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Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures' effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived. [ABSTRACT FROM AUTHOR]

To improve the performance of valves in relation to the leakage rate, a comprehensive evaluation of the valve characteristics and behavior during pressure exposure is important. Often, these low gas flow rates below 0.1 cm3/min cannot be accurately measured with conventional flow sensors. This paper presents a small and low-cost test rig for measuring gas leakage rates accurately, even far below 0.1 cm3/min, with the pressure decay method. These leakage flows are substantiated with a flow model, where we demonstrate the feasibility of modeling those gas flows with an extended Navier–Stokes framework to obtain more accurate theoretical predictions. As expected, the comparison to the experimental results proves that the classical Navier–Stokes system is unsuitable for modeling Knudsen flows. Hence, self-diffusion of gas, a wall-slip boundary condition, and an effective mean free path model were introduced in a physically evident manner. In terms of the calculated mass flow, while self-diffusion and slip boundary conditions explain deviations from the classical Navier–Stokes equation for Knudsen numbers already smaller than 1, the effective mean free path model has an effect, especially when Kn > 1. For simplified conditions, an analytical solution was presented and compared to the results of an OpenFOAM CFD-solver for flow rates through more complex gap-flow geometries of the flap valve. Hereby, acceptable deviations between 10% and 20% were observed. A comparison with measurement results was carried out. The reproducibility of the measurement method was verified by comparing multiple measurements of one silicon microvalve sample to a state-of-the-art flow sensor. Three geometrically similar passive silicon microvalves were measured with air overpressure decreasing from 15 kPa relative to atmospheric pressure. Maximum gas volume flowing in a blocking direction of 1–26 µL/min with high reproducibility and marginal noise were observed. [ABSTRACT FROM AUTHOR]

Particle–particle and particle–gas processes significantly impact planetary precursors such as dust aggregates and planetesimals. We investigate gas permeability (⁠|$\kappa$|⁠) in 12 granular samples, mimicking planetesimal dust regoliths. Using parabolic flights, this study assesses how gravitational compression – and lack thereof – influences gas permeation, impacting the equilibrium state of low-gravity objects. Transitioning between micro- and hyper-gravity induces granular sedimentation dynamics, revealing collective dust–grain aerodynamics. Our experiments measure |$\kappa$| across Knudsen number (Kn) ranges, reflecting transitional flow. Using mass and momentum conservation, we derive |$\kappa$| and calculate pressure gradients within the granular matrix. Key findings: (i) As confinement pressure increases with gravitational load and mass flow, |$\kappa$| and average pore space decrease. This implies that a planetesimal's unique dust-compaction history limits subsurface volatile outflows. (ii) The derived pressure gradient enables tensile strength determination for asteroid regolith simulants with cohesion. This offers a unique approach to studying dust-layer properties when suspended in confinement pressures comparable to the equilibrium state on planetesimals surfaces, which will be valuable for modelling their collisional evolution. (iii) We observe a dynamical flow symmetry breaking when granular material moves against the pressure gradient. This occurs even at low Reynolds numbers, suggesting that Stokes numbers for drifting dust aggregates near the Stokes–Epstein transition require a drag force modification based on permeability. [ABSTRACT FROM AUTHOR]

We investigate and characterize the effect of compressibility and rarefaction on vortex structures in the benchmark lid-driven cavity flow. Direct numerical simulations are performed, employing the unified gas kinetic scheme to examine the changes in vortex generation mechanisms and the resulting flow structures at different Mach and Knudsen numbers. At high degrees of rarefaction, where inter-molecular interactions are minimal, the molecules mainly collide with the walls. Consequently, the dominant flow structure is a single vortex in the shape of the cavity. It is shown that increasing compressibility or decreasing rarefaction lead to higher molecular density in the cavity corners, due to more frequent inter-molecular collisions. This results in lower flow velocities, creating conditions conducive to the development of secondary and corner vortices. The physical processes underlying vortex formations at different Knudsen numbers, Mach numbers, and cavity shapes are explicated. A parametric map that classifies different regimes of vortex structures as a function of compressibility, rarefaction, and cavity shape is developed. [ABSTRACT FROM AUTHOR]

The influence of the deposition of nanoparticles of an aerosol, moving in a continuous reactor at a constant velocity, on the channel walls of the reactor and of the coagulation of these particles as a result of their Brownian diffusion on the nanoaerosol parameters was investigated. A simple one-dimensional model, adequately defining the diffusion, coagulation, and deposition of nanoaerosol particles in a wide range of change in its Knudsen number, has been constructed. It is shown analytically that, as the distance from the inlet of the reactor increases, the volume fraction of particles in the nanoaerosol decreases by the exponential law, and the radius of the clusters formed in the nanoaerosol as a result of the coagulation of its particles increases and tends to a limiting (maximum) value. A nonlinear integro-differential equation for the radius of such clusters has been obtained, and, from it, compact formulas for approximate calculation of its limiting radius have been derived. The characteristic distributions of the radii of clusters and of their concentrations along the reactor channel, calculated by the numerical method, are presented. It was established that, if this channel has a fairly large length, the clusters moving in it increase to their limiting size. The influence of the determining parameters of the flow of a nanoaerosol at the inlet to the continuous reactor on the distribution of its dispersion characteristics along the reactor channel, on the limiting size of the clysters in it, and on the characteristic length of the channel, at which the processes of deposition and coagulation of nanoaerosol particles are completed, is discussed. A comparison of the results of calculations of the parameters of a nanoaerosol moving in a continuous reactor by the one- and two-dimensional models has shown that the simple one-dimensional model defines the behavior of these parameters quite adequately. [ABSTRACT FROM AUTHOR]

Revealing the gas transport patterns at the microscale and nanoscale is of great scientific and engineering significance for unconventional oil and gas exploration and development. This paper first systematically analyzes the properties of gas transport mechanism under different Knudsen number conditions. Second, the coupling modes of the cross‐scale multi‐drive mechanism are systematically categorized, and three typical coupling calculation methods are pointed out. Again, the rationality of the cross‐scale multi‐agency coupling is quantitatively calculated. The results show that (a) Under the influence of Fick's diffusion equation, when Knr > 0, the coupled 'slip flow–Fick diffusion–Knudsen diffusion' equation does not converge to the Knudson diffusion equation. (b) The 'Fick diffusion–Knudsen diffusion' coupled equation is calculated to be more than 102 times as large as the Knudsen diffusion equation. [ABSTRACT FROM AUTHOR]

In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al2O3, for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/Dh), and volume fraction of Al2O3 nanoparticles (ϕ) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or ϕ would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/Dh ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and ϕ = 0.1 (Pr = 0.729). Finally, Nuavg, Nux, U/Um, and ReCf were corelated with Kn, Pr, Re, and x/Dh with proper coefficient of determination (R2) values. [ABSTRACT FROM AUTHOR]

In this work, we explore the Boltzmann equation with Fermi-Dirac statistics (briefly, BFD equation), which models the dilute gases when quantum effects are taking into consideration. Specifically, we firstly establish the uniform energy estimate and construct the global-in-time classical solutions of the scaled BFD equations under small assumption on the initial data. Then we use this uniform estimate to derive the acoustic limit from the scaled BFD equations within the context of classical solutions. Compared with our companion article Jiang and Zhou (2024) [23] , our uniform estimate in Knudsen number in this paper is crucial and hard to be obtained for the compressible Euler scaling and the acoustic limit is global-in-time, rather than almost global-in-time. [ABSTRACT FROM AUTHOR]

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number. [ABSTRACT FROM AUTHOR]

Due to its unique chemical structure, hydrogen energy inherently has a high calorific value without reinforcing global warming, so it is expected to be a promising alternative energy source in the future. In this work, we focus on nanoconfined hydrogen flow performance, a critical issue in terms of geological hydrogen storage. For nanopores where the pore scale is comparable to hydrogen's molecular size, the impact on hydrogen molecules exerted by the pore surface cannot be neglected, leading to the molecules near the surface gaining mobility and slipping on the surface. Furthermore, hydrogen adsorption takes place in the nanopores, and the way the adsorption molecules move is completely different from the bulk molecules. Hence, the frequently applied Navier–Stokes equation, based on the no-slip boundary condition and overlooking the contribution of the adsorption molecules, fails to precisely predict the hydrogen flow capacity in nanopores. In this paper, hydrogen molecules are classified as bulk molecules and adsorption molecules, and then models for the bulk hydrogen and the adsorption hydrogen are developed separately. In detail, the bulk hydrogen model considers the slip boundary and rarefaction effect characterized by the Knudsen number, while the flow of the adsorption hydrogen is driven by a chemical potential gradient, which is a function of pressure and the essential adsorption capacity. Subsequently, a general model for the hydrogen flow in nanopores is established through weight superposition of the bulk hydrogen flow as well as the adsorption hydrogen, and the key weight coefficients are determined according to the volume proportion of the identified area. The results indicate that (a) the surface diffusion of the adsorption molecules dominates the hydrogen flow capacity inside nanopores with a pore size of less than 5 nm; (b) improving the pressure benefits the bulk hydrogen flow and plays a detrimental role in reducing surface diffusion at a relatively large pressure range; (c) the nanoconfined hydrogen flow conductance with a strong adsorption capacity (PL = 2 MPa) could reach a value ten times greater than that with a weak adsorption capacity (PL = 10 MPa). This research provides a profound framework for exploring hydrogen flow behavior in ultra-tight strata related to adsorption phenomena. [ABSTRACT FROM AUTHOR]

The interaction of rarefied gases with functionalized surfaces is of great importance in technical applications such as gas separation membranes and catalysis. To investigate the influence of functionalization and rarefaction on gas flow rate in a defined geometry, pressure-driven gas flow experiments with helium and carbon dioxide through plain and alkyl-functionalized microchannels are performed. The experiments cover Knudsen numbers from 0.01 to 200 and therefore the slip flow regime up to free molecular flow. To minimize the experimental uncertainty which is prevalent in micro flow experiments, a methodology is developed to make optimal use of the measurement data. The results are compared to an analysis-based hydraulic closure model (ACM) predicting rarefied gas flow in straight channels and to numerical solutions of the linearized S-model and BGK kinetic equations. The experimental data shows that if there is a difference between plain and functionalized channels, it is likely obscured by experimental uncertainty. This stands in contrast to previous measurements in smaller geometries and demonstrates that the surface-to-volume ratio of 0.4 μ m - 1 seems to be too small for the functionalization to have a strong influence and highlights the importance of geometric scale for surface effects. These results also shed light on the molecular reflection characteristics described by the TMAC. [ABSTRACT FROM AUTHOR]

Featured Application: This study aims to fill a knowledge gap in rarefied gas flows, addressing the complexities related to wall temperatures and pressure differentials in the simulation of gas–solid interactions in nanoscale and microscale geometries. The findings are relevant to diverse microfluidic applications, encompassing devices such as micro–nano electronic devices. Simulations were carried out in non-dimensional form so that the results can be extended to all noble gases. As computer capabilities improve, Molecular Dynamics simulations are becoming more important for solving various flow problems. In this study, Couette and Poiseuille flows at different wall temperatures were investigated using a hard-sphere Molecular Dynamics simulation approach. Although a low spacing ratio was used in the simulations, the results are valid for rarefied gas flows when proper scaling based on the Knudsen number was used because only binary collisions with a hard-sphere model were considered. The main focus of this study was the examination of the effects of various wall speeds, pressure gradients, and wall temperatures. A pressure gradient was generated by developing a modified selective periodicity condition in the flow direction. With the combined effect of the pressure gradient and the wall velocities, subsonic, transonic, and supersonic speeds in nanochannels were examined. With the combination of different parameters, 1260 simulation cases were conducted. The results showed that there are temperature and velocity slips that are dependent on not only the temperature and velocity values but also on the magnitudes of a pressure gradient. The pressure gradient also caused nonlinearities in temperature and velocity profiles. [ABSTRACT FROM AUTHOR]

The objective of this study is to construct a refined microscopic transport model that elucidates the transport mechanisms of gas flow within micro-nano pores and fractures. The collective impact of various microscopic transport mechanisms was explained through the apparent permeability model, specifically related to gases such as methane and carbon dioxide, within the shale matrix. The apparent permeability models, taking into account microscopic transport mechanisms such as slippage flow, Knudsen diffusion, transition flow, and surface diffusion, were established individually. Subsequently, the influencing factors on apparent permeability were analyzed. The results demonstrate that the apparent permeability of the shale reservoir matrix is significantly influenced by pore pressure, temperature, pore size, and total organic carbon (TOC). As pressure decreases, the apparent permeability of Knudsen diffusion and surface diffusion increases, while the apparent permeability of slippage flow decreases. In addition, the apparent permeability of the reservoir matrix initially decreases and then increases. With increasing temperature, the apparent permeability of slippage flow, Knudsen diffusion, and surface diffusion all increase, as does the apparent permeability of the reservoir matrix. As pore size increases, the apparent permeability of surface diffusion and Knudsen diffusion decreases, while the apparent permeability of slippage flow and the reservoir matrix increases. Furthermore, an increase in TOC leads to no change in the apparent permeability of slippage flow and Knudsen diffusion, but an increase in the apparent permeability of surface diffusion and the reservoir matrix. The model presented in this paper enhances the multi-scale characterization of gas microflow mechanisms in shale and establishes the macroscopic application of these micro-mechanisms. Moreover, this study provides a theoretical foundation for the implementation of carbon capture, utilization, and storage (CCUS) in shale gas production. [ABSTRACT FROM AUTHOR]

As the condensation phenomenon occurs in the low-pressure stages of steam turbines, an accurate modelling of the condensing flows is very crucial and has a significant impact on the development of highly efficient steam turbines. In order to accurately simulate condensing steam flows, it is essential to choose the right condensation model. Further research to enhance condensation models is of special importance because the outcomes of numerical studies of condensation models in recent years have not been entirely compatible with the experiments and there are still uncertainties in this area. Therefore, the main aim of this paper is to evaluate a proposed droplet growth model for modelling condensation phenomenon in condensing steam flows. The new model is derived to profit from the advantages of models based on the continuum approach for large droplets and those based on the kinetic theorem for small droplets, which results in the model being robust for a wide range of Knudsen numbers. The model is implemented into a commercial CFD tool, ANSYS Fluent 2022 R1, using UDFs. The results of the CFD simulations are validated against experimental data for linear cascades within the rotor and stator blade geometries of low-pressure steam turbine stages. The findings clearly demonstrate the superiority of the new model in capturing droplet growth, particularly for very small droplets immediately following nucleation. In contrast, widely used alternative droplet growth models tend to either underpredict or overpredict the droplet growth rate. This research significantly contributes to the ongoing efforts to enhance condensation modeling, providing a more accurate tool for optimizing the design and operation of low-pressure steam turbines, ultimately leading to a higher energy efficiency and a reduced environmental impact. [ABSTRACT FROM AUTHOR]

In the present work, the gas flows through diverging channels driven by small, moderate, and large pressure drops are studied, considering a wide range of the gas rarefaction from free molecular limit through transition flow regime up to early slip regime. The analysis is performed using the Shakhov kinetic model, and applying the deterministic DVM method. The complete 4D flow problem is considered by including the upstream and downstream reservoirs. A strong effect of the channel geometry on the flow pattern is shown, with the distributions of the macroscopic quantities differing qualitatively and quantitatively from the straight channel flows. The mass flow rate data set from the complete solution is compared with the corresponding set obtained from the approximate kinetic methodology, which is based on the fully developed mass flow rate data available in the literature. In addition, the use of the end-effect approach significantly improves the applicability range of the approximate kinetic methodology. The influence of the wall temperature on the flow characteristics is also studied and is found to be strong in less-rarefied cases, with the mass flow rate in these cases being a decreasing function of the temperature wall. Overall, the present analysis is expected to be useful in the development and optimization of technological devices in vacuum and aerospace technologies. [ABSTRACT FROM AUTHOR]

Gas flow in shales follows a number of physical mechanisms that include Knudsen diffusion, Darcy flow, and adsorption in the matrix and micro pores. The aim of the study is to resolve the interplay of gas transport in these media at increased effective stress as well as net pore pressure. In this research, we investigated the nature of gas transport in the matrix of shale by sending He, CH4 and CO2 gases through a transient upstream pressure pulse decay instrument. A series of experiments were conducted at constant pore pressures and a gradually increasing confining pressure. The same study was done in three different scenarios, injecting He, CO2 and CH4. At a constant pore pressure, gas permeability appears to decrease with an increasing confining pressure and effective stress. With increasing effective stress, the slip factor also decreases along with the permeability. The decrease in slip could be attributed to prestressing, that is likely to create new fractures. Among the three purged gases, permeability of shale to CH4 is the highest, and that to CO2 is the lowest owing to its high adsorption. Higher permeability of CH4 against He, could be attributed to the dual transport mechanism. [ABSTRACT FROM AUTHOR]

Thermal transpiration flow, a flow from cold to hot, driven by a temperature gradient along a wall under a high Knudsen number condition, was studied using the molecular dynamics method with a two-dimensional channel consisting of infinite parallel plates with nanoscale clearance based on our previous study. To accelerate the numerical analysis, a dense gas was employed in our previous study. In this study, the influence of the number density of gas was investigated by varying the height of the channel while keeping the number of molecules to achieve the flow ranging from dense to dilute gas while maintaining a constant Knudsen number. From the flow velocity profile compared to the number density profile, the thermal transpiration flow was observed for all number density conditions from dense to dilute gas. A similar flow structure was exhibited regardless of the number density. Thus, the numerical analysis in a dense gas condition is considered to be valid and useful for analyzing the thermal transpiration flow. [ABSTRACT FROM AUTHOR]

Traditional research on apparent permeability in shale reservoirs has mainly focussed on effects such as poromechanics and porosity-assisted adsorption layers. However, for a more realistic representation of field conditions, a comprehensive multi-scale and multi-flowing mechanism model, considering the fracturing process, has not been thoroughly explored. To address this research gap, this study introduces an innovative workflow for dynamic permeability assessment. Initially, an accurate description of the pore size distribution (PSD) within three major mineral types in shale is developed using focussed ion beam-scanning electron microscopy (FIB-SEM) and nuclear magnetic resonance (NMR) data. Subsequently, an apparent permeability model is established by combining the PSD data, leading to the derivation of dynamic permeability. Finally, the PSD-related dynamic permeability model is refined by incorporating the effects of imbibition resulting from the fracturing process preceding shale gas production. The developed dynamic permeability model varies with pore and fracture pressures in the shale reservoir. The fracturing process induces water blockage, water-film formation, and water-bridging phenomena in shale, requiring additional pressure inputs to counteract capillary effects in hydrophilic minerals in shale, But also increases the overall permeability from increasing permeability at larger scale pores. Unlike traditional reservoirs, the production process commences when the fracture is depleted to 1–2 MPa exceeds the pore pressure, facilitated by the high concentration of hydrophobic organic matter pores in shale, this phenomenon explains the gas production at the intial production stage. The reduction in adsorption-layer thickness resulting from fracturing impacts permeability on a nano-scale by diminishing surface diffusion and the corresponding slip flow of gas. this phenomenon increases viscous-flow permeability from enlarged flow spacing, but the increased viscous flow does not fully offset the reduction caused by adsorbed-gas diffusion and slip flow. In addition to the phenomena arising from various field conditions, PSD in shale emerges as a crucial factor in determining dynamic permeability. Furthermore, considering the same PSD in shale, under identical pore spacing, the shape factor of slit-like clay minerals significantly influences overall permeability characteristics, much more slit-shaped pores(higher shape factor) reduce the overall permeability. The dynamic permeability-assisted embedded discrete fracture model (EDFM) showed higher accuracy in predicting shale gas production compared to the original model. [ABSTRACT FROM AUTHOR]

In this paper, we study the hydrodynamic limit of Boltzmann equations for gas mixture by Hilbert expansion method. We formally derive all the terms in the Hilbert expansion of Boltzmann equations according to different order about the Knudsen number. Then we truncate the expansion and justify the hydrodynamic limit of Boltzmann equations by establishing the uniform estimates of the remainder term. Our approach is based on L 2 − L ∞ framework, which is motivated by the study of the single Boltzmann equation in [22]. [ABSTRACT FROM AUTHOR]

The effect of phonon focusing on electron–phonon drag and thermopower in nanostructures based on potassium single crystals at low temperatures is studied. The role of quasi-longitudinal and quasi-transverse phonons, as well as shear waves, in the drag thermopower of the nanostructures is considered. It is shown that, in the Knudsen flow regime of a phonon gas, the slow quasi-transverse t2 mode makes the dominant contribution to the drag thermopower of the nanostructures and, only in directions close to the focusing of longitudinal phonons (L-phonons), their contribution become comparable to the contribution of the t2 mode. The directions of heat flux in which the maximum and minimum values of drag thermopower are achieved in nanowires, films, and nanoplates based on potassium single crystals are determined. The study of the effect of focusing on the phonon propagation in potassium single crystals made it possible to calculate a number of new, unusual effects in the anisotropy of drag thermopower in potassium-based nanostructures. These effects are mainly due to the competition between the contributions of the t2 mode and L-phonons to the drag thermopower. Since the relaxation rate of L-phonons on electrons in potassium is 25 times higher than for the t2 mode, with an increase in the transverse dimensions of potassium nanostructures, the anisotropy of the drag thermopower in them, in contrast to the anisotropy of thermal conductivity in dielectric nanostructures, changes nonmonotonically. It first increases, reaching a maximum, then decreases, and vanishes when the dimensions become macroscopic (D ≥ 10–1 cm). One of the interesting effects calculated in this work is the orientational anisotropy of drag thermopower in potassium nanoplates. In two identical nanoplates with a rectangular cross section, the thermopower in the direction of the temperature gradient [011] for the orientation of the wide faces of the {100} plates turns out to be significantly greater than for the {110} orientation. With increasing plate width, the orientational anisotropy of thermopower increases to 37%. It is shown that the orientational anisotropy of the thermopower is due to the effect of focusing on the phonon propagation in the plates. The competition between the contributions of the t2 mode and L-phonons, which determine the maximum and minimum values, leads to a nonmonotonic dependence of the orientational anisotropy of the drag thermopower on the thickness of the nanoplate. It is shown that, for square potassium films with {100} and {111} orientations of planes, the drag thermopower is isotropic in the film plane, but, for the {110} orientation, it becomes ellipsoidal with its major axis in the [001] direction. A characteristic feature of drag thermopower in square films is orientation anisotropy. For the [011] directions of the temperature gradient, the drag thermopower in potassium films with the {100} orientations of planes turns out to be significantly greater than with the {110} orientations. It behaves nonmonotonically, reaching a maximum of 57% at a thickness D = 2.2 × 10–5 cm. It is obvious that the effects calculated in this work open up new prospects for experimental studies of electron–phonon drag in metal films. [ABSTRACT FROM AUTHOR]

The aerodynamic optimization of a Gurney flap attached to the NACA 0012 airfoil in rarefied gas flow is studied in this study. In order to investigate the effects of Gurney flap geometry (height, mounting angle, and mounting location) and angle of attack on the aerodynamic characteristics of the airfoil in the rarefied gas flow, the flow fields around NACA 0012 airfoils with Gurney flap attached are simulated by using the direct simulation Monte Carlo method. Furthermore, the multi-objective aerodynamic optimization of the airfoil with Gurney flap is performed at the single design point, and the Pareto front is obtained. Based on the benchmark configuration (obtained from the Pareto front), aerodynamic optimization by controlling the mounting angle of the Gurney flap and the angle of attack is investigated over a wide range of Mach numbers (ranging from 2 to 4) and Knudsen numbers (ranging from 0.024 to 0.24) by constructing an artificial neural network model. The results show that through optimization, the lift-to-drag ratio of the airfoil is increased by up to 29.25% under the combination of different Mach numbers and Knudsen numbers, which significantly improves the aerodynamic characteristics. [ABSTRACT FROM AUTHOR]

Chemical vapor deposition (CVD) is a common industrial process that incorporates a complex combination of fluid flow, chemical reactions, and surface deposition. Understanding CVD processes requires rigorous and costly experimentation involving multiple spatial scales, from meters to nanometers. The numerical modeling of deposition over macro-scale substrates has been conducted in the literature and results show compliance with experimental data. For smaller-scale substrates, where the corresponding Knudsen number is larger than zero, continuum modeling does not provide accurate results, which calls for the implementation of molecular-level modeling techniques. In the current study, the finite-volume method (FVM) and Direct Simulation Monte Carlo (DSMC) method were combined to model the reactor-scale flow with CVD around micro- and nano-scale fibers. CVD at fibers with round cross-sections was modeled in the reactor, where fibers were oriented perpendicularly with respect to the feedstock gas flow. The DSMC method was applied to modeling flow around the matrix of nano-scale circular individual fibers. Results show that for smaller diameters of individual fibers with the same filling ratio, the residence time of gas particles inside the fibrous media reduces, and, consequently, the amount of material surface deposition decreases. The sticking coefficient on the fibers' surface plays an important role; for instance, increasing the sticking coefficient from 20% to 80% will double the deposition rate. [ABSTRACT FROM AUTHOR]

Microchannel heat exchangers are heat exchangers with a tube diameter of less than 1 mm. Conventional cooling approaches such as the forced‐air cooling technique fail in high technological compact systems because of the small‐sized surfaces of chips and circuits. In comparison, microchannel heat exchangers are being extensively utilized in compact‐sized devices where a high heat‐transfer medium is required. Moreover, consumers' continued desire for compact products has prompted researchers to study microchannel heat exchangers for their ability to boost the rate of heat transfer that ensures the safety of compact designs. This study presents the evaluation of performance parameters and the manufacturing aspects of microchannel heat exchangers. This study also examines how microchannel heat exchangers are affected by several parameters, including the type of working fluid used, Brownian motion, geometry of the channel, Reynolds number, Nusselt number, Knudsen number, wall resistance of the channel, the effect of gravity, and inlet and outlet arrangement for fluid. Investigating the various geometries for the microchannel indicates that the least pressure drop occurs in square shape cross‐section channels while the highest pressure drop occurs in channels with triangular cross‐sections. Moreover, it has been observed that, with the addition of nanoparticles to the working fluid, the thermal properties of the exchangers as well as the pressure drop increases while at the same time it reduces the boundary layer thickness. In addition, the Reynolds number affects the performance irrespective of the channel geometry. When the fluid is added with nanoparticles, like, Al2O3 and copper oxide (CuO) with different volumetric fractions (φ) of 0%, 0.5%, 1%, 1.5%, and 2%, the performance of the microchannel rises with rising the Reynolds number but conversely when the fluid is used in pure form the performance decreases with the rising value of Reynolds number. In addition, it has been observed that the overall improvement is obtained at φ = 2% and Re = 100 for CuO–water nanofluid. Apart from this, the least heat transfer is recorded at φ = 0.5% and Re = 1.00 for both nanofluids. Moreover, this study concludes that the Nusselt number is independent of the Reynolds number in the regime of laminar flow. It is further evident that as the nanoparticle size reduces, the Nusselt number rises when all the remaining conditions are the same. Apart from this, investigating the inlet/outlet arrangement through finite volume method for D‐, I‐, N‐, S‐, U‐, and V‐type arrangements, it is evident that the V‐type sink has overall greater performance. In terms of gravity, it is observed that it has no effect on the performance of microchannel heat exchangers. This study further illustrates the effects of the fabrication method on the performance of the microchannel heat exchangers. [ABSTRACT FROM AUTHOR]

By way of mathematical and numerical simulation of an nonisothermic flow of a gas with nanoparticles in a tubular continuous-flow reactor with an nonuniform temperature field, the influence of the diffusion (Brownian diffusion and thermodiffusion) of nanoparticles in this flow and their diffusion deposition on the walls of the reactor on the parameters of the gas-suspension flow in it was investigated. The problem on the two-dimensional flow of a nanogas suspension with a nonuniform transverse velocity profile in such a reactor was solved. The longitudinal and transverse distributions of the concentration of nanoparticles in this suspension and its temperature in the reactor were obtained by the numerical finite difference method. The influence of the initial concentration of nanoparticles in the gas flow at the inlet cross section of the reactor and the Knudsen number of the nanoparticles (their sizes in fact) on the distributions of the characteristics of the disperse-mixture flow in the reactor was determined. [ABSTRACT FROM AUTHOR]

We have studied the impact of the nonextensivity on the transport coefficients related to charge and heat in thermal QCD. For this purpose, the electrical ( σ el ), Hall ( σ H ), thermal (κ ) and Hall-type thermal ( κ H ) conductivities are determined using the kinetic theory approach in association with the nonextensive Tsallis statistical mechanism. The effect of nonextensivity is encoded in the nonextensive Tsallis distribution function, where the deviation of the parameter q from 1 signifies the degree of nonextensivity in the concerned system. The thermal and electrical conductivities are found to increase with the introduction of nonextensivity, which means that the deviation of the medium from thermal equilibrium enhances both charge and heat transports. With the magnetic field, the deviations of σ el , σ H , κ and κ H from their respective equilibrated values increase, whereas these deviations decrease with the chemical potential. We have also studied how the extent of the nonextensivity modulates the longevity of magnetic field. Present work is further extended to the study of some observables associated with the aforesaid transport phenomena, such as the Knudsen number and the elliptic flow within the nonextensive Tsallis framework. [ABSTRACT FROM AUTHOR]

Potential CO2 leakage from deep geologic reservoirs requires evaluation on a site-specific basis to assess risk and arrange mitigation strategies. In this study, a heterogeneous and realistic numerical model was developed to investigate CO2 migration pathways and uprising time in a shaly overburden, located in the Malaysian off-shore. Fluid flow and reactive transport simulations were performed by TOUGHREACT to evaluate the: (1) seepage through the caprock; (2) CO2-rich brine leakage through a fault connecting the reservoir with seabed. The effect of several factors, which may contribute to CO2 migration, including different rock types and permeability, Fickian and Knudsen diffusion and CO2 adsorption in the shales were investigated. Obtained results show that permeability mainly ruled CO2 uprising velocity and pathways. CO2 migrates upward by buoyancy without any important lateral leakages due to poor-connection of permeable layers and comparable values of vertical and horizontal permeability. Diffusive flux and the Knudsen flow are negligible with respect to the Darcy regime, despite the presence of shales. Main geochemical reactions deal with carbonate and pyrite weathering which easily reach saturation due to low permeability and allowing for re-precipitation as secondary phases. CO2 adsorption on shales together with dissolved CO2 constituted the main trapping mechanisms, although the former represents likely an overestimation due to estimated thermodynamic parameters. Developed models for both scenarios are validated by the good agreement with the pressure profiles recorded in the exploration wells and the seismic data along a fault (the F05 fault), suggesting that they can accurately reproduce the main processes occurring in the system. [ABSTRACT FROM AUTHOR]

The ultra-fast laser heating process of nano-films is characterized by an ultra-short duration and ultra-small space size, in which the classical Fourier law based on the hypothesis of local equilibrium is no longer applicable. Based on the Cattaneo–Vernotte (CV) model and the dual-phase-lag (DPL) model, the two-dimensional analytical solutions of heat conduction in nano-films under ultra-fast laser are obtained using the integral transformation method. The results show that there is a thermal wave phenomenon inside the film, which becomes increasingly evident as the elapse of the lag time of the temperature gradient. Moreover, the wave amplitude in the vertical direction is much larger than that in the horizontal direction of the nano-film. By comparing the numerical result of the two models, it is found that the temperature distribution inside the nano-film based on the DPL model is gentler than that of the CV model. Additionally, the temperature distribution in the two-dimensional solution is lower than that in the one-dimensional solution under the same Knudsen number. In the comparison results of the CV model, the maximum peak difference in the thermal wave reaches 75.08 K when the Knudsen number is 1.0. This demonstrates that the horizontal energy carried by the laser source significantly impacts the temperature distribution within the film. [ABSTRACT FROM AUTHOR]

• Experimental determination of H 2 O(v) transport through packed beds of Lunar Highland and Lunar Mare Simulants. • Piecewise model developed to predict H 2 O(v) transport in slip and Knudsen flow regimes. • Diffusion and viscous flow permeability dependent on simulant particle size distribution. H 2 O(v) transport through packed beds of lunar mare and lunar highland simulants was examined for relevant in-situ resource utilization conditions to inform volatile H 2 O extraction from the lunar surface. Experiments were conducted with different packed beds at average bed pressures of 105 and 3,960 Pa at ∼ 350 K for different flow regimes in the range of 0.47 < Kn ¯ < 20.7. A piecewise model was used to describe the transition between the advective flow regime and the Knudsen flow regime. Non-linear regression was used to determine a tortuosity shape factor of 2.6175 ± 0.0092 and 0.0937 ± 0.0008, a transition Knudsen number of 1.5984 and 4.0995, and a viscous flow permeability of 0.8238 ± 0.0010 × 10-12 m2 and 5.4805 ± 0.0061 × 10-12 m2 for the lunar mare and lunar highland simulants, respectively. The resulting Knudsen diffusivities were 6.6530 ± 0.0018 cm2·s−1 and 18.9008 ± 0.0100 cm2·s−1, respectively. These results are necessary for informing the development of in-situ resource utilization technologies for the thermal extraction of H 2 O. [ABSTRACT FROM AUTHOR]

We show theoretically that the mean turbulent dynamics can be described by a kinetic theory representation with a single free relaxation time that depends on space and time. A proper kinetic equation is constructed from the Klimontovich-type kinetic equation for fluid elements, which satisfies the Navier–Stokes hydrodynamics exactly. In a suitably averaged form, the turbulent kinetic energy plays the role of temperature in standard molecular thermodynamics. We show that the dynamics of turbulent fluctuations resembles a collision process that asymptotically drives the mean distribution towards a Gaussian (Maxwell–Boltzmann) equilibrium form. Non-Gaussianity arises directly from non-equilibrium shear effects. The present framework overcomes the bane of most conventional turbulence models and theoretical frameworks arising from the lack of scale separation between the mean and fluctuating scales of the Navier-Stokes equation with an eddy viscous term. An averaged turbulent flow in the present framework behaves more like a flow of finite Knudsen number with finite relaxation time, and is thus more suitably described in a kinetic theory representation. [ABSTRACT FROM AUTHOR]

An improved dual-phase-lagging model which reflects size effects caused by nanostructures is utilized to investigate the 2-D thermal conduction of nanosilicon films irradiated by ultrafast laser. The integral transformation method is used to solve the conduction governing equation based on the improved dual-phase-lagging model. The variation of the internal temperature along the thickness direction and the radial direction of the thin film is analyzed. We find that the temperature increases rapidly in the heated region of the film, and as time goes by, the energy travels from the heated end to another end in a form of wave. Although both the improved dual-phase-lagging model and the dual-phase-lagging model can obtain similar thermal wave temperature fields, the temperature distribution in the film obtained by the improved dual-phase-lagging model is relatively flat, especially for high Knudsen number. Under the same Knudsen number, the temperature obtained by the 2-D improved dual-phase-lagging model is higher than that obtained by the 1-D model, and the temperature difference becomes larger and larger as time elapses. [ABSTRACT FROM AUTHOR]

The present study investigates the shock wave propagation and diffraction characteristics in a micro-shock tube with sudden expansion and compares with the well-established classical shock wave diffraction in macro-length scale sudden expansions using computational techniques. The Knudsen number for the present micro-shock tube falls in the slip regime and therefore the fluid flow is simulated using the continuum-based Navier–Stokes equation with Maxwell's slip jump boundary condition. It is found that the shock wave attenuates rapidly in micro-shock tube compared to the shock wave propagation in macro-shock tube. The shock wave diffraction in micro-steps shows similar characteristics compared to macro-steps, such as reflection of the diffracted shock wave from the outer wall and the subsequent transition from regular reflection to Mach reflection, the vortex formation at the step corner, Mach reflection shock structure in the shock-processed gas exiting from the shock tube. However, the secondary shock wave formed due to the interaction of the reflected shock wave with the corner vortex is not seen for the micro-step case compared to the macro-step case. This can be attributed to the reduction in shock strength produced by the thick boundary layer in micro-shock tubes. Different step sizes have been compared for the micro-shock tube with sudden expansion ranging from the step size 1.5 to 3. Also, a detailed comparison has been done between micro- and macro-shock tube with sudden expansion. It is also found that the use of slip velocity increases the shock wave propagation speed compared to the no-slip boundary condition. [ABSTRACT FROM AUTHOR]

The influence of the inertia of submicron particles on their deposition from a Stokes flow in model fine-fiber filters is considered at low Reynolds numbers. The fiber collection efficiencies are calculated by the limiting trajectory method for a cell model of the filter and for a row of parallel fibers oriented perpendicularly to the direction of the gas flow for the ranges of interception parameter R = 0.01–1, Stokes number Stk = 0–20, and Knudsen number Kn = 0–1. The simulation results are consistent with the experimental data. [ABSTRACT FROM AUTHOR]

The evaporation/decomposition behavior of the ionic liquid 1-butyl-3-methylimidazolium chloride (BMImCl) was studied with various techniques, such as thermogravimetry (TG), Knudsen effusion mass loss (KEML), and Knudsen effusion mass spectrometry (KEMS), in order to investigate the competition between the simple evaporation of the liquid as gaseous ion pairs (NIP: neutral ion pair) and the thermal decomposition releasing volatile species. TG/DSC experiments were carried out from 293 to 823 K under both He and N2 flowing atmospheres on BMImCl as well as on BMImNTf2 (NTf2: bis(trifluoromethylsulfonyl)imide). Both ionic liquids were found undergoing a single step of mass loss in the temperature range investigated. However, while the BMImNTf2 mass loss was found to occur in different temperature ranges, depending on the inert gas used, the TG curves of BMImCl under helium and nitrogen flow were practically superimposable, thus suggesting the occurrence of thermal decomposition. Furthermore, KEML experiments on BMImCl (in the range between 398 and 481 K) indicated a clear dependence of the unit area mass loss rate on the effusion hole diameter, an effect not observed for the ILs with NTf2 anion. Finally, KEMS measurements in the 416–474 K range allowed us to identify the most abundant species in the vapor phase, which resulted in methyl chloride, butylimidazole, butyl chloride, and methylimidazole, which most probably formed from the decomposition of the liquid. [ABSTRACT FROM AUTHOR]

The dynamics behavior and stability of axially functionally graded fluid-conveying nanotube is investigated, in this paper. The simultaneous influence of both fluid flow and variation of modulus of elasticity on the behavior of simply-simply supported (S-S) and clamp-clamp (C-C) boundary conditions conveying fluid were studied. Small-scale effects are considered using nonlocal couple stress theory in the solid part and in the fluid part. Based on the nonlocal couple stress theory, Bernoulli-Euler beam theory, and Hamilton's principle, the governing equation of motion, and associated boundary conditions were derived to explain fluid-structure interaction (FSI). These equations were solved using Galerkin numerical method and temporal differential equation analysis method. The effects of some parameters such as Knudsen number, density, size parameter, and ... were investigated. According to the results, it can be seen that the present method has created an equilibrium for the effect of the size parameters (µ, l) on the critical velocity. The higher value of the Knudsen number caused sooner divergence and flutter instabilities to happen. The results show that if the parameters of the size effect are not considered, it causes errors in the calculations. The obtained results confirm the crucial effects of size. [ABSTRACT FROM AUTHOR]

Two-dimensional developing flow in the entrance of a microchannel has been studied numerically. Due to its nature, a microchannel can be used in tight space applications and the length of channel can get very small values. Furthermore, if the hydrodynamic development length of flow in microchannel has comparably the same value with the channel length, the channel entrance parameters play critical role on the flow performance of a microscale channel. Lattice Boltzmann Method (LBM) was considered for studying and simulating the developing slip flows through a rectangular microchannel. A unique computational code for this study was developed by using LBM. The slip velocity boundary condition along with Knudsen number values in the slip flow regime was used for this model. The bounce-back boundary condition was considered at the top and bottom walls of the microchannel. The effects of the Reynolds numbers (1-100) and Knudsen numbers (0.001, 0.01, 0.1) on the hydrodynamic entrance length has been examined. The numerical results have been compared with the previous studies in the literature and the similarities have been found satisfactory. The entrance length is found to be increasing with the increase of Reynolds and Knudsen numbers. A correlation for hydrodynamic development length as a function of Knudsen and Reynolds numbers was obtained by using the data extracted from LBM simulations performed in this study. [ABSTRACT FROM AUTHOR]

Efficient modeling of rarefied flow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad's distribution function for 13 moments-based moment gas kinetic solver (G13-MGKS) and the macroscopic governing equations are derived based on the moment integral of the discrete Boltzmann equation under the finite volume framework. Numerical fluxes at the cell interface related to the macroscopic variables, stress and heat flux can be reconstructed from the Boltzmann equation along the characteristic line directly. The initial distribution function is approximated by Grad's distribution function for 13 moments at the cell interface, so the explicit expression of numerical fluxes could be derived to release the present solver from the discretization and numerical integration in the molecular velocity space. The G13-MGKS with the discrete and explicit form of numerical fluxes are examined by several tests covering the steady and unsteady flows from the continuum regime to rarefied flow regimes. Numerical results indicate that the G13-MGKS could simulate continuum flows accurately and present reasonable predictions for rarefied flows at moderate Knudsen numbers. Moreover, the consumption of computations and memory demonstrates that the present framework could preserve high efficiency. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics simulations of fibrous filters with 56 combinations of different fiber sizes, packing densities, face velocities, and thicknesses were conducted for developing models that predict pressure drops across nanofiber filters. The accuracy of the simulation method was confirmed by comparing the numerical pressure drops to the experimental data obtained for polyacrylonitrile electrospun nanofiber filters. In the simulations, an aerodynamic slip effect around the surface of the small nanofibers was considered. The results showed that, unlike in the case of conventional filtration theory, pressure drops across the thin layers of electrospun nanofiber filters are not proportional to the thickness. This might be a critical factor for obtaining precise pressure drops across the electrospun nanofiber filters with extremely thin layers. Finally, we derived the product of drag coefficient and Reynolds number as a function of packing density, Knudsen number, and ratio of thickness to fiber diameter to get the correlation equation for pressure drop prediction. The obtained equation predicted the pressure drops across the nanofiber filters with the maximum relative difference of less than 15%. [ABSTRACT FROM AUTHOR]

In this study, we propose a new sub-diffusion two-temperature model and its accurate numerical method by introducing the Knudsen number ( K n ) and two Caputo fractional derivatives ( 0 < α , β < 1 ) in time into the parabolic two-temperature model of the diffusive type. We prove that the obtained sub-diffusion two-temperature model is well posed. The numerical scheme is obtained based on the L 1 approximation for the Caputo fractional derivatives and the second-order finite difference for the spatial derivatives. Using the discrete energy method, we prove the numerical scheme to be unconditionally stable and convergent with O (τ min { 2 − α , 2 − β } + h 2) , where τ , h are time and space steps, respectively. The accuracy and applicability of the present numerical scheme are tested in two examples. Results show that the numerical solutions are accurate, and the present model and its numerical scheme could be used as a tool by changing the values of the Knudsen number and fractional-order derivatives as well as the parameter in the boundary condition for analyzing the heat conduction in porous media, such as porous thin metal films exposed to ultrashort-pulsed lasers, where the energy transports in phonons and electrons may be ultraslow at different rates. [ABSTRACT FROM AUTHOR]

• A unified CFD-particle method is proposed for multiscale rarefied flows. • By introducing the simplified hydrodynamic-wave flux, the particle solver can transfer to the CFD solver adaptively. • Error analysis proves that the simplified treatment preserves the second-order accuracy of the present method. • Tens of times speedup ratio could be achieved compared to the DVM. Coupling the Computational Fluid Dynamics (CFD) with the stochastic particle method to address multi-scale rarefied flows remains of great interest to many researchers. Rather than involving the field decomposition and the information exchange, the simplified hydrodynamic-wave particle method (SHWPM) has been proposed in this paper to automatically switch from the stochastic particle solver to the conventional CFD method in the multi-scale simulation. The weights to couple the respective numerical fluxes are derived based on the integral solution of the Boltzmann equation. By introducing the simplified hydrodynamic-wave flux that can be computed by the linear combination of inviscid and viscous fluxes from the conventional CFD solver, the collision effects of particles are calculated in a macroscopic approach and the number of sampling particles could be significantly reduced in the near-continuum regime. Error analysis demonstrates that the simplified treatment can preserve the second-order accuracy and asymptotic preserving property of the present method in both the continuum and free molecular limits. Several numerical cases over a wide range of Knudsen and Mach numbers exhibit the capability of SHWPM for modeling the multiscale flow accurately and efficiently. The example of hypersonic flow passing a cylinder shows that the SHWPM could achieve tens of times speedup ratio compared to the discrete velocity method (DVM) in the continuum regime. [ABSTRACT FROM AUTHOR]

The derivation of analytical equations of non-continuum macroscopic transport phenomena is underpinned by approximate descriptions of the particle distribution function and is required due to the inability of the Navier–Stokes equations to describe flows at high Knudsen number (Kn ∼ 1). In this paper, we present a compact representation of the second-order correction to the Maxwellian distribution function and 13-moment transport equations that contain fewer terms compared to available moment-based representations. The intrinsic inviscid and isentropic assumptions of the second-order accurate distribution function are then relaxed to present a third-order accurate representation of the distribution function, using which corresponding third-order accurate moment transport equations are derived. Validation studies performed for Grad's second problem and the force-driven plane Poiseuille flow problem at non-zero Knudsen numbers for Maxwell molecules highlight an improvement over results obtained by using the Navier–Stokes equations and Grad's 13-moment (G13) equations. To establish the ability of the proposed equations to accurately capture the bulk behavior of the fluid, the results of Grad's second problem have been validated against the analytical solution of the Boltzmann equation. For the planar Poiseuille flow problem, validations against the direct simulation Monte Carlo method data reveal that, in contrast to G13 equations, the proposed equations are capable of accurately capturing the Knudsen boundary layer. [ABSTRACT FROM AUTHOR]

The dynamic coefficients of a dry gas seal affect the dynamic characteristics of rotor-seal systems. Fluid films in a dry gas seal can be laminar, turbulent or with slip conditions, according to various operating conditions and design parameters. They can be defined as laminar or turbulent, depending on the Reynolds number, and as slip or non-slip, depending on the Knudsen number. However, previous research did not consider the effect of laminar, turbulent and slip conditions on the dynamic coefficients of a dry gas seal. We proposed a mathematical perturbation method to calculate the dynamic coefficients of the dry gas seal according to laminar, turbulent, and slip effects. We derived the perturbed equations of the modified Reynolds equation, which includes the effects of laminar, turbulent and slip conditions. The pressure of the modified Reynolds equation was solved using the finite element method and the Newton–Raphson method, and the perturbed pressures with respect to three degrees of freedom were calculated by substituting the calculated pressure into the perturbed equations. We verified the proposed method by comparing the simulated results with prior studies. The dynamic coefficients of a T-grooved dry gas seal were investigated according to laminar, turbulent, and slip conditions in a fluid film with different clearances. [ABSTRACT FROM AUTHOR]

The deposition of aerosol particles from a Stokes flow in filters composed of nanofibers has been considered at Knudsen numbers ∼ 1. The efficiency of particle collection by model filters with 2D and 3D structures has been determined by numerical simulation as depending on particle radius , filter parameters (nanofiber radius , packing density , and filter thickness), and filtration conditions taking into account the gas slip at the fibers. It has been shown that the efficiencies of particle collection by nanofibers in model 2D and 3D filters are almost equal at the same low packing density < 0.02. It has been found that the dependence of the penetration of particles on their radius at a constant velocity on the order of several centimeters per second and at ∼ 1 passes through a maximum, which corresponds to particle radius . The calculated sizes of the most penetrating particles agree with experimental data. The results obtained will be used when selecting aerosols for testing nanofibrous filters. [ABSTRACT FROM AUTHOR]

We are proposing a model mathematical description of droplet evaporation using the kinetic approach. We have obtained the basic equation of the theory by using the law of conserving the full power of the vapor–liquid system, which has not been done before. We have found the range of droplet sizes at which it is stable. We have given a comparison of the obtained results with the known traditional ones. We have given numerical estimates for the critical size of the fine-dispersed phase up to the value of which ordinary evaporation takes place (that is for Knudsen number K n = l R , inequality K n ≪ 1 must be fulfilled, where l − is the free path of the molecule and R − is the droplet radius). We have given the optimal droplet size which is the most effective from the point of view of technical use in extinguishing flammable oil transformers. [ABSTRACT FROM AUTHOR]

Shale gas has become one of the important contributors to the global energy supply. The declining pattern of the gas production rate with time from an unconventional gas reservoir is due to the depletion of shale gas stored in the nanovoids of the shale formation. However, there are only limited ways to predict the variation of the gas production rate with time from an unconventional gas reservoir. This is due to the multiple transport mechanisms of gas in nano-scale pores and changes in shale gas permeability with pressures in nano-scale pores, which is impacted by the pore structure of the shale. In this study, the permeability-pressure (K-p) relationship for different shales (Eagle Ford, Haynesville, Longmaxi and Opalinus) were determined using an equivalent anisotropic pore network model (PNM). This PNM has REV-scale shale gas flow in randomly generated nanovoids and their connection in the shale matrix, and the multiphase flow of shale gas including viscous flow, slip flow and Knudsen diffusion. These predicted K-p correlations were then used in a finite element model (FEM) to predict the variation of the gas production rate with time (flux-time curves) at the macroscale. The simulation results show that the flux-time curves can be simplified to two linear segments in logarithmic coordinates, which are influenced by the fracture length and initial gas pressure. The predicted results using the PNM-FEM were validated by comparing them with the reported field test data. The method described in this study can be used to upscale the gas transport process from micro- to macroscale, which can provide a predictive tool for the gas production in shales. [ABSTRACT FROM AUTHOR]

The size of micro- and nanofluidic devices accounts for their operation in modes that differ significantly from those for the corresponding macroscopic counterparts. Deep understanding of gas-dynamic processes occurring in micro- and nanofluidic systems opens new opportunities for the practical use of molecular transport at the micro- and nanoscale. Models and simulation methods with high reliability are described. The article also outlines the important flow parameters which must be considered in the first place to correctly simulate gas-dynamic processes in micro- and nanofluidic systems. The review will be useful as a reference for researchers interested in implementing preliminary analysis in the development and optimization of micro- and nanofluid devices. [ABSTRACT FROM AUTHOR]

Accurate representations of slip and transitional flow regimes present a challenge in the simulation of rarefied gas flow in confined systems with complex geometries. In these regimes, continuum-based formulations may not capture the physics correctly. This work considers a regularized multi-relaxation time lattice Boltzmann (LB) method with mixed Maxwellian diffusive and halfway bounce-back wall boundary treatments to capture flow at high Kn. The simulation results are validated against atomistic simulation results from the literature. We examine the convergence behavior of LB for confined systems as a function of inlet and outlet treatments, complexity of the geometry, and magnitude of pressure gradient and show that convergence is sensitive to all three. The inlet and outlet boundary treatments considered in this work include periodic, pressure, and a generalized periodic boundary condition. Compared to periodic and pressure treatments, simulations of complex domains using a generalized boundary treatment conserve mass but require more iterations to converge. Convergence behavior in complex domains improves at higher magnitudes of pressure gradient across the computational domain, and lowering the porosity deteriorates the convergence behavior for complex domains. [ABSTRACT FROM AUTHOR]

The direct simulation Monte Carlo (DSMC) method, which is a probabilistic particle-based gas kinetic simulation approach, is employed in the present work to describe the physics of rarefied gas flow in super nanoporous materials (also known as mesoporous). The simulations are performed for different material porosities ( 0.5 ≤ ϕ ≤ 0.9 ), Knudsen numbers ( 0.05 ≤ Kn ≤ 1.0 ), and thermal boundary conditions (constant wall temperature and constant wall heat flux) at an inlet-to-outlet pressure ratio of 2. The present computational model captures the structure of heat and fluid flow in porous materials with various pore morphologies under rarefied gas flow regime and is applied to evaluate hydraulic tortuosity, permeability, and skin friction factor of gas (argon) flow in super nanoporous materials. The skin friction factors and permeabilities obtained from the present DSMC simulations are compared with the theoretical and numerical models available in the literature. The results show that the ratio of apparent to intrinsic permeability, hydraulic tortuosity, and skin friction factor increase with decreasing the material porosity. The hydraulic tortuosity and skin friction factor decrease with increasing the Knudsen number, leading to an increase in the apparent permeability. The results also show that the skin friction factor and apparent permeability increase with increasing the wall heat flux at a specific Knudsen number. [ABSTRACT FROM AUTHOR]

A computational investigation of the dynamics of gas expansion due to intense nanosecond laser evaporation into vacuum has been carried out. The problem is solved in a one-dimensional approximation, which simplifies calculations and at the same time allows one to analyze the main features of the expansion dynamics. For analysis we use three different approaches. Two of them are based on kinetic analysis via the direct simulation Monte Carlo (DSMC) method and numerical solution of the model Bhatnagar–Gross–Krook (BGK) equation. The third one focuses on derivation of an analytical continuum solution. Emphasis is placed on the analysis of the velocity distribution function and the average energy of particles passing through the time-of-flight detector on the normal to the evaporation surface, which is important for interpreting experimental measurements. The formulated problem is quite difficult as the considered flow is time-dependent, contains discontinuities in boundary conditions and involves large variations of local Knudsen numbers as well as steep gradients of the velocity distribution function. Data were obtained on the particle energy in the time-of-flight distribution for the range of regimes from the free molecular flow to continuum one. The maximum attainable average energy of particles in the time-of-flight distribution is determined. The non-monotonicity of the energy increase was found, which is explained based on analysis of the velocity distribution of particles. [ABSTRACT FROM AUTHOR]

In the present study, we propose the use of a light, inert carrier gas to support deposition uniformity and rate in continuous physical vapor deposition, in which closely spaced slots or nozzles are required to achieve a sufficiently high deposition rate. Interaction shocks between the emerging rarefied plumes cause undesired nonuniformities in the deposited coating. The present work evaluates the effect of adding a carrier gas on the interaction shock. We study the interaction between two sonic plumes consisting of a binary mixture, i.e., silver as coating material and helium as a light inert carrier gas, by direct simulation Monte Carlo. While the inlet Mach and Knudsen numbers were kept constant, the fraction of carrier gas was varied to single out the effect of species separation. The influence of rarefaction on species separation was also studied. Species separation produces a high carrier-gas fraction in the periphery and an accumulation of the heavier species in the jet core. The resulting change in the speed of sound alters the local expansion characteristics and, thus, shifts the shock location and weakens the shock. These phenomena intensify with the degree of rarefaction. It is shown that adding a light carrier gas increases deposition rate may enhance uniformity and reduce stray deposition. [ABSTRACT FROM AUTHOR]

As a key technical aspect contributing to shale gas development, nanoconfined methane flow behavior has received tremendous research interest, which remains challenging to understand clearly. The majority of previous contributions put emphasis on the mechanism model for methane confined in a single nanopore; at the same time, the other part focusing on an upscaling approach fails to capture the spatial pore-network characteristics as well as the way to assign pressure conditions to methane flow behavior. In light of the current knowledge gap, pore-network modeling is performed, in which a pore coordination number, indicating the maximum pores a specified pore can connect, gas flow regimes classified by Knudsen numbers, as well as different assigned pressure conditions, are incorporated. Notably, the pore-network modeling is completely self-coded, which is more flexible in adjusting the spatial features of a constructed pore network than a traditional one. In this paper, the nanoconfined methane flow behavior is elaborated first, then the pore network modeling method based on the mass conservation principle is introduced for upscaling, and in-depth analysis is implemented after that. Results show that (a) as for porous media with pore sizes ranging from 5~80 nm, dramatic advancement on apparent gas permeability takes place while pressure is less than 1 MPa; (b) apparent gas permeability evaluated at a specified pressure shall be underestimated by as much as 31.1% on average compared with that under the pressure-difference condition; (c) both a large pore size and a high coordination number are beneficial for strong gas flow capacity through nanoscale porous media, and the rising ratio can reach about 6 times by altering the coordination number from 3 to 7, which is quantified and presented for the first time. [ABSTRACT FROM AUTHOR]