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The Vlasov–Maxwell–Landau (VML) system and the Vlasov–Maxwell–Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the hydrodynamic limits of both the VML and the noncutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or noncutoff VMB system converges globally over time to the smooth global solution of the Euler–Maxwell system as the Knudsen number approaches zero. The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau‐type equations and noncutoff Boltzmann‐type equations with a magnetic field. Furthermore, the approach developed in this paper can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations. [ABSTRACT FROM AUTHOR]

A gas pressure distribution calculation method for viscous laminar and intermediate flows is developed. By introducing the pseudo-conductance for viscous laminar flow, linearized equations describing pressure distribution are obtained. In intermediate flow, the pressure distribution is iteratively obtained. The validity of the method is confirmed by demonstrating a pressure in a long-tube flow path with various flow rates. The result smoothly connects theoretical curves of molecular flow and viscous laminar flow between two regions. Then, the calculation method is applied to an actual device and is compared to the measurement. The comparison between the calculation and measurement shows the qualitative agreement and reveals the requirement for a more detailed implementation of the actual conditions. [ABSTRACT FROM AUTHOR]

The article examines the thermohydrodynamics of rarefied Poiseuille flow in a finite length channel, emphasizing the impact of dilatation and non-isochoric effects. Variations in pressure-driven and acceleration-driven Poiseuille flows are discussed, with a focus on the saturation of mass flow rate at high Knudsen numbers in pressure-driven flow. The study highlights the significance of dilatation in explaining differences in hydrodynamic fields, rheology, and flow-induced heat transfer between the two flows, as well as the implementation of boundary conditions and averaging procedures in the DSMC method. The research suggests that further exploration is needed to understand the implications of dilatation in various flow scenarios and discusses the challenges in solving the Boltzmann equation using the DSMC method. [Extracted from the article]

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]

Copyright of Petroleum Geology & Oilfield Development in Daqing is the property of Editorial Department of Petroleum Geology & Oilfield Development in Daqing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the context of eccentric micro-scale Taylor–Couette flow, variations in localized flow scales result in a non-uniform fluid–solid interface slip state, distinct from the typically studied uniform slip velocity distribution. This study introduces a boundary condition definition method aimed at characterizing partial slip states, complemented by a coupled iterative analysis system tailored to address this complexity. Key contributions include the development of a method for calculating the limiting shear stress, which considers local velocity gradients and pressures. Validation demonstrates that the locally derived slip state aligns more closely with Knudsen number distributions of local flow scales compared to traditional uniform slip models, and exhibits greater consistency with experimentally measured pressure distributions. Additionally, the study reveals that eccentric Taylor–Couette flow, characterized by significant variations in local flow scales and strong self-induced pressure effects, leads to complex distributions of local pressure, velocity gradients, and differences in local slip velocities. Specifically, the non-uniform distribution of local pressure gradients due to eccentricity results in partial slip occurring predominantly on the rotor in regions with positive pressure gradients, and on the stator in regions with negative pressure gradients. Furthermore, the variation in gap height exerts a greater influence on local slip compared to rotational speed and eccentricity ratio. Under certain conditions influenced by pressure gradients, the slip velocity on the rotor may exceed its tangential speed. [ABSTRACT FROM AUTHOR]

Although the Boltzmann equation is instrumental in capturing the dynamics of rarefied gases, finding its solutions in engineering problems is challenging. Therefore, over the past century and a half, numerous partial differential equations based on a few macroscopic variables have been introduced. However, they not only have complicated forms but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial–temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time t and position x is determined by the velocity/temperature gradient in the nearby spatial–temporal coordinates, via convolution operators. Utilizing solutions of the Boltzmann equation for the Couette/Fourier/Poiseuille flow and the spontaneous Rayleigh–Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Subsequent validation through sound propagation and backward-facing step flow demonstrates that the NiST constitutive relation is capable of accurately forecasting rarefied gas flows across a broad spectrum of Knudsen numbers. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the hydrodynamic limit of Boltzmann equations for a gas mixture containing two kinds of particles, where one is assumed to be near a vacuum and the other is near a Maxwellian equilibrium state. By the method of Hilbert expansion, we could derive the compressible Euler systems together with the terms of Boltzmann equations according to the different orders of the Knudsen number. Next, we truncate the expansion and establish the uniform estimates of the remainder term by using $ L^2 \,- \, L^{\infty } $ L 2 − L ∞ estimate. [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]

Multiple flow mechanisms that coexist in nanoscale porous media are responsible for deviations from the linear Klinkenberg equation. The use of mathematical models in the literature has obvious limitations in evaluating this flow phenomenon because the viscosity/diffusion coefficients of nanoscale porous media are more accurate only in the limited Knudsen number region. By introducing, the concept of an effective molecular mean free path, this paper proposes single models of viscosity/diffusion for the full Knudsen number range to replace the combination model in the literature. On this basis, a new apparent permeability model is developed with multiple coexisting mechanisms for the full Knudsen number range, and the effectiveness of the proposed model is verified by using published data. The discontinuous problem of the combination model of the viscosity/diffusion coefficient in the literature for the full Knudsen number range is solved using the new viscosity and diffusion coefficient models. The new apparent permeability model accurately predicts the absolute permeability and explains the phenomenon of deviation from the linear Klinkenberg equation. This paper further discusses the influence of different mechanisms on the permeability. The rarefaction effect weakens the diffusion ability in porous media but increases the contribution of Darcy flow to permeability. The viscous flow increment, absolute permeability and slippage effect were the most important flow mechanisms in nanopores. Article Highlights: We present the equation of the gas viscosity/diffusion coefficient in nanopores for the full Knudsen number range. We present a new apparent permeability model with multiple coexisting mechanisms for the full Knudsen number range. Our model predicts the absolute permeability of nanoscale porous media. [ABSTRACT FROM AUTHOR]

We present a comprehensive theoretical analysis which integrates the Klinkenberg plot into the pulse decay method (PDM) to effectively address the slippage effect on permeability measurement of micro/nanoporous media. Employing an asymptotic perturbation analysis on the Navier–Stokes equation within a capillary model, our work fills a critical gap in the interpretation of PDM experimental data, particularly by considering the influence of Knudsen number on permeability. Our findings substantiate the reliability of the Klinkenberg plot in interpreting PDM data, particularly when the ratio between the pore volume and the upstream or downstream chamber is below 0.1. It is noteworthy that our study underscores the persistent presence of the slippage effect when one chamber is sealed, emphasizing the necessity for careful consideration in permeability measurements under such conditions. The robustness of the theoretical framework is validated through experimental results, providing strong supports for the accuracy and applicability of our approach in heat and mass studies in micro/nanoporous media. [ABSTRACT FROM AUTHOR]

Application of two-dimensional lattice Boltzmann equations of various orders on standard lattices to the description of slow isothermal rarefied flows is considered. A two-dimensional Poiseuille flow at different Knudsen numbers is used as a test problem. This problem is solved numerically using several lattice Boltzmann equations of low and high orders that have from nine to 53 discrete velocities. The results are compared with the solutions to the linearized Boltzmann and Bhatnagar–Gross–Crook equations, which are used as test ones. Numerical experiments showed that increasing the order of the lattice Boltzmann equation (i.e., the number of first moments of the local Maxwell distribution reproduced by the discrete local equilibrium of the lattice Boltzmann equation) does not always lead to improved accuracy. In particular, a new low-order LB model with 16 velocities which reproduces diffuse reflection boundary conditions at a qualitative level is proposed. It is shown that for this model it is possible to obtain accurate values of the volumetric flow rate slip velocities for a wide range of Knudsen numbers in comparison with other models under consideration. [ABSTRACT FROM AUTHOR]

Copyright of Experimental Technology & Management is the property of Experimental Technology & Management Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

In this paper, we propose an efficient, high-order accurate and asymptotic-preserving (AP) semi-Lagrangian (SL) method for the BGK model with constant or spatially dependent Knudsen number. The spatial discretization was performed by a mass conservative nodal discontinuous Galerkin (NDG) method, while the temporal discretization of the stiff relaxation term was realized by stiffly accurate diagonally implicit Runge-Kutta (DIRK) methods along the characteristics. Extra order conditions are enforced in [10] for the asymptotic accuracy (AA) property of DIRK methods when they are coupled with a semi-Lagrangian algorithm in solving the BGK model. A local maximum principle-preserving (LMPP) limiter was added to control numerical oscillations in the transport step. Thanks to the SL and implicit nature of time discretization, the time stepping constraint was relaxed and much larger than that from an Eulerian framework with explicit treatment of the source term. Extensive numerical tests are presented to verify the high-order AA, efficiency, and shock-capturing properties of the proposed schemes. [ABSTRACT FROM AUTHOR]

Gurney flap is a simple and effective high-lift device that has the potential to reduce the takeoff-and-landing distance for transport aircraft. It is also a good option for enhancing the airfoil cruising characteristics. However, its effectiveness in non-continuum regimes has rarely been studied. The Unified Gas Kinetic Scheme algorithm, which is valid for all flow regimes, is further developed and used to simulate the flow field around a cambered airfoil and a high-speed quadrilateral airfoil with and without the Gurney flap in the supersonic non-continuum flow regimes. The distribution function shapes at different spatial locations are provided and analyzed. The effects of angle of attack, free-stream Knudsen number, free-stream Mach number, Gurney flap height, and Gurney flap mounting angle on the aerodynamic characteristics of the two airfoils are studied. The results show that the lift and drag of the airfoil with the attached Gurney flap are increased. The pressure rise on the lower surface of the airfoil is the primary factor contributing to the increase in lift. The overall increase in drag mainly comes from the Gurney flap, which also generates a small amount of negative lift. When the angle of attack is less than the critical angle of attack, the Gurney flap can increase the lift-to-drag ratio of the airfoil and improve its aerodynamic performance. The critical angle of attack decreases with the increase in the free-stream Knudsen number and the free-stream Mach number. It decreases with increasing Gurney flap height and increases with increasing Gurney flap mounting angle. [ABSTRACT FROM AUTHOR]

During atmospheric reentry, the vehicle surface is exposed to highly non-equilibrium flow. The vehicle surface can experience heterogeneous recombination of reactive atoms, which contributes to its aerothermodynamic heating. This process is followed by chemical energy accommodation (CEA), where the released energy is either transferred to the surface or the internal energy modes of the recombined molecule. Heterogeneous recombination can be categorized into Eley–Rideal (ER) and Langmuir–Hinshelwood mechanisms, which differ in their methods of molecule formation and degrees of CEA. The complete CEA assumption may not consider the dependency of CEA on the mechanisms of heterogeneous recombination. This study aims to consider the mechanism-specific CEA for a more accurate prediction of surface heat flux. The authors implement mechanism-specific CEA within the direct simulation Monte Carlo framework using the finite-rate surface chemistry model, resolving elementary surface reactions and assigning a CEA coefficient, β, to each mechanism. The model is verified through comparisons with analytical solutions of surface coverage and validated against benchmark references. A parametric investigation of rarefied hypersonic flow over a two-dimensional cylinder is conducted under different freestream Mach and Knudsen numbers. Results show a reduction in total heat flux of up to 14.44% using mechanism-specific CEA compared to the complete CEA assumption. The reduction is attributed to the relative contribution of the ER mechanism, which can be a function of atomic partial pressure at the boundary layer. [ABSTRACT FROM AUTHOR]

Estimating gas transport through a hierarchical micro/nanoporous system is challenging due to non-equilibrium gas dynamics. The primary difficulty lies in determining the rarefaction level, because identifying a representative flow dimension in a complex porous system with multiple pore scales is not straightforward. Our study performed a pore-level analysis for gas permeability in dual-scale porous media with varying porosity, throat size, and secondary pore size under different rarefaction conditions. We found that secondary porosity negatively affects permeability due to increased friction forces, with this influence growing as the secondary pore size and porosity increase until the secondary pore becomes comparable to the throat. However, rarefaction reduces the effects of secondary pores due to boundary slip. Traditional Knudsen number (Kn) calculations based on Darcy-defined height failed to accurately describe the rarefaction effects on gas permeability. Instead, we introduced an equivalent diameter to calculate the Kn, which provided an accurate normalization of apparent gas permeability independent of pore geometry. The extended Kozeny–Carman–Klinkenberg model developed in our previous study successfully yielded a macroscopic model for apparent gas permeability in hierarchical micro/nanoporous systems as a function of the traditional Darcy height and porosity. [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]

The article presents the results of an analytical study of the flow dynamics in a microdiffuser. An expression for the velocity profile is obtained with account for slip effects. The effect of the Knudsen number on the velocity profiles is shown. The effect of the microdiffuser angle on the flow velocity profile and the friction coefficient is analyzed. The opening angle of the microdiffuser was determined, at which slip effects do not affect the velocity profile. [ABSTRACT FROM AUTHOR]

A free argon jet flow accompanied by small clusters formation is studied with the direct simulation Monte Carlo method. Some near-continuum flow regimes characterized by Knudsen numbers in the 2 × 10 − 4 − 2 × 10 − 3 range are considered. A model for the argon clusters' growth/decay is proposed, taking into account the phase state of the clusters. The model consists of a chain of reactions leading to the clusters' formation, including the clusters' growth via triple/pair collisions of particles, and the clusters decay according to the collisional/unimolecular mechanism. The cluster size distributions in the jet far field are obtained. The results are compared with two experimental datasets. Good agreement is shown for most of the considered range of parameters. The triple particle collisions' influence on the argon clusters growth process is studied, and their important role in small cluster formation is demonstrated. It has been established that the cluster formation process is limited to an enough small spatial zone near the source outlet, of the order of several exit orifice diameters. The simulation shows a significant influence of cluster formation on the temperature and Mach number distributions, and a weak influence on the flow velocity. The formed clusters' translational temperatures and their velocities are close to the argon atoms' corresponding parameters. A non-equilibrium state, featured by a significant difference between the clusters' internal temperatures and the flow temperature, develops with distance from the source outlet. [ABSTRACT FROM AUTHOR]

In this paper we describe the long‐time behavior of the non‐cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (that is, infinite Knudsen number 1/ν→∞$1/\nu \rightarrow \infty$). Specifically, we prove that for initial data sufficiently small (independent of the Knudsen number), the solution displays several dynamics caused by the phase mixing/dispersive effects of the transport operator v·∇x$v \cdot \nabla _x$ and its interplay with the singular collision operator. For x$x$‐wavenumbers k$k$ with |k|≫ν$|k|\gg \nu$, one sees an enhanced dissipation effect wherein the characteristic decay time‐scale is accelerated to O(1/ν11+2s|k|2s1+2s)$O(1/\nu ^{\frac{1}{1+2s}} |k|^{\frac{2s}{1+2s}})$, where s∈(0,1]$s \in (0,1]$ is the singularity of the kernel (s=1$s=1$ being the Landau collision operator, which is also included in our analysis); for |k|≪ν$|k|\ll \nu$, one sees Taylor dispersion, wherein the decay time‐scale is accelerated to O(ν/|k|2)$O(\nu /|k|^2)$. Additionally, we prove almost uniform phase mixing estimates. For macroscopic quantities such as the density ρ$\rho$, these bounds imply almost uniform‐in‐ν$\nu$ decay of (t∇x)βρ$(t\nabla _x)^\beta \rho$ in Lx∞$L^\infty _x$ due to phase mixing and dispersive decay. [ABSTRACT FROM AUTHOR]

This work focuses on the study of natural convection in a flat porous microchannel with asymmetric heating. The novelty of the work lies in the fact that for the first time the method of discrete symmetries was used to analyze the complete system of Navier–Stokes and energy equations in a two-dimensional approximation. Analytical solutions for velocity and temperature profiles have been derived based on symmetry analysis, taking into account boundary conditions such as slip and temperature jump at the channel walls. The effect of Grashof, Knudsen, Darcy, and Prandtl numbers on the flow characteristics in the microchannel and heat transfer coefficients was elucidated. At high Grashof numbers, an ascending flow near the hot wall and a descending flow near the cold wall arise. Increasing the Knudsen number leads to an increase in the velocity, temperature jump at the walls and a decrease in heat transfer coefficients. As the Darcy number increases, velocities amplify in both ascending and descending flows. The temperature jump at the hot wall grows up, while it remains unchanged at the cold wall. In the same time, the heat transfer coefficient at the hot wall decreases. [ABSTRACT FROM AUTHOR]

This work presents an efficient implicit gas kinetic Lax–Wendroff scheme for steady isothermal gas flows in all Knudsen number (Kn) regimes. In the scheme, the discrete velocity Bhatnagar–Gross–Krook model equations (DVE) and the associated conservation moment equations (CME) are coupled and solved by matrix-free implicit schemes. Thanks to obtaining the fluxes of the CME by multiplying the fluxes of the DVE with a projection matrix and utilizing the equilibrium distribution functions at the new time predicted by the CME, both the complicated macro fluxes reconstruction of the CME and the calculation of the Jacobian matrix of the equilibrium distribution functions are not needed in the scheme, which makes the scheme lightweight. Moreover, to enhance the accuracy of the predicted equilibrium distribution functions at the new time to improve the convergence, a symmetric Gauss–Seidel scheme with inner iterations is used to solve the CME system. Due to the coupling between the DVE and the CME, the highly efficient implicit scheme for the CME drives the DVE system to converge quickly for the continuum and near-continuum flows. Furthermore, to verify the accuracy and high efficiency of the proposed implicit scheme, comparison studies of several two-dimensional isothermal rarefied gas flow cases simulated by the present implicit scheme and the explicit gas kinetic Lax–Wendroff scheme are also provided. The numerical results show that the present implicit scheme can be as accurate as its explicit counterpart with one to two orders times speed-up in all Kn number flow regimes. [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]

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime. [ABSTRACT FROM AUTHOR]

A gas flow in a square cavity driven by a lid sliding in the direction of its line of contact with the cavity wall is considered. The steady behavior of the gas is numerically investigated based on the linearized Bhatnagar–Gross–Krook kinetic equation and the diffuse reflection boundary condition. When one applies the Stokes equation and the no-slip boundary condition to the system considered here, the flow velocity becomes multivalued at the corner between the lid and the cavity wall, and the shear stress diverges at the corner inversely proportionally to the distance from there, which is known as the so-called corner singularity. In the present work, the behavior of the gas near the corner is examined based on numerical results obtained from the kinetic theory. Although the range of the flow velocity value in the kinetic solution is limited due to the significant velocity slip near the corner, the flow velocity is, nevertheless, multivalued at the corner. The shear stress varies inversely proportionally to the distance from the corner up to the position that is a few tens of mean free paths away from there. The increase in the stress is suppressed at positions closer to the corner and its magnitude remains bounded. Thus, the total forces acting on the lid and the side cavity walls are bounded as well. Due to the distinctive behavior of the stress near the corner, the resulting nondimensional total forces behave with an unconventional rate Kn ln Kn for small Knudsen numbers Kn. [ABSTRACT FROM AUTHOR]

Data-driven discovery of governing equations is of great significance for helping us understand intrinsic mechanisms and build physical models. Recently, numerous highly innovative algorithms have emerged, aimed at inversely discovering the underlying governing equations from data, such as sparse regression-based methods and symbolic regression-based methods. Along this direction, a novel dimensional homogeneity constrained gene expression programming (DHC-GEP) method is proposed in this work. The DHC-GEP simultaneously discovers the forms and coefficients of functions using basic mathematical operators and physical variables, without requiring preassumed candidate functions. The constraint of dimensional homogeneity is capable of filtering out the overfitting equations effectively. The key advantages of DHC-GEP compared with the original gene expression programming, including being more robust to hyperparameters, the noise level and the size of datasets, are demonstrated on two benchmark studies. Furthermore, DHC-GEP is employed to discover the unknown constitutive relations of two representative non-equilibrium flows. Galilean invariance and the second law of thermodynamics are imposed as constraints to enhance the reliability of the discovered constitutive relations. Comparisons, both quantitative and qualitative, indicate that the derived constitutive relations are more accurate than the conventional Burnett equations in a wide range of Knudsen numbers and Mach numbers, and are also applicable to the cases beyond the parameter space of the training data. [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]

The drag force on the small particle in high-speed flows is influenced by the combined effects of fluid viscosity, compressibility, and rarefaction. The existing drag coefficient models are still insufficient in accuracy and efficiency for gas-particle flow simulation. This study comprehensively considers these effects and conducts high-fidelity numerical simulations. A new drag coefficient is generated using a symbolic regression method reasonably based on the particle Mach number, Reynolds number, and Knudsen number, which are related to particle diameter, gas-particle relative velocity, and other parameters. The new drag coefficient possesses clear physical significance, high predictive accuracy, low computational cost, and consistency with theory in limiting conditions. The application of the new drag coefficient to three typical gas-solid two-phase flow cases demonstrated its excellent performance. [ABSTRACT FROM AUTHOR]

A microscale lubrication flow of a gas between eccentric circular cylinders with an arbitrary temperature difference is studied on the basis of kinetic theory. The dimensionless curvature, defined as the mean clearance divided by the radius of the inner cylinder, is small, whereas the temperature ratio and the Knudsen number based on the mean clearance take arbitrary values. The Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation in bipolar coordinates is studied analytically using the slowly varying approximation. The leading-order term of the perturbation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by the free molecular solution or an equilibrium solution at rest. Two macroscopic lubrication models are derived, along with a numerical database that enables one to use the models quickly. Direct numerical analysis of the BGKW equation is also conducted, and the validity of the lubrication models is assessed. The heating of either cylinder enhances both the eccentric force and the torque acting on the inner cylinder. When the Knudsen number is small, there is little difference in the eccentric force between the cases in which the rotating inner cylinder is heated and the stationary outer cylinder is heated. However, this difference becomes significant as the Knudsen number increases, with heating of the outer cylinder yielding the greater eccentric force. If the two lubrication models are applied complementarily depending on the Knudsen number, they provide a reasonable result for the eccentric force over a wide range of the Knudsen number. [ABSTRACT FROM AUTHOR]

The gas-particle flow with multiple dispersed solid phases is associated with a complicated multiphase flow dynamics. In this paper, a unified algorithm is proposed for the gas-particle multiphase flow. The gas-kinetic scheme (GKS) is used to simulate the gas phase and the multiscale unified gas-kinetic wave-particle (UGKWP) method is developed for the multiple dispersed solid particle phase. For each disperse solid particle phase, the decomposition of deterministic wave and statistic particle in UGKWP is based on the local cell's Knudsen number. The method for solid particle phase can become the Eulerian fluid approach at the small cell's Knudsen number and the Lagrangian particle approach at the large cell's Knudsen number. This becomes an optimized algorithm for simulating dispersed particle phases with a large variation of Knudsen numbers due to different physical properties of the individual particle phase, such as the particle diameter, material density, etc. The GKS-UGKWP method for gas-particle flow unifies the Eulerian-Eulerian and Eulerian-Lagrangian methods. The particle and wave decompositions for the solid particle phase and their coupled evolution in UGKWP come from the consideration to balance the physical accuracy and numerical efficiency. Two cases of a gas-solid fluidization system, i.e. one circulating fluidized bed and one turbulent fluidized bed, are simulated. The typical flow structures of the fluidized particles are captured, and the time-averaged variables of the flow field agree well with the experimental measurements. In addition, the shock particle-bed interaction is studied by the proposed method, which validates the algorithm for the polydisperse gas-particle system in the highly compressible case, where the dynamic evolution process of the particle cloud is investigated. [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]

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]

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]