Gas Flow In Nanochannels Research Articles

Quantum effects of gas flow in nanochannels

Abstract Based on the thermal theory of Newtonian mechanics, the pressure difference in the macro channels will drive the gas flow until the pressure difference inside is zero. However, the 12-year vacuum packaging experiments in our laboratory showed that when the macroscopic channel is reduced to a critical size and reaches the nanometer level, the gas flow inside the channel is hindered, that is, the differential pressure cannot become zero. To explain this paradoxical phenomenon, this study analyzes the flow of air molecules in the channel by using the De Broglie’s matter waves and Heisenberg’s uncertainty principle. Based on the law of quantum mechanics, when the diameter of the nanochannel is reduced to a certain size, it has a localized high pressure in the channel, which impedes the gas flow. This article introduces quantum mechanics into nanochannel’s gas fluid dynamics for the first time, expanding the new direction of fluid mechanics.

Molecular dynamics simulation on the splitting of shear flow in nanochannels

With the vigorous development of micro-/nanoscience and micro-/nanotechnology, fluid flows at the micro-/nanoscale have become an important research field. The molecular dynamics simulations of Couette flow in a nanochannel are carried out in this paper. In order to evaluate the non-equilibrium effect of the rarefied flow field, a “sampling-classification” method is proposed. Through this newly developed method, we found that the rarefied gas flow in nanochannels can be regarded as the superposition of two independent shear flows with the same shear rate. A nondimensional quantity “vd” is proposed to quantificationally evaluate the degree of splitting, or more specifically, the non-equilibrium state, of the flow field. Further study shows that the growth in roughness will aggravate this rarefied non-equilibrium effect, while the increase in system temperature leads to an opposite result. The “sampling-classification” method developed in this article can provide a new analytical idea for subsequent rarefied flow researchers, and the splittable phenomenon of shear flow discovered can also be regarded as an important property of rarefied flows that is worthy of further study.

Molecular Dynamics Simulation of Rarefaction Effect on Shear-driven Gas Flow in Nanochannels

The nanoscale gas flow at normal temperature and pressure varies from the slip flow regime to the transition regime, of which the character length changes across several nanometers to several thousand nanometers. The difference in the degree of rarefaction leads to different rules of the flow in nanochannels. In order to study the influence of rare gas effect on the nanoscale gas flow, we use three-dimensional molecular dynamics method to simulate the shear flow confined by two parallel plate under different Knudsen numbers, and then obtain the distribution of flow velocity, density, normal stress and shear stress, thus calculating and analyzing the variation of the tangential momentum accommodation coefficient. Counting the gas molecules according to the velocity with positive and negative values respectively, we find that the gas flow is decomposed into two independent shear flows, which indicates strong non-equilibrium characteristics in the nanochannel.

Surface effects on Couette gas flows in nanochannels

A three-dimensional non-equilibrium molecular dynamics method is adopted to investigate the influence of wall force field on the nanoscale gas flow in the transition regime. For the gas flow under nanoscale condition, the dominant effect of the wall force field on the flow field is more obvious, and the flow physical quantity is more sensitive to the change of the wall condition and system temperature. The motion of the wall atoms is governed by the Einstein theory, with using an elastic coefficient <i>k</i> to model the surface stiffness. The results indicate that the surface stiffness has little effect on the physical quantity distribution of the bulk flow region, but a certain influence on that of the near wall region. Increasing the value of the stiffness changes the velocity peak of the gas in the near-wall region and the tangential momentum adaptation coefficient (TMAC) towards lower values, thus demoting the momentum adaptability of the gas molecules to the surface. The wall roughness is simulated by a typical pyramidal model. It is found that the influence of wall roughness on the flow is very obvious, whether it is in the bulk flow region or in the near wall region. For the former case, the increase of roughness leads gas velocity and shear stress to increase, with density and normal stress remaining constant. The linear distribution of physical quantities is also affected to some extent. While for the latter case, as the roughness increases, the velocity of the fluid increases rapidly and approaches to the wall velocity. The peak of density increases, and the adsorption of gas molecules at the surface is obvious. The TMAC approaches to 1, suggesting that the gas and the surface achieve a complete momentum adaptation. Besides, the influence of system temperature on the gas flow in the nanochannel is also studied. The system temperature is controlled by the Nose-Hoover thermostat, making the flow field maintained at the target temperature through the damping coefficient. The results show that the effect of temperature is global in the whole flow region. The increase of temperature causes the flow velocity of the whole flow field to decrease, while the normal stress and shear stress to increase. A higher temperature leads to more frequent collisions between gas molecules, thus increasing the effective viscosity of the gas. At the same time, the degree of gas molecule adsorption in the near-wall region is reduced, contributing to a smaller TMAC value, and consequently a weaker gas-surface interaction.

Scaling law for slip flow of gases in nanoporous media from nanofluidics, rocks, and pore-scale simulations

In unconventional reservoirs, as the effective pore size becomes close to the mean free path of gas molecules, gas transport in porous media begins to deviate from Darcy’s law. The objective of this study is to explore the similarities of gas flows in nanochannels and core samples as well as those simulated by direct simulation BGK (DSBGK), a particle-based method that solves the Bhatnagar-Gross-Krook (BGK) equation.Due to difficulties in fabrication and experimentation, previous study on gas flow experiments in nanochannels is very limited. In this work, steady-state gas flow was measured in reactive-ion etched nanochannels with a controlled channel size on a sillicon wafer. A core-based permeability measurement apparatus was used to perform steady-state gas flow measurements on carbonate and shale samples. Klinkenberg permeability was obtained under varying pore pressures but constant temperature and effective stress. Methane was used in nanofluidic and rock experiments, making them directly comparable. Results from both experiments were then compared to gas flow simulations by DSBGK method carried out on several independently constructed geometry models. DSBGK uses hundreds of millions of simulated molecules to approximate gas flow inside the pore space. The intermolecular collisions are handled by directly integrating the BGK equation along each molecules trajectory, rather than through a sampling scheme like that in the direct simulation Monte-Carlo (DSMC) method. Consequently, the stochastic noise is significantly reduced, and simulation of nano-scale gas flows in complex geometries becomes computationally affordable.The slippage factors obtained from these independent studies varied across three orders of magnitude, yet they all appear to collapse on a single scaling relation where the slippage factor in the slip flow regime is inversely proportional to the square root of intrinsic permeability over porosity. Our correlation could also fit the data in the literature, which were often obtained using nitrogen, after correcting for temperature and gas properties. This study contributes to rock characterization, well testing analysis as well as the understanding of rarefied gas transport in porous media.

Molecular dynamics simulations of surface effects on Couette gas flows in nanochannels

Molecular dynamics method is used to investigate gas flows in nanoscale channels. A set of Couette gas flows with the same Knudsen number but different channel heights and densities is simulated to study the dimensional effects on dynamically similar flow conditions. Results show that the gas flow in the channels is divided into two regions:near wall region affected by a wall force field and bulk flow region affected by no wall force field. The flow characteristics in the bulk flow region are in good accordance with the kinetic theory predictions, which are characterized by constant density, normal stress, shear stress and linear velocity distribution while within the near wall region, the velocity, density, normal stress and shear stress distributions exhibit deviations from the kinetic theory predictions. The density and velocity sharply increase, accompanied with a single peak appearing. The normal stress which is dominated by the surface virial is anisotropic and changes drastically. Shear stress value is constant in bulk flow region and part of the near wall region, while the surface virial induces variation at a place about one atom diameter far from the wall. In the near wall region, the normalized density, velocity and stress tensor are constant under different channel heights and densities, which indicates that the gas flow characteristics in this area are determined by the wall force field. Besides, the tangential momentum accommodation coefficient (TMAC) values for different cases can be obtained through the relationship between TAMC and shear stress. It is found that under the same Knudsen number, the TMAC remains constant no matter what the height and density are. Furthermore, another set of Couette gas flows with different gas-surface potential strength ratios but the same channel height and density is simulated to study the gas-surface interaction effects on nanoscale gas flow. The results show that the gas density and velocity in the near wall region increase with increasing potential strength ratio between wall atoms and gas molecules. Large potential strength ratio cases (C 3.0) result in velocity sticking on the surface, which is induced by the gas molecule accumulation and surface adsorption. Using the same approach, the TMAC values for various potential strength ratios are calculated, varying from 0.63 to 0.96 for different cases (C=0.5-4.0), which indicates that the stronger the potential energy acting on the gas molecules, the more easily the gas molecules generate the diffuse reflection on the walls

Effect of various surface conditions on nanochannel flows past permeable walls

In this paper, effects of surface conditions on the gas flow in nanochannels with permeable walls have been investigated by molecular dynamics simulations. The hydrodynamic characteristics of the gas flow in nanochannels, including the density distributions, slip length and boundary friction coefficient, have been significantly influenced by the molecular interactions between gas molecules and wall atoms. The density layering phenomena are observed at the fluid–wall interface under a strong fluid–wall interaction (FWI). Particularly, there is a peak of the gas density on the permeable surface where the gas density is increased and about 3 times larger than the bulk one under the strong FWI. It indicates a strong non-continuum density distribution on the permeable surface and the step down in density from nanopores to the bulk region. On the other hand, the nanoscale vortices are produced in the nanopores. Moreover, the mass flux of gas flow in nanopores is reduced, and the hydrodynamic boundary has been shifted above the permeable surface further under the weak FWI. Slip characteristics on the permeable surface under various conditions are explored. It has been found that the slip length on the permeable surface may vary as a logarithmic function with the molecular mean free path. Apparently, the skin friction on the permeable surface is affected by the velocity slip. These results are significant in the understanding of nanoscale hydrodynamics.

Geometry effects on rarefied nanochannel flows

A three dimensional molecular dynamics method was used to study the effect of different geometries for rarefied gas flows in nanochannels. Argon molecules have been used. The velocity profiles in the channel were obtained and analyzed with three different channel geometries: a circular, a rectangular (square), and a slit channel. A channel width of 50 nm was used for the simulation. It was found that when using the same driving force, the maximum velocity of the flow increases when the geometry changes in the order from circular to rectangular to slit geometry, where the latter becomes 2–2.5 times as large compared with either the rectangular or circular channel. For Kn larger than 1.0, the rectangular channel showed a similar maximum and slip velocity as the circular channel while the velocity profile was qualitatively similar to the slit channel. The effect of different Knudsen numbers on the velocity profiles was also investigated. We found that for Kn larger than 2–3, the Knudsen number has a relatively small influence on the slip velocity for circular channels and rectangular channels. The effect of the accommodation coefficient on the average flow velocity for all three geometries was studied and expressed as an allometric equation model.

Simulation of High Knudsen Number Gas Flows in Nanochannels via the Lattice Boltzmann Method

Using a modified Lattice Boltzmann Method (LBM), pressure driven flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen number, Kn, covering the slip, transition and to some extend the free molecular regimes. The results agree very well with exiting empirical and numerical data.

Thermal Lattice Boltzmann Simulation of Rarefied Gas Flows in Nanochannels for Wide Range of Knudsen Number

Using a modified Lattice Boltzmann Method (LBM), developing thermal flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity and thermal conductivity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen numbers, Kn,. The results show that in spite of the standard LBM, the temperature distributions and the local Nusselt number obtained from this modified thermal LBM, agree well with the other numerical and empirical results in a wide range of Knudsen numbers.

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.

Molecular dynamics simulations of energy accommodation coefficients for gas flows in nano-channels

The energy accommodation coefficient (EAC) used in thermal boundary condition in micro- and nano-gas flows is reported to be always less than unity and greatly influenced by wall characteristics, for example, the wall temperature. A statistical EAC definition was described to calculate the EAC for thermal conduction in argon gas between two smooth platinum plates from two-dimensional non-equilibrium molecular dynamics simulations. The non-equilibrium EAC at the upper wall was calculated for different upper wall temperatures and a fixed bottom wall temperature. The equilibrium EAC at each temperature can then be extrapolated from a series of non-equilibrium EACs as the temperature difference between the two walls approaches zero. The analyses of the effects of wall temperature for various Knudsen number on non-equilibrium and equilibrium EACs show that, for a given lower bottom wall temperature, the non-equilibrium EAC at a high temperature wall increases with an increase in the wall temperature. For a given wall temperature difference, the non-equilibrium EAC increases with the increase in the wall temperatures. The equilibrium EAC also becomes larger at higher temperatures.