value of α. Silica capillaries are therefore not atomically smooth. The flow at small Kn has α=0.91 and at large Kn has α close to one, consistent with the redefinition of accommodation coefficient by Arya et al., which also resolves a problem in the literature where there are many observations of α of less than one at small Kn and many equal to one at large Kn. Silica capillaries are an excellent choice for an accurate flow control system.

Effect of random surface topography on the gaseous flow in microtubes with an extended slip model

The gas slip flow in microtubes is studied incorporating the effect of three-dimensional (3D) random surface topography as characterized by the fractal geometry. The modified two-variable Weierstrass-Mandelbrot function is utilized to describe the multi-scale self-affine roughness. An extended first-order slip model suitable for random rough surfaces is proposed to characterize the gas–solid interactions at the wall. The flow field in microtubes is numerically analyzed by solving the 3D Navier–Stokes (N–S) equation with the extended slip model. The effect of rarefication, compressibility, roughness height and fractal dimension are investigated and discussed. The results indicate that the effect of surface roughness increases with the increasing rarefication effect. The increase in the fractal dimension makes the Poiseuille number more sensitive to the Mach number. In addition, the 3D surface topography has a significant effect on the tangential momentum accommodation coefficient.

Effect of Gas Species on Gas–Monolayer Interactions: Tangential Momentum Accommodation

The tangential momentum accommodation coefficient (TMAC) of five gas species—He, N2, Ar, CO2, and SF6—was measured on an octadecyltrichlorosilane-coated glass surfaces at 1.0 atm and 24 ± 2 °C. The TMAC was determined from measurement of the damping on a glass sphere near a glass plate when the separation between the sphere and plate was less than 1500 nm so that the flow was at or near the slip-flow regime. The results show that the damping depends on the gas species and that the fitted accommodation coefficient for these gases decreases as the molar mass increases. This trend can be explained using a simple physical model of the collision between two spheres, consisting of an incoming sphere to model the gas and an initially stationary sphere to model part of the monolayer adsorbed on the solid. In this simple model, heavier incoming molecules conserve more average tangential momentum than do lighter molecules. We also consider the possibility of separating a mixture of gases based on differences in TMACs.

Parametric studies of the thermal and momentum accommodation of monoatomic and diatomic gases on solid surfaces

The thermal accommodation coefficient (TAC) and the momentum accommodation coefficient (MAC) are the two fundamental parameters quantifying the solid–gas energy and momentum exchange efficiencies. We use molecular dynamics (MD) simulations to study the effect of individual interfacial parameters including, (i) solid–gas interaction strength, (ii) gas–solid atomic mass ratio, (iii) solid elastic stiffness, and (iv) temperature, on TAC and MAC at solid surfaces in contact with monoatomic and diatomic gases. In addition to offering a fundamental understanding on how these individual parameters affect the nature of gas–solid collisions, we provide an extensive database for the TAC and MAC. We also study the effect of surface functionalization with molecular monolayers on the energy and momentum transfer at the interface. These results are useful in developing interfaces with enhanced heat transfer under various operation conditions.

Molecular beam study of the scattering behavior of water molecules from a graphite surface.

Gas flow in nanospaces is greatly affected by the scattering behavior of gas molecules on solid surfaces, resulting in unique mass transport properties. In this paper, the molecular beam scattering experiment of water molecules on a graphite surface was conducted to understand their scattering dynamics in an incident energy range that corresponds to their thermal velocity distribution at room temperature (35-130 meV). Because of the large adsorption energy (∼100 meV), the scattering behavior is quite sensitive to the incident energy even within this narrow energy range. For relatively large incident energies, the direct-inelastic and trapping-desorption channels have comparable contributions to the scattering process on the surface at 300 K. In contrast, when the incident energy decreases well below the adsorption energy on the surface, the trapping-desorption channel becomes dominant, changing the scattering pattern from directional to diffusive scattering. As a result, the tangential momentum accommodation coefficient (TMAC), which significantly impacts the mass transport in nanospaces, largely depends on the incident energy. A decrease in the incident energy from 130 to 35 meV doubles the TMAC (0.42 to 0.86). In addition to the incident energy, the TMAC shows a strong dependence on the surface temperature. With increasing the surface temperature from 300 to 500 K, the scattering becomes more directional because of the increasing contribution of the direct-inelastic channel, which reduces the TMAC for the incident beam energy of 35 meV to 0.48.