Gas Rarefaction Research Articles

An Experimental Research of Gaseous Flow in Rough Microchannels

With the development of MEMS technology and its increasing applications in many engineering fields, the experimental research on micro-scale fluidic theory has become a spotlight topic in the past decade. In this paper, numerical and experimental investigations on the effects of roughness, compressibility and gas rarefaction on the nitrogen flow in rough microchannels had been investigated. Microchannels based on silicon substrates were fabricated by the MEMS process. Roughness surfaces of the microchannels had been obtained by KOH and TMAH solutions with different solubility etching on (100) silicon wafer. The quality of the microchannels was performed with a SEM and the measurements and the overall size of the microchannels were carried out with a step profiler. The Pyrex® 7740 and silicon wafers were packaged using the anodic bonding method. The testing platform was designed and fabricated, and checked for the gas sealing. Finally, the experimental device was constructed, and the results of gas flow in rough microchannels were measured.

A Comparative Study of Thin-Film and Reynolds Equation Simulation Models for Squeeze Film Damping in MEMS Plate Structures

Squeeze film damping effect of MEMS parallel plate structure was analyzed based on thin film and Reynolds Equation in ANSYS under the different Knudsen numbers. Perforation effect of parallel plate with certain size and operating frequency was achieved under the different Knudsen numbers, the simulation results of two methods are very close. For unperforated plate, when Knudsen number is below 0.01, the discrepancy of two simulations is nonsignificant, and it grows up with Knudsen number. But gas rarefaction effects related with Knudsen number was considered in heat transfer analogy theory and used viscosity modification according to Veijola model, two simulations get the same result. For perforated plate, the simulation discrepancy of two methods will be great because of channel flow's effect and also grow up with Knudsen number, it can't be avoided even if the channel flow's effect and viscosity modification were concerned in heat transfer analogy theory.

Poiseuille flow of moderately rarefied gases in annular channels

In this study, rarefaction effects in pressure-driven gas flows in annular micro-channels are investigated. The influence of gas rarefaction, aspect ratio of the annulus, and surface accommodation coefficient on wall friction, mass flow rate, and thermal energy flow rate is studied. For this, the linearized Navier–Stokes–Fourier (NSF) and regularized 13-moment (R13) equations are solved analytically. The results are compared to available solutions of the Boltzmann equation to highlight the advantages of the R13 over the NSF equations in describing rarefaction effects in the process. Moreover, a second-order slip boundary condition is proposed to improve the accuracy of the classical NSF equations.

Simplified Second Order Model of Reynolds Equation for Simulating the Ultra-Thin Air Bearing Film in Hard Disk Drivers

To more accurately simulate the pressure distribution of the ultra-thin air bearing film, Reynolds equation must be modified to account for the gas rarefaction effect. Starting from a widely used model of Reynolds equation, a new simplified second order model is proposed to simulate the ultra-thin air bearing film in hard disk drives. The new model of Reynolds equation possesses simpler mathematical form than that of the previous model. The new model is solved using a least square finite difference method and the resultant numerical results are compared with those of the previous model. The computational efficiencies of the new model and the previous model are also compared.

RF-MEMS 스위치용 마이크로 외팔보의 감쇠특성

A theoretical approach is carried out to predict the quality factors of flexible modes of a microcantilever on a squeeze-film. The frequency response function of an inertially-excited microcantilever beam is derived using an Euler-Bernoulli beam theory. The external force due to squeeze-film phenomenon is developed from the Reynolds equation. Slip boundary conditions are employed at the interfaces between the fluid and the structure to consider the gas rarefaction effect, and pressure boundary condition at both ends of fluid analysis region is enhanced to increase the exactness of predicted quality factors. To the end, an approximate equation is derived for the first bending mode of the microcantilever. Using the approximate equation, the quality factors of the second and third bending modes are calculated and compared with experimental results of previously reported work. The comparison shows the feasibility of the current approach.

Study on the Performance of Gas Journal Bearings for Power MEMS

Gas journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in Power MEMS deriving from the extremely shallow structures. With the reference Knudsen number being included, the modified Reynolds equation for gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The boundary condition for modified Reynolds equation is given. The numerical method is employed to solve the modified Reynolds equation to obtain the pressure profiles, load capacities and attitude angles of gas journal bearings for Power MEMS under different reference Knudsen numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with the reference Knudsen number increasing, and the attitude angle changes conversely. Moreover, when the eccentricity ratio is smaller, the effect of gas rarefaction on the attitude angle is less.

Rarefied gas flow through a thin slit at an arbitrary pressure ratio

Rarefied gas flow through a thin slit is studied on the basis of the direct simulation Monte Carlo method. The flow rate and flow field are calculated over the whole range of gas rarefaction for various values of the pressure ratio. It is found that at all values of the pressure ratio a significant variation of the flow rate occurs in the transition regime between the free-molecular and hydrodynamic regimes. In the hydrodynamic regime, the flow rate tends to a constant value. In the case of finite pressure ratio, the flow field qualitatively differs from that for outflow into vacuum, namely, vortices appear in the down-flow container in the vicinity of the hydrodynamic regime. Then, in the hydrodynamic regime the gas flow forms a strong jet.

Numerical modeling of rarefied gas flow through a slit into vacuum based on the kinetic equation

A rarefied gas flow through a thin slit into vacuum is calculated on the basis of the kinetic model equations applying the discrete velocity method. The calculations are carried out for the whole range of the gas rarefaction from the free-molecular regime to the hydrodynamic one. Numerical data on the flow rate and distributions of density, bulk velocity and temperature along the symmetry axis are reported. A comparison with the corresponding results obtained previously by the direct simulation Monte Carlo method is performed. A good agreement between these results shows a reliability of the model equations which require less computational effort than the Monte Carlo method.

Data on the Velocity Slip and Temperature Jump on a Gas-Solid Interface

The present review is dedicated to the velocity slip and temperature jump coefficients applied to modeling of gas flows. Such coefficients are used when a moderate gas rarefaction must be taken into account. In this case, calculations of gas flows can be performed on the basis of continuum mechanics equations applying the velocity slip and temperature jump boundary conditions. Thus, the velocity slip and temperature jump coefficients have the same importance in gas dynamics as the transport coefficients such as viscosity, thermal conductivity, and diffusion coefficients. A critical analysis of theoretical and experimental data on the slip and jump coefficients available in the open literature is presented in an accessible form so that it can be easily understandable for nonspecialists in rarefied gas dynamics. The most reliable results are selected and tabulated. The results cover a single gas with the complete and noncomplete accommodation on a solid surface, gaseous mixtures, and polyatomic gases. Many examples of applications of the slip and jump boundary conditions are given. The review will be useful as a reference for mathematicians, physicists, and engineers dealing with flows of moderately rarefied gases.

Flows of rarefied gaseous mixtures with a low mole fraction. Separation phenomenon

An approach to a model of rarefied gaseous mixtures with a low mole fraction of one species based on the linearized Boltzmann equation is proposed. As an example, the separation phenomenon in a binary gaseous mixture flowing through a long tube into a vacuum is considered by assuming an arbitrary pressure at the tube’s entrance. In this situation, the regime of gas flow along the tube can vary from hydrodynamic to free molecular. The calculations were carried out for a mixture of Helium–Xenon considering two limits, first when the mole fraction of Helium is low and second when the mole fraction of Xenon is low. As a result, flow rates of each species and their density distributions along the tube are calculated in a wide range of gas rarefaction in the tube inlet. The advantages of the present methodology in comparison to that developed previously for an arbitrary mole fraction are pointed out.

Discharge physics of high power impulse magnetron sputtering

High power impulse magnetron sputtering (HIPIMS) is pulsed sputtering where the peak power exceeds the time-averaged power by typically two orders of magnitude. The peak power density, averaged over the target area, can reach or exceed 107W/m2, leading to plasma conditions that make ionization of the sputtered atoms very likely. A brief review of HIPIMS operation is given in a tutorial manner, illustrated by some original data related to the self-sputtering of niobium in argon and krypton. Emphasis is put on the current–voltage–time relationships near the threshold of self-sputtering runaway. The great variety of current pulse shapes delivers clues on the very strong gas rarefaction, self-sputtering runaway conditions, and the stopping of runaway due to the evolution of atom ionization and ion return probabilities as the gas plasma is replaced by metal plasma. The discussions are completed by considering instabilities and the special case of “gasless” self-sputtering.

Thermal transpiration flow: A circular cross-section microtube submitted to a temperature gradient

Thermal transpiration is the macroscopic movement of rarefied gas molecules induced by a temperature gradient. The gas moves from the lower to the higher temperature zone. An original method is proposed here to measure the mean macroscopic movement of gas in the case of a long circular cross-section glass microtube onto which a gradient of temperature is applied. The mass flow rate and the thermomolecular pressure difference have been measured by monitoring the absolute pressure evolution in time at both ends of the capillary using high-speed response pressure gauges. Two gases, nitrogen and helium, are studied and three different temperature differences of 50, 60, and 70 °C are applied to the tube. The analyzed gas rarefaction conditions vary from transitional to slip regime.

Influence of gas rarefaction on the lateral resolution achievable by thermocapillary patterning

Molten polymer nanofilms subject to a large transverse thermal gradient can undergo a thermocapillary instability leading to the growth of nanopillar arrays on the cooler side. The array pitch can be estimated from the fastest growing wavelength from linear stability analysis. Here we quantify the influence of gas rarefaction on thermal conduction for cases in which the gas layer thickness above the film approaches dimensions of the molecular mean free path. For experimentally relevant parameters, rarefaction increases the pitch by as much as 65%, an important consideration for noncontact three-dimensional structure formation by thermocapillary lithography.

Studies of hysteresis effect in reactive HiPIMS deposition of oxides

High power impulse magnetron sputtering (HiPIMS) has proven to be capable of substantial improvement of the quality of deposited coatings. Lately, there have been a number of reports indicating that the hysteresis effect may be reduced in HiPIMS mode resulting in an increase of the deposition rate of stoichiometric compound as compared to a direct current magnetron sputtering process in oxide mode. In this contribution, we have studied the hysteresis behaviour of Ti metal targets sputtered in Ar+O2 mixtures. For fixed pulse on time and a constant average power, there is an optimum frequency minimizing the hysteresis. The effect of gas dynamics was analyzed by measurements of the gas refill time and rarefaction. Results indicate that the gas rarefaction may be responsible for the observed hysteresis behaviour. The results are in agreement with a previous study of Al oxide reactive process.

Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation

Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane and the forces of the gas acting on the boundaries are provided for a wide range of the gas rarefaction degree and the oscillation frequency. The flow is characterized by a coupling of heat conduction and sound waves caused by repetitive expansion and contraction of the gas. For a small gas rarefaction degree, the energy transfer is mainly conducted by sound waves, except for very low frequencies, and is strongly affected by the resonance of the waves. For a large gas rarefaction degree, the resonance effects become insignificant and the energy transferred to the unheated plane decreases nearly monotonically as the frequency increases. The force of the gas acting on the heated boundary shows a remarkable minimum with respect to the frequency even in the free molecular limit.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar–Gross–Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., “A diffusion model for rarefied flows in curved channels,” Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Characteristics of micro-gas journal bearings based on kinetic theory

According to Poiseuille and Couette flow rate correctors, Q ˜ p ( D , α 1 , α 2 ) and Q ˜ C ( D , α 1 , α 2 ) , the modified molecular gas lubrication (MMGL) equation is applied for the analysis of micro-gas journal bearings. The effects of gas rarefaction are considered for arbitrary inverse Knudsen numbers ( D) and non-symmetric accommodation coefficients (AC) conditions ( α 1≠ α 2). The combined effects of Q ˜ p ( D , α 1 , α 2 ) and Q ˜ C ( D , α 1 , α 2 ) on the performance of micro-gas journal bearings are firstly discussed. The results show that the surface property (AC) of moving surface affects the bearing performance more significantly than that of stationary surface does. The load carrying capacity increases as the AC of moving surface increases or the inverse Knudsen number increases.

Impact of the gas-surface scattering and gas molecule-molecule interaction on the mass flow rate of the rarefied gas through a short channel into a vacuum

The rarefied gas flow through a short channel into a vacuum has been investigated computationally using the direct simulation Monte Carlo method. Taking into account the gas-surface scattering and the gas molecule-molecule interaction, the mass flow rate is calculated as a function of gas rarefaction and the length to height ratio. This study demonstrates that the effects of the gas molecule-molecule interaction and the gas-surface scattering can make a noticeable impact on the mass flow rate of the rarefied gas through a short channel into a vacuum. The maximum manifestation of these effects was evaluated.

Numerical simulation of turbomolecular pump over a wide range of gas rarefaction

A gas flow through a turbomolecular pump is modeled by the direct-simulation Monte Carlo method over a wide range of gas rarefaction covering the free-molecular, transitional, and hydrodynamic regimes. Several values of the rotor speed are considered. The main characteristics of the pump, such as maximum pumping speed and compression ratio, are reported. It is pointed out that in the range between the free-molecular and transitional regimes, the pump characteristics change slightly, but they vary significantly in the hydrodynamic regime. It is shown that the pumping speed increases in the hydrodynamic regime when the rotor speed is high, but it decreases for a small value of the speed. The compression ratio always decreases when approaching the hydrodynamic regime.

Distance-dependent plasma composition and ion energy in high power impulse magnetron sputtering

The plasma composition of high power impulse magnetron sputtering (HIPIMS) has been studied for titanium and chromium targets using a combined energy analyser and quadrupole mass spectrometer. Measurements were done at distances from 50 to 300 mm from the sputtering target. Ti and Cr are similar in atomic mass but have significantly different sputter yields, which gives interesting clues on the effect of the target on plasma generation and transport of atoms. The Ti and Cr HIPIMS plasmas operated at a peak target current density of ∼0.5 A cm−2. The measurements of the argon and metal ion content as well as the ion energy distribution functions showed that (1) singly and doubly charged ions were found for argon as well as for the target metal, (2) the majority of ions were singly charged argon for both metals at all distances investigated, (3) the Cr ion density was maintained to distances further from the target than Ti. Gas rarefaction was identified as a main factor promoting transport of metal ions, with the stronger effect observed for Cr, the material with higher sputter yield. Cr ions were found to displace a significant portion of the gas ions, whereas this was less evident in the Ti case. The observations indicate that the presence of metal vapour promotes charge exchange and reduces the electron temperature and thereby practically prevents the production of Ar2+ ions near the target. The content of higher charge states of metal ions depends on the probability of charge exchange with argon.