Sound Propagation Through a Gas in Microscale

2009 ◽  
Author(s):  
Felix Sharipov ◽  
Denize Kalempa
Keyword(s):  
Kinetic Equation ◽  
Free Path ◽  
Sound Wave ◽  
Gas Flow ◽  
Sound Propagation ◽  
Rarefied Gas ◽  
Mean Free Path ◽  
Sound Waves ◽  
Wave Source ◽  
Wide Range

A sound wave propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation by taking into account the influence of the receptor of sound waves on the solution of the problem. In order to do so, a plate oscillating in the normal direction to its own plane is considered as a sound wave source while a stationary one is considered as being the receptor of sound waves. The distance between the plates can be of the order of the molecular mean free path. It is assumed a fully established oscillation so that the solution of the kinetic equation depends on time harmonically. The main parameters of the problem are the oscillation speed parameter, defined as the ratio of intermolecular collision frequency to the sound frequency, and the Knudsen number, defined as the ratio of the molecular mean free path to a characteristic scale of the gas flow. The problem is solved over a wide range of both parameters and the amplitudes and phases of all the macrocharacteristics of the gas flow are calculated.

Lattice Boltzmann Simulation of Rarefied Gas Flow Along Moving Rigid Objects in Micro-Cavities

2015 ◽  
Author(s):  
Weilin Yang ◽  
Hongxia Li ◽  
TieJun Zhang ◽  
Ibrahim M. Elfadel
Keyword(s):  
Free Path ◽  
Lattice Boltzmann ◽  
Path Length ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Free Path Length ◽  
Mean Free Path ◽  
Fluid Simulation ◽  
Transition Flow ◽  
Rarefied Gas Flow

Rarefied gas flow plays an important role in the design and performance analysis of micro-electro-mechanical systems (MEMS) under high-vacuum conditions. The rarefaction can be evaluated by the Knudsen number (Kn), which is the ratio of the molecular mean free path length and the characteristic length. In micro systems, the rarefied gas flow usually stays in the slip- and transition-flow regions (10−3 < Kn < 10), and may even go into the free molecular flow region (Kn > 10). As a result, conventional design tools based on continuum Navier-Stokes equation solvers are not applicable to analyzing rarefaction phenomena in MEMS under vacuum conditions. In this paper, we investigate the rarefied gas flow by using the lattice Boltzmann method (LBM), which is suitable for mesoscopic fluid simulation. The gas pressure determines the mean free path length and Kn, which further influences the relaxation time in the collision procedure of LBM. Here, we focus on the problem of squeezed film damping caused by an oscillating rigid object in a cavity. We propose an improved LBM with an immersed boundary approach, where an adjustable force term is used to quantify the interaction between the moving object and adjacent fluid, and further determines the slip velocity. With the proposed approach, the rarefied gas flow in MEMS with squeezed film damping is characterized. Different factors that affect the damping coefficient, such as pressure of gas and frequency of oscillation, are investigated in our simulation studies.

New low-frequency waves and negative mass instability in dusty plasmas

2010 ◽  
Vol 76 (6) ◽  
pp. 929-937
Author(s):  
D. P. RESENDES ◽  
R. BINGHAM ◽  
S. MOTA ◽  
V. N. TSYTOVICH
Keyword(s):  
Electron Temperature ◽  
Free Path ◽  
Collision Frequency ◽  
Low Frequency ◽  
Mean Free Path ◽  
Sound Waves ◽  
Ion Temperature ◽  
Plasma Particle ◽  
Charging Mode ◽  
Dust Charging

AbstractLow-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered taking into account elastic and charging collisions of plasma particles with dust and neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effectice collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions, the properties of the waves are different from those considered previously. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals, this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability, a new dust oscillation, a dust charging mode, is found, whose frequency is almost constant over a certain range of wave numbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperature, as for the usual dust sound waves, with the electron temperature substantially exceeding the ion temperature.

The electrical properties of graphite

1953 ◽  
Vol 217 (1128) ◽  
pp. 9-26 ◽  
Keyword(s):  
Single Crystal ◽  
Free Path ◽  
Hall Coefficient ◽  
Mean Free Path ◽  
Free Electrons ◽  
Satisfactory Explanation ◽  
Wide Range ◽  
The Mean ◽  
Positive Holes ◽  
Crystalline Graphite

The Hall coefficient and resistivity of a range of polycrystalline graphites with different crystal sizes and a single crystal of Travancore graphite have been measured over a wide range of temperature. The number of free electrons has been found to be approximately 6x10 18 per cm 3 at room temperature; the variation with temperature cannot be accurately determined. The deficit of electrons in poorly crystalline graphite gives rise to positive Hall coefficients. Quenching removes electrons, and a study of this process has enabled the ratio of the mobilities of positive holes and electrons to be estimated at 0·80. An interesting effect has been observed in the variation of the Hall coefficient of the single crystal with field; no satisfactory explanation has been found for this phenomenon. The resistivity of polycrystalline graphite depends on the density and on the orientation and size of the crystals. From the variation of resistivity with temperature and the size of the crystals, the mean free path due to thermal scattering, has been found to be 2350 Å at 273° K; the variation of mean free path with temperature has been deduced. The product of effective mass and velocity of the free electrons has been determined as a function of temperature; the accuracy is limited by uncertainties in the number of free electrons.

scholarly journals Oscillatory rarefied gas flow inside rectangular cavities

2014 ◽  
Vol 748 ◽  
pp. 350-367 ◽  
Author(s):  
Lei Wu ◽  
Jason M. Reese ◽  
Yonghao Zhang
Keyword(s):  
Aspect Ratio ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Scaling Law ◽  
Frequency Range ◽  
Damping Force ◽  
Driven Cavity ◽  
Linearized Boltzmann Equation ◽  
Wide Range ◽  
Oscillation Frequencies

AbstractTwo-dimensional oscillatory lid-driven cavity flow of a rarefied gas at arbitrary oscillation frequency is investigated using the linearized Boltzmann equation. An analytical solution at high oscillation frequencies is obtained, and detailed numerical results for a wide range of gas rarefaction are presented. The influence of both the aspect ratio of the cavity and the oscillating frequency on the damping force exerted on the moving lid is studied. Surprisingly, it is found that, over a certain frequency range, the damping is smaller than that in an oscillatory Couette flow. This reduction in damping is due to the anti-resonance of the rarefied gas. A scaling law between the anti-resonant frequency and the aspect ratio is established, which would enable the control of the damping through choosing an appropriate cavity geometry.

scholarly journals A rarefied gas flow around a rotating sphere: diverging profiles of gradients of macroscopic quantities

2019 ◽  
Vol 862 ◽  
pp. 5-33 ◽  
Author(s):  
Satoshi Taguchi ◽  
Kazuyuki Saito ◽  
Shigeru Takata
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Velocity Distribution Function ◽  
Normal Derivative ◽  
Accommodation Coefficient ◽  
Jump Discontinuity ◽  
Rotating Sphere ◽  
Wide Range ◽  
Normal Distance ◽  
The Moment

The steady behaviour of a rarefied gas around a rotating sphere is studied numerically on the basis of the linearised ellipsoidal statistical model of the Boltzmann equation, also known as the ES model, and the Maxwell diffuse–specular boundary condition. It is demonstrated numerically that the normal derivative of the circumferential component of the flow velocity and that of the heat flux diverge on the boundary with a rate $s^{-1/2}$, where $s$ is the normal distance from the boundary. Further, it is demonstrated that the diverging term is proportional to the magnitude of the jump discontinuity of the velocity distribution function on the boundary, which originates from the mismatch of the incoming and outgoing data on the boundary. The moment of force exerted on the sphere is also obtained for a wide range of the Knudsen number and for various values of the accommodation coefficient.

The Comparative Study of Non-Equilibrium and Equilibrium MD Simulation Results on Gas Flow in Nanopore

2013 ◽  
Vol 328 ◽  
pp. 684-689
Author(s):  
Qi Xin Liu ◽  
Zhi Yong Cai ◽  
Xiao Ping Yu
Keyword(s):  
Free Path ◽  
Density Profile ◽  
Gas Flow ◽  
Md Simulation ◽  
Md Simulations ◽  
Mean Free Path ◽  
Number Density ◽  
Gas Molecules ◽  
Simulation Results ◽  
Non Equilibrium

Now the non-equilibrium MD simulations are frequently used to study the gas flow characteristic at nanoscale. In the non-equilibrium MD simulations, one force which is several magnitude orders larger than the actual force was added on all gas molecules. Its very necessary to study whether such large force added in non-equilibrium MD simulation will affect the simulation results. The present paper carried out the comparative studies on the simulation results of gas flow in nanopores by non-equilibrium and equilibrium MD. The gas number density profile and the gas molecular mean free path are studied in this paper, our simulation results indicate that both non-equilibrium and equilibrium MD produce no obvious difference on simulation results of the gas number density profile and the gas molecular mean free path. It could be concluded that even the force added on every gas molecules is very large in non-equilibrium MD simulation; the added force doesnt obviously affect the simulation results.

Theoretical Considerations of Molecular Mean Free Path Influenced Slip in Self-Acting Gas-Lubricated Plain Journal Bearings

1984 ◽  
Vol 198 (1) ◽  
pp. 25-31 ◽  
Author(s):  
M Malik
Keyword(s):  
Steady State ◽  
Beneficial Effect ◽  
Free Path ◽  
Dynamic Performance ◽  
Mean Free Path ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Wide Range ◽  
Theoretical Investigations ◽  
Theoretical Considerations

The purpose of this paper is to study the effect of slip under the influence of molecular mean free path on the steady state and dynamic performance characteristics of plain gas journal bearings. The theoretical investigations have been made over a wide range of compressibility number. It is found that slip usually impairs the bearing performance, particularly at low compressibility numbers, A; the effect of slip, however, diminishes with increasing values of A. In fact at high compressibility numbers, theory suggests that slip has a beneficial effect of improving the dynamic performance of the bearing.

Sign in / Sign up

Export Citation Format

Share Document