The effect of inelastic collisions on the diatomic gas temperature jump in the vicinity of a solid surface

The problem on temperature jump in the vicinity of a solid surface is solved by the method of half-space moments using the previously suggested model kinetic equation which takes into account the rotational degrees of freedom of molecules of a diatomic gas. The temperature jump coefficient is obtained in the form of a function dependent on the coefficient of accommodation of tangential momentum, the coefficients of accommodation of translational and rotational components of energy, thermophysical parameters, and the frequency of inelastic collisions of gas molecules. The temperature jump coefficient is calculated for a number of diatomic gases. Graphs are given of the dependence of the temperature jump coefficient on the inelastic collision frequency and on the accommodation coefficients.     

The Effect of Inelastic Collisions of Molecules of a Diatomic Gas with Rotational Degrees of Freedom

The problem on Barnett slip of gas along a plane surface is solved within the suggested kinetic model for a diatomic gas with rotational degrees of freedom of molecules, which takes into account transitions from rotational degrees of freedom to translational and vice versa. The Barnett slip coefficient is obtained in the form of a function dependent on the frequency of inelastic collisions of gas molecules and on the coefficient of accommodation of tangential momentum.     

The Temperature Dependence of the Coefficients of Thermal and Isothermal Slip of a Diatomic Gas with Rotational Degrees of Freedom

A model kinetic equation is suggested for diatomic gases with rotational degrees of freedom of molecules. The free parameters of the model are related to Eucken's partial factors. This model is used to solve the problem on the slip of a diatomic gas along a plane surface. The coefficients of thermal and isothermal slip are obtained in the form of functions dependent on the transport coefficients and the frequency of inelastic collisions of gas molecules and, as a consequence, on the temperature.     

Direct simultaneous measurement of rotational and translational accomodation coefficients

When molecules of a low density diatomic gas strike a solid surface both translational energy and the internal energy modes of rotation and vibration will contribute the energy exchange that occurs. Theoretical studies indicate that accomodation coefficient for rotational energy should be less than that for translational energy, and this is confirmed by experimental results. The experimental apparatus described in this paper uses the electron bream fluorescence detector to measure simultaneously both rotational and translational energy accommodation coefficients of room temperature nitrogen reflecting from a solid surface. A bakeable ultra high vacuum system was built to provide a clean vacuum environment for control of the solid surface properties. In addition to being the only known direct measurement of rotational accomodation coefficient the system offers an advantage over some previous methods of translational accommodation measurement in that there are few restrictions on solid surface temperature or composition.     

Slip flow and heat transfer in rectangular and circular microchannels using hybrid FE/FV method

Rarefied gas flows typically encountered in MEMS systems are numerically investigated in this study. Fluid flow and heat transfer in rectangular and circular microchannels within the slip flow regime are studied in detail by our recently developed implicit, incompressible, hybrid (finite element/finite volume) flow solver. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix‐free, implicit, cell‐centered finite volume method. The Poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable, which is closely related to pressure and is used to update the velocity field and pressure field. The hybrid flow solver has been extended for applications in MEMS by incorporating first order slip flow boundary conditions. Extended inlet boundary conditions are used for rectangular microchannels, whereas classical inlet boundary conditions are used for circular microchannels to emphasize on the entrance region singularity. In this study, rarefaction effects characterized by Knudsen number (Kn) in the range of 0 ⩽ Kn ⩽ 0.1 are numerically investigated for rectangular and circular microchannels with constant wall temperature. Extensive validations of our hybrid code are performed with available analytical solutions and experimental data for fully developed velocity profiles, friction factors, and Nusselt numbers. The influence of rarefaction on rectangular microchannels with aspect ratios between 0 and 1 is thoroughly investigated. Friction coefficients are found to be decreasing with increasing Knudsen number for both rectangular and circular microchannels. The reduction in the friction coefficients is more pronounced for rectangular microchannels with smaller aspect ratios. Effects of rarefaction and gas‐wall surface interaction parameter on heat transfer are analyzed for rectangular and circular microchannels. For most engineering applications, heat transfer is decreased with rarefaction. However, for fluids with very large Prandtl numbers, velocity slip dominates the temperature jump resulting in an increase in heat transfer with rarefaction. Depending on the gas‐wall surface interaction properties, extreme reductions in the Nusselt number can occur. Present results confirm the existence of a transition point below and above wherein heat transfer enhancement and reduction can occur. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytical solution of the problem on thermal slip of second order for molecular gases

Results obtained using exact analytical methods in the problem on thermal slip of second order for molecular gases with allowance for the rotational degrees of freedom of molecules have been presented. Numerical calculations of the thermal-slip coefficient for a number of molecular gases have been carried out. The dependence of the velocity of thermal slip of second order of a molecular gas on the Prandtl number has been shown. The found value of the coefficient of thermal slip of second order theoretically confirms the existence of negative (in the direction of the temperature gradient) thermophoresis for molecular gases. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 3, pp. 190–194, May–June, 2006.     

Stokes flow with slip caused by the axisymmetric motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid

The first part of this paper investigates the motion of a solid spherical particle in an incompressible axisymmetric micropolar Stokes flow. A linear slip, Basset-type, boundary condition has been used. Expressions for the drag force and terminal velocity has been obtained in terms of the parameter characterizing the slip friction. In the second part, we consider the flow of an incompressible axisymmetrical steady semi-infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid. Two cases are considered for the motion of the sphere: perpendicular translation to the free surface and rotation about a diameter which is also perpendicular to the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. Also a linear slip, Basset-type, has been used. The analytical expressions for velocity and microrotation components are determined in terms of modified Bessel functions of second kind and Legendre polynomials. The drag for the translation case and the couple for the rotational motion on the submerged half sphere are calculated and expressed in terms of nondimensional coefficients whose variation is studied numerically. The variations of the drag and couple coefficients with respect to the micropolarity parameter and slip parameter are tabulated and displayed graphically.     

Rotational and translational accommodation coefficients of nitrogen on nickel,silver and gold

An electron beam excited fluorescence technique was used to make simultaneous measurements of rotational and translational accommodation of nitrogen on nickel, silver, gold and stainless steel solid surfaces. In addition to the advantage of being able to make independent measurements of rotational accommodation, this apparatus allows a wide range of solid surface temperatures to be used and operates at lower gas density than most previous experiments.Rotational accommodation coefficients for nickel and gold varied from α_R = 0.12 at 400°K to α_R = 0.18 at 850°K while the value of α_R for silver increased more quickly from α_R = 0.03 at 430°K to α_R = 0.2 at 700°K.A linear variation of translational accommodation coefficient, α_T, with surface temperature was observed. An empirical relationship based on molecular weights was able to account for variation in dα_T/dT_s observed. The metal surfaces used were thought to be free of adsorbed gas and oxide layers.     

Measurements of the relative momentum accommodation coefficient for different gases with a viscosity vacuum gauge

The viscosity vacuum gauges are based on the gas momentum transfer phenomena between a moving part of the gauge and a stationary surface. Thus, they may be used for the study of the momentum accommodation coefficient for various combinations of gas species and surfaces. The aim of the present work is to determine the momentum accommodation coefficient by means of the viscosity vacuum gauge with vibrating metal ribbon. The relative accommodation coefficient was computed from the measurements for Xe, Ar, He and H₂ on the bronze ribbon of the gauge in the molecular conditions. The values of the relative coefficients were 0.90 for Xe, 0.95 for Ar, 1 for He (values were normalised to data obtained for He) and 0.94 for H₂.     

Determination of tangential momentum accommodation coefficient and slip coefficients for rarefied gas flow in a microchannel

This paper presents an experimental study of rarefied gas flow in a trapezoidal microchannel with a constant depth of 103 µm, top width of 1143 µm, bottom width of 998 µm and length of 2 cm. The aim of the study is to verify the upper limit of the validity of the second-order slip boundary condition to model rarefied gas flows. The slip coefficients and the tangential momentum accommodation coefficient (TMAC) are determined for three different gases, viz. argon, nitrogen and oxygen, and it is observed that they compare well to the literature values. The range of mean Knudsen number (Kn_m) investigated is 0.007–1.2. The non-dimensional mass flow rate exhibits the well-known Knudsen minimum in the transition regime (Kn_m?~?1). It is seen that the Navier–Stokes equation with a second-order boundary condition fits the data satisfactorily with a high value of correlation coefficient (r²?>?99.95%) in the entire range of Kn_m investigated. This work contributes by extending the range of Knudsen number studied in the context of validity of the second-order slip boundary condition.     

Experimental study of heat exchange in a moderately rarefied gas

An experimental study is performed of heat exchange in multiatomic gases at moderate Knudsen numbers in coaxial geometry. The data obtained are described well by the Liu-Lees theory of multiatomic gases.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 4, pp. 579–585, October, 1985.     

微机电系统径向气体轴承特性研究

充分考虑气体滑流边界条件的影响,结合硬球分子模型,提出一种可变温度二阶滑流修正Reynolds方程,并运用Newton-Kantorovich法(NKM)分析微机电系统(MEMS)径向气体轴承的特性,结果表明,微气体轴承与传统气体轴承相比,其承载能力有所降低;在大偏心率条件下,随着温度的升高,工作气体粘度及其分子平均自由程增大,使微气体轴承的承载能力进一步降低;针对微旋转机械转速高、长径比小等特点,讨论了转子转速、长径比及温度对径向微气体轴承特性的影响。     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation

Understanding the effect of surface roughness on gas flow in microchannels is highly desirable in microfluidic devices. Non-equilibrium molecular dynamics simulation is applied to investigate the effect of the surface roughness on slip flow of gaseous argon in submicron platinum channels. The geometries of the surface roughness are modeled by triangular, rectangular, sinusoidal and randomly triangular waves respectively. The results show that the boundary conditions of velocity slip, including slip, no-slip and negative slip, depend not only on the Knudsen number but also on the surface roughness. Induced by the roughness, the slip length of gas microflow over a rough surface is less than that predicted by the Maxwell model and shows a non-linear relationship with the Knudsen number. The friction coefficient increases not only with decreasing the Knudsen number but also with increasing the surface roughness. The impacts of the surface roughness and the gas rarefaction on the friction coefficient of gas microflow are strongly coupled. The roughness geometry also shows significant effects on the boundary conditions and the friction characteristics. The distortion of the streamlines and the enhancement of the penetrability near the rough surface are demonstrated to be responsible for the roughness effect.     

Calculation of the Velocity of Second-Order Thermal Slip Using the Model Kinetic Equation with a Variable Collision Frequency

The problem on the calculation of the second-order thermal slip velocity is solved. For this purpose, an exact solution of an inhomogeneous model Boltzmann kinetic equation with the collision operator in the form corresponding to the BGK model with the collision frequency proportional to the module of intrinsic velocity of gas molecules is constructed. Comparison with the available results is performed.     

Gas-surface scattering effect on vacuum gas flows through rectangular channels

Flow of a rarefied gas through a channel of rectangular cross section is investigated numerically and experimentally. Emphasis is given on the study of the molecular scattering law influence at the wall boundary surfaces. The Cercignani-Lampis boundary conditions are considered in detail for the current problem, along with the linearized BGK kinetic model and the discrete velocity method. Numerical conductance values are tabulated for certain aspect ratios and accommodation coefficients in the whole range of the Knudsen number and compared with corresponding experimental results for certain gas-surface combinations. Compared to the classical Maxwell diffuse boundary conditions, the Cercignani-Lampis gas-surface interaction allows a better agreement with the measurements.     

Modeling of Influence of Gas Atmosphere and Pore-Size Distribution on the Effective Thermal Conductivity of Knudsen and Non-Knudsen Porous Materials

Application of porous insulation materials in various gas atmospheres changes their effective thermal conductivity due to many structural and thermal influences. One of those is the pore-size distribution of the material. In this paper a study of the influence and modeling of the modification of the effective thermal conductivity of various materials is presented by exchanging the gas atmosphere. For this purpose 11 different materials with various pore-size distributions are investigated. The experimental work included thermal conductivity measurements along with an analysis of the porous structure. Two additional important effects of thermal accommodation and radiation will be clearly identified as caused by the exchange of the filling gas. Modeling the gas thermal conductivity for different polydisperse systems is carried out based on kinetic theory and the Knudsen effect of rarefaction of the gas in a wide range of the Knudsen number. Development of the single pore model of the gas thermal conductivity to a new predictive model with an exponential parameter gives good agreement with the experimental results.     

Numerical investigation of supersonic flow past blunt bodies of intricate shape at an angle of attack and slip angle

A supersonic flow of viscous homogeneous gas past blunt bodies of intricate shape at an angle of attack and slip angle is investigated numerically within the model of complete three-dimensional viscous shock layer using the time relaxation method. The main regularities are studied of the general structure of flow and of the distribution of pressure and heat flux along the surface. An analysis is performed of their dependence on the shape of the body, angle of attack and slip angle, Mach and Reynolds numbers, and on other determining parameters of the problem. The accuracy and range of validity of a number of approximate approaches to the solution of the problem are estimated.