Free-molecular Gas Flow Research Articles

Interaction of an ensemble of microparticles with a free molecular gas flow escaping from an orifice

The motion of microparticles interacting with a free molecular gas flow escaping from an orifice has been numerically simulated with allowance for asymptotic properties of the flow. Specific features of collective properties of the ensemble of microparticles and the evolution of uncertainty in the initial conditions of a separate particle are considered.

Free-molecular gas flow through an oscillating membrane

Free-molecular gas flow through a membrane oscillating in its own plane is investigated. The probability of the passage through the membrane by gas molecules is calculated as a function of dimensionless parameters characterizing the channel geometry, themolecularmass, the gas temperature, and the membrane oscillation frequency and amplitude. It is shown that the membrane permeability for one or another gas can be controlled by means of changing the forced oscillation parameters.

Free-Molecular Gas Flow in a Narrow (Nanosize) Channel

We have analyzed a free-molecular gas flow in cylindrical channels (capillaries) with impermeable walls for various schemes of the scattering of molecules by channel walls, taking account of the surface diffusion of adsorbed molecules, and a gas flow in such channels with allowance for phase transformations on their walls. A substantial influence of surface diffusion on the mass transfer in gaseous mixtures in the indicated channels has been revealed. The modification of the phenomenological relations of the nonequilibrium thermodynamics of discontinuous systems is considered. The problem of uniform deposition of thin films on the inner surface of a cylindrical channel is discussed.

Application of moment equations to the mathematical simulation of gas microflows

An approach to the simulation of moderately rarefied gas flows in a transition zone is developed. The applicability of the regularized Grad 13-moment (R13) equations to the numerical simulation of a transition flow between the continual and free-molecular gas flow regimes is explored. For the R13 equations, a numerical method is proposed that is a higher order accurate version of Godunov’s explicit method. A numerical procedure for implementing solid-wall boundary conditions is developed. One- and two-dimensional test problems are solved, including the shock wave structure and the Poiseuille flow in a plane channel. The possibility of applying the R13 equations to the simulation of plane channel and jet flows in a transition regime is explored. To this end, the flow in a square cavity generated by the motion of one of the walls is studied and the operation of the Knudsen pump is analyzed.

Limiting self-similar motion of a solid particle in a free-molecular gas flow escaping from an orifice

A problem of motion of a single spherical solid particle in the far wake of a free-molecular gas flow escaping from an orifice is considered. It is shown that the spatial distributions of macroscopic parameters of the gas are completely determined by functions of one variable: coordinate along an arbitrary straight line normal to the axis of symmetry. Based on this property, a dimensionless equation of particle motion is derived, which has self-similar solutions: trajectories of motion and particle coordinates (traces) on the target for different initial conditions. Conditions of determining the gas flow behavior on the basis of particle traces on the target are considered.

Thermal transpiration in mixed cellulose ester membranes: Enabling miniature, motionless gas pumps

In this paper, we introduce the use of thin mesoporous mixed cellulose ester (polymer) membranes as the enabling element of miniature, motionless gas pumps. The pores within these membranes serve as channels that constrain gas molecules to the free molecular or transitional gas flow regimes. A temperature gradient across the membranes causes a transpiration based gas flow from the cold side to the hot side; this type of flow is the basis of Knudsen pumps. Gas flow characteristics and vacuum generation capabilities of polymer membranes with three different pore-sizes are reported. In this group, membranes with 25 nm pore-size provide superior functionality. For an input power of 1.4 W/cm 2, Knudsen pump test structures based on this membrane material provide a typical gas flow rate of ≈0.93 sccm/cm 2 in the absence of pressure load. The transient pressure response is used to quantify various non-idealities. Experiments suggest that these polymer membranes are relatively defect-free as compared to bulk microporous ceramics that were previously evaluated for similar applications. In longevity tests performed to date, a polymer pump has operated continuously for ≈6000 h without significant deterioration in its performance.

Numerical simulations of gas-dynamic conductivity of microchannels with allowance for their surface structure

The effect of the microchannel surface structure on the free-molecular gas flow is studied by the test-particle method. Simulations are performed for channels whose surface either is obtained by means of statistical modeling or is reconstructed from the data of atomic-force microscopy of real surfaces. Dependences of monochromatic molecular beam scattering on the angle of incidence and the average height of microscopic roughness elements on the surface are considered. It is demonstrated that the method developed allows one to obtain the distribution function for particles reflected from a rough surface and to use it in the boundary conditions in problems of rarefied gas dynamics.

Heat transfer in vacuum packaged microelectromechanical system devices

This study analyzes heat transfer effects inside vacuum packaged microelectromechanical system (MEMS) devices. A packaged device is simplified as four plates forming a square cavity, the bottom plate represents a hot chip, while the other three plates are maintained at room temperature. For a highly rarefied free molecular internal gas flow scenario, the corresponding detailed density and temperature fields are analytically determined with a proposed speculation. This speculation indicates that for a steady free molecular gas flow inside a convex closure domain formed by walls maintained at different temperatures: (1) the velocity distribution functions for those molecules diffusely reflected at different walls and traveling away from them are Maxwellian with different number densities; (2) for each distribution, niTi is a constant, where ni is the number density for the group of reflected molecules, and Ti is the temperature for the ith plate. For a near continuum flow scenario, the governing energy equation degenerates to Laplace’s equation with several temperature-jump wall boundary conditions. This study also includes discussions and comparisons among analytical results, simulation results from the direct simulation Monte Carlo method, and results by solving the Navier–Stokes equations with proper wall boundary conditions. The approach used in this study is generally applicable to study internal flows and heat transfer effects in other vacuum packaged MEMS devices with different shapes.

Efficient numerical solution of the Clausing problem

The Clausing integral equation for free-molecular gas flow in a cylindrical tube of arbitrary length is solved by an efficient numerical method. The current numerical results improve upon the precision of values for the molecular transmission probabilities (molecular flow rates or Clausing factors) reported previously in the literature. The basic approach involves the use of a singularity subtraction technique to smooth the kernel of the Clausing integral equation, which is a Fredholm integral equation of the second kind, before solving it via the use of Gauss-Legendre quadratures. The singularity subtraction technique is further modified by the additional subtraction of Clausing’s long tube solution prior to the use of the Gauss-Legendre quadratures. This modification has been shown to improve the speed of the computations, the rate at which the results converge, and the precision of the results, particularly for medium length tubes and in the long tube limit.

Free-molecular gas flow in channels (pores) with physicochemical transformations on the surface

The problems of free-molecular flow of a gas in channels are considered. The literature on the problem is reviewed. The possibility of uniform deposition of a substance on the inside surface of a cylindrical channel is analysed for the case of physicochemical transformations on this surface. The questions of spatial distribution of the molecules outgoing from the channel are discussed.

The design and performance of an effusive gas source of conical geometry for photoionization studies

The design, construction, and performance of an effusive gas source of conical geometry is reported. This gas jet enables experiments that require the gas and photon beams to be essentially collinear and has a focusing multicapillary array with the central portion left free for the photon beam. In total, the source comprises 90 “tubes” in three layers and has been designed by modeling free molecular gas flow and optimizing for highest gas density ∼2–3 mm from the jet’s exit plane. The nature of the gas flow through the source and its focusing properties are investigated theoretically and experimentally.

Influence of the State of a Surface on the Formation of a Rarefied Gas Flow in a Channel

The results of experimental investigation of free-molecular gas flow in channels with an atomically pure and adsorbed surface are presented. The data obtained made it possible to formulate the basic principles which reflect the character of the effect of the chemical composition of a surface on the gas-dynamic conductivity of the channel. Qualitative interpretation of the obtained experimental results is given within the framework of the existing formalism in the description of the scattering of molecular beams by the surface of a solid body. The diffusion factors e have been calculated for different surfaces and gases from experimental data. Satisfactory agreement between numerical simulation by the Monte Carlo method and the experimental data is seen.

Chemical deposition of substance from gas phase in nonisothermal channels

The possibility of using nonisothermality effect in filling semi-closed channels by means of deposition of gas molecules on the inner channel surface is analyzed. The case of chemical deposition is investigated for free-molecular gas flow in the cylindrical channel with the temperature-dependent coefficient which characterizes the efficiency of collisions of molecules with the surface. It is shown that decrease in the surface temperature from the bottom to the open end of the channel enables one to obtain both the substance film which is sufficiently uniform in thickness and the film with monotonous decrease in the thickness towards the exit from the channel. The last factor is important for the problem of filling the channel by the substance without formation of cavities. The possibility of realization of the above temperature distribution along the channel by means of the microwave radiation is considered.

Mass and energy transport in sublimating cometary ice cracks

As the spacecraft encounters to comet Halley have confirmed, comets seem to be bodies of rather low bulk density; i.e., they must contain a rather large fraction of hollow space both on a microscopic scale and on a macroscopic scale. Cracks of different sizes are most probably very common topological features on a cometary surface. Furthermore, if the cometary ice contains a lot of pore space, the thermal behavior and, consequently, the net sublimation rate might be affected. In the present paper we develop a model which describes the mass and energy transport by the gas in a rectangular crack of arbitrary cross section and depth. The model is valid as long as the conditions of free molecular gas flow inside the crack are fulfilled. Hereby it is assumed that the gas sublimates from the walls according to the local ice temperature and that the molecules hitting the ice walls recondense there. The model allows us to calculate gas flux and recondensation rates inside the gap and at its exit provided the temperature profile along the walls is known. It is found that the sublimation rate from an icy surface with many small pores is almost the same as in the case of a flat surface, while the existence of a few larger holes (leading to the same total pore cross section) may drop the sublimation rate of the surface to 80%. If an inverse temperature profile (inward increasing) exists in the ice, gaps can be the major source of emission. Energetically the recondensation of particles in the deeper parts of the gaps does not significantly contribute to the heating of the ice. On the other hand, cooling by net sublimation from the ice walls is important.

Code Development for Analysis of TSTA Compound Cryopumps

A Monte Carlo computer code for analyzing free molecular gas flow has been developed to study the pumping characteristics of compound cryopumps for plasma chamber evacuation of fusion reactors. The code can deal with complex internal geometries of the pumps which commonly consist of cryopumping surfaces surrounded with elements like baffles, shields, and reservoirs. This code was used to study the pumping performance of a compound cryopump in the Tritium Systems Test Assembly (TSTA) at Los Alamos National Laboratory. The results show that the calculated pumping speeds are strongly effected by the geometrical models employed in the calculations, and that an analysis based on a detailed model is essential to estimate the performance of compound cryopumps.

On laser monitoring of transport processes in capillary porous bodies

Some trends in the diffusion of gases in capillaries exposed to resonance laser radiation are considered. The case of a free-molecular gas flow regime is studied in which the interactions of molecules with the walls of capillaries exert a substantial influence on the transport processes, the resonance radiation effect manifesting itself in the variation of such parameters as the energy and time of adsorption and the sticking probability. In fairly fine capillaries, when the surface transport of particles is significant, a change in the above parameters leads to the redistribution of the adsorbed phase density along the capillary length, as a result of which there appears a resultant flux of molecules even in the system previously in an equilibrium state. The problem of the radiation-induced drift of molecules in wide enough capillaries, when the transfer of particles over the surface may be neglected, is also considered. It is shown that radiation may cause a change in the course of the unsteady-state diffusion of gases in porous bodies.

Controlling deposition of a substance onto the inner surface of a cylindrical channel

The problem of material deposition on the inner surface of a channel with freemolecular gas flow is considered.

Gas flow in a capillary with an external disturbance varying the coefficient of molecular adhesion

The effect of change in the molecular adhesion coefficient on mass transfer in a capillary is studied for the free-molecular gas flow regime.

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn ∼ 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn ∼ 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.

An aerodynamic wake in a hypersonic free-molecular gas flow

An experimental investigation was made of the form of an aerodynamic wake and the flow in it for the case where the flow is set up using a point source and is propagated in a motionless residual gas. It is shown that the geometry of the wake is determined by the mutual arrangement of the source and model, that the ground pressure is negligibly small, and that the flow in the wake is part of the oncoming flow, scattered by the residual gas. The value of the transverse velocity ratio exceeds by several orders of magnitude the value of the longitudinal ratio.