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In the case of microscopic particles, the momentum exchange between the particle and the gas flow starts to deviate from the standard macroscopic particle case, i.e. the no-slip case, with slip flow occurring in the case of low to moderate particle Knudsen numbers. In order to derive new drag force models that are valid also in the slip flow regime for the case of non-spherical particles of arbitrary shapes using computational fluid dynamics, the no-slip conditions at the particle surface have to be modified in order to account for the velocity slip at the surface, mostly in the form of the Maxwell’s slip model. To allow a continuous transition in the boundary condition at the wall from the no-slip case to the slip cases for various Knudsen (Kn) number value flow regimes, a novel specific slip length model for the use with the Maxwell boundary conditions is proposed. The model is derived based on the data from the published experimental studies on spherical microparticle drag force correlations and Cunningham-based slip correction factors at standard conditions and uses a detailed CFD study on microparticle fluid dynamics to determine the correct values of the specific slip length at selected Kn number conditions. The obtained data on specific slip length are correlated using a polynomial function, resulting in the specific slip length model for the no-slip and slip flow regimes that can be applied to arbitrary convex particle shapes.Graphic abstract

An analysis is presented for the steady thermophoresis and photophoresis of a homogeneous dispersion of identical aerosol spheres of typical physical properties and surface characteristics. The analysis assumes a moderately small Knudsen number (less than about 0.1), such that the gas motion lies within the slip-flow regime, including thermal creep, temperature jump, thermal stress slip, and frictional slip at the particle surfaces. Under conditions of low Peclet and Reynolds numbers, the coupled momentum and energy equations are analytically solved using a unit cell approach that explicitly incorporates interparticle interactions. Closed-form expressions are derived for the mean particle migration velocities in both thermophoresis driven by a uniform temperature gradient and photophoresis induced by an incident radiation field. The results reveal that the normalized particle velocities, referenced to those of an isolated particle, generally decrease with increasing particle volume fraction, though exceptions occur for thermophoresis. While thermal stress slip and thermal creep exert no influence on the normalized thermophoretic velocity, they markedly affect the normalized photophoretic velocity, which rises with the thermal stress slip to the thermal creep coefficient ratio. For both phenomena, the normalized migration velocities increase monotonically with the particle-to-fluid thermal conductivity ratio.

To improve the understanding of gas transport processes in tight rocks (e.g., shales), systematic flow tests with different gases were conducted on artificial micro- to nanoporous analogue materials. Due to the rigidity of these systems, fluid-dynamic effects could be studied at elevated pressures without interference of poro-elastic effects. Flow tests with narrow capillaries did not reveal any viscosity anomaly in a confined space down to capillary diameters of 2 µm. Experiments with nanoporous ceramic disks (> 99% Al 2 O 3 ) conducted at confining pressures from 10 to 50 MPa did not indicate any stress dependence of permeability coefficients. Analysis of the apparent permeability coefficients over a mean gas pressure range from 0.2 to 30.5 MPa showed essentially linear Klinkenberg trends with no indication of second-order slip flow. The Klinkenberg-corrected permeability coefficients measured with helium were consistently higher than those measured with all other gases under the same conditions. This “helium anomaly” was, however, less pronounced than the same effect observed in natural rocks, indicating that it is probably not related to fluid-dynamic effects but rather to gas–solid interactions (e.g., sorption). Permeability tests with CO 2 on the nanoporous membrane show significant deviations from the linear Klinkenberg trend around the critical point. This is due to the drastic changes of the thermodynamic properties, in particular the isothermal compressibility, in this pressure and temperature range. Helium pycnometry, mercury intrusion porosimetry and low-pressure nitrogen sorption showed good agreement in terms of porosity (~ 28%) and the most prominent pore diameter (~ 68.5 nm). Article Highlights Slip flow-corrected permeability coefficients measured with helium are consistently higher than those measured with other gases (“He anomaly”). Second-order gas slippage was not detectable in artificial porous media with pore diameters > 10 nm and at pressures > 1 MPa. Small corrections of isothermal compressibility improve the consistency of CO 2 permeability coefficients near the critical temperature.

In the present paper, forced convection of a laminar gas flow inside two concentric micro-cylinders with constant wall heat flux condition is numerically investigated. For this purpose, the energy equation is solved in the continuum and slip flow regimes for the thermally developing condition using the lattice Boltzmann method. To the authors’ best knowledge, the simultaneous effects of viscous dissipation, rarefaction, axial conduction, and radius ratio in the thermally developing region of a micro-annulus channel have not been considered in the literature. In the present work, the effects of the mentioned parameters on the heat transfer characteristics are studied in detail. Furthermore, the lattice Boltzmann method is developed to apply the viscous dissipation source term in axisymmetric slip flows under constant wall heat flux condition. The results show that in the absence of viscous dissipation, due to energy balance in the fluid, the bulk fluid temperature is independent of the Knudsen number, and its value increases linearly along the microchannel. However, the bulk fluid temperature changes with the Knudsen number by including the viscous dissipation. Also, increasing the rarefaction effect, reduces the impacts of Brinkman number and radius ratio on the local Nusselt number. Moreover, the influence of viscous dissipation is more significant at higher radius ratios.

The intention of this article is to examine a second order slip flow and magnetic field on boundary layer flow of micropolar fluid past a stretching sheet. Employing appropriate similarly transformation and non-dimensional variables, the governing non-linear boundary-value problems were reduced into coupled higher order non-linear ordinary differential equation. Then, solution for velocity, microrotation and temperature has been obtained numerically. The equations were numerically solved using the function bvp4c from the matlab for different values of governing parameters. Numerical results have been discussed for non-dimensional velocity, temperature, microrotation, the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of slip parameter γ increase. However, the local Nusselt number -θ′(0) decreases as both slip parameter γ and δ increase. A comparison with previous studies available in the literature has been done and an excellent agreement is obtained.

In this paper, a pitching NACA 0012 airfoil is simulated in the slip flow regime by solving the Navier–Stokes equations subjected to the Maxwell slip and Smoluchowski jump boundary conditions. The rhoCentralDyMFoam solver of the OpenFOAM software has been modified to handle these boundary conditions. The effects of several parameters such as reduced frequency, mean angle of attack, amplitude of oscillation and the Knudsen (Kn) number on aerodynamic coefficients are investigated. It was shown that Kn has no significant effect on lift coefficient but changes drag coefficient significantly. Moreover, the reduced frequency changes the lift coefficient considerably but its effect on the drag coefficient is negligible.

A new experimental setup for flow rate measurement of gases through microsystems is presented. Its principle is based on two complementary techniques, called droplet tracking method and constant-volume method. Experimental data on helium and argon isothermal flows through rectangular microchannels are presented and compared with computational results based on a continuum model with second-order boundary conditions and on the linearized kinetic BGK equation. A very good agreement is found between theory and experiment for both gases, assuming purely diffuse accommodation at the walls. Also, some experimental data for a binary mixture of monatomic gases are presented and compared with kinetic theory based on the McCormack model.

The tangential momentum accommodation coefficient (TMAC) was investigated experimentally from the mass flow rate through a single microtube under the slip flow and the early part of the transition regime. The measurements were carried out by the constant-volume method under the mean Knudsen number smaller than 0.3, which is based on the mean pressure of the inlet and the outlet of the microtube, to apply the second-order slip boundary condition. To measure TMACs on various materials, quite large microtube was employed, which require the reduction in leakage. TMAC was obtained from the slip coefficient determined by the relation of the mass flow rate to the mean Knudsen number. The obtained mass flow rate was well explained by the theoretical equation. TMACs of deactivated-fused silica with argon, nitrogen, and oxygen were measured, showing the tangential momentum was not accommodated completely to the surface, and the values showed good agreement with previous studies. From the comparison between microtubes with different inner diameter, it is showed that TMAC is determined mainly by gas species and surface material.

In this paper, we consider the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of power law fluid over a flat plate with slip boundary conditions. We use a similarity transformation to convert the governing nonlinear partial differential equations into a system of ordinary differential equations and solve the resulting system numerically using MATLAB's boundary value solver, bvp4c, and the shooting method. We present velocity and temperature profiles within the boundary layer and demonstrate the effect of changing the magnetic parameter, Prandtl number, and slip parameters.

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