scholarly journals Experimental and theoretical studies of the behaviour of slow electrons in air. I

1949 ◽  
Vol 196 (1046) ◽  
pp. 402-426 ◽  
Keyword(s):  
Drift Velocity ◽  
Mean Free Path ◽  
Free Electrons ◽  
Direct Measurements ◽  
Electronic Motion ◽  
The Mean ◽  
Gas Molecules ◽  
Slow Electrons ◽  
Experimental And Theoretical Studies ◽  
Unit Pressure

This paper is an account of an experimental investigation of the motions of free electrons in air by the method developed by Townsend. An improved form of apparatus is described with the appropriate theory. The following parameters of the electronic motion were determined as functions of the ratio Z/p of the electric field strength Z to the gas pressure p : Townsend’s energy factor k r the drift velocity W , the mean free path at unit pressure L and the mean proportion n of its energy lost in collisions with gas molecules. The experimental data are given in the form of tables and curves. The drift velocity W is found by a new procedure based on the Hall effect and by comparing the velocities W so obtained with the direct measurements of W by Nielsen & Bradbury it is seen that the velocities of agitation are distributed approximately according to Druyvesteyn’s law when Z/p exceeds 0.5. Bailey’s factor G , which is of importance in ionospheric studies, is obtained from the experimental dependence of η on k r . Theoretical formulae are derived for k r and W in terms of L, G and Z/p . The theory of the new method for measuring W is given in an appendix.

scholarly journals The Diffusion of Slow Electrons in Deuterium

1955 ◽  
Vol 8 (4) ◽  
pp. 468 ◽  
Author(s):  
Barbara IH Hall
Keyword(s):  
Cross Section ◽  
Mean Free Path ◽  
Lateral Spread ◽  
Electron Stream ◽  
Collisional Cross Section ◽  
The Mean ◽  
Energy Coefficient ◽  
Slow Electrons ◽  
Deuterium Molecule ◽  
Unit Pressure

The agitational energies and drift velocities of slow electrons diffusing in deuterium are measured as a function of the ratio Z/p of the electric field strength Z to the gas pressure p. The lateral spread of the diffusing electron stream is measured, which enables Townsend's energy coefficient to be calculated. Drift velocities are measured using a magnetic deflection method. On the basis of the kinetic theory of gases these measurements are used to calculate values for the mean free path L of the electrons at unit pressure, the mean proportion η of the energy lost by an electron in a collision with a deuterium molecule, and the collisional cross section A of the molecules in collisions with the electrons. The values obtained are compared with those of Crompton and Sutton (1952) for hydrogen.

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 Maximum Possible Colling Rate in Ultrafast Chip Nanocalorimetry: Fundamental Limitations Due to Thermal Resistance at the Membrane/Gas Interface

2021 ◽  
Author(s):  
Alexander A. Minakov ◽  
Christoph Schick
Keyword(s):  
Thermal Resistance ◽  
Cooling Rate ◽  
Materials Science ◽  
Mean Free Path ◽  
Heat Conducting ◽  
Controlled Cooling ◽  
Fundamental Limitations ◽  
The Mean ◽  
Gas Molecules ◽  
Hot Zone

Ultrafast chip nanocalorimetry opens up remarkable possibilities in materials science by allowing samples to be cooled and heated at extremely high rates. Due to heat transfer limitations, controlled ultrafast cooling and heating can only be achieved for tiny samples in calorimeters with a micron-thick membrane. Even if ultrafast heating can be controlled under quasi-adiabatic conditions, ultrafast controlled cooling can be performed if the calorimetric cell is located in a heat-conducting gas. It was found that the maximum possible cooling rate increases as 1/r0 with decreasing radius r0 of the hot zone of the membrane. The possibility of increasing the maximum cooling rate with decreasing r0 was successfully implemented in many experiments. In this regard, it is interesting to answer the question: what is the maximum possible cooling rate in such experiments if r0 tends to zero? Indeed, on submicron scales, the mean free path of gas molecules lmfp becomes comparable to r0, and the temperature jump that exists at the membrane/gas interface becomes significant. Considering the limitation associated with thermal resistance at the membrane/gas interface and considering the transfer of heat through the membrane, we show that the controlled cooling rate can reach billions of K/s, up to 1010 K/s.

Applicability of the Wright Polynomial Correction for Time-Resolved Laser-Induced Incandescence in the Transition Regime

2012 ◽  
Author(s):  
K. J. Daun ◽  
S. C. Huberman
Keyword(s):  
Heat Conduction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Transition Regime ◽  
Time Resolved ◽  
Laser Induced Incandescence ◽  
The Mean ◽  
Gas Molecules

Sizing aerosolized nanoparticles through time-resolved laser-induced incandescence (TiRe-LII) requires an accurate model of the heat conduction from the laser-energized particle to the surrounding gas. Under transition regime conditions this is often done using Fuchs’ boundary-sphere method, which requires the analyst to specify the thickness of a collisionless layer surrounding the particle, representing the Knudsen layer. Traditionally the boundary layer thickness is set to the mean free path of the gas at the boundary temperature, but recently some TiRe-LII practitioners have adopted a more complex treatment that accounts for particle curvature and directional distribution of gas molecules. This paper presents a critical reassessment of this approach; while this modification is more representative of the true Knudsen layer thickness, it does not improve the accuracy of heat conduction rates estimated using Fuchs’ boundary sphere methods under conditions prevailing in most TiRe-LII experiments.

DSMC Simulation of Supersonic Gas Flow in Microchannel

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Gas Flow ◽  
Characteristic Length ◽  
Flow Characteristics ◽  
Mean Free Path ◽  
Incoming Flow ◽  
Characteristic Length Scale ◽  
Flow Pressure ◽  
Supersonic Gas Flow ◽  
The Mean ◽  
Gas Molecules

The present study is concerned with the flow characteristics of a microchannel supersonic gas flow. The direct simulation Monte Carlo (DSMC) method is employed for predicting the density, velocity and temperature distributions. For gas flows in micro systems, the continuum hypothesis, which underpins the Navier-Stokes equations, may be inappropriate. This is because the mean free path of the gas molecules may be comparable to the characteristic length scale of the device. The Knudsen number, Kn, which is the ratio of the mean free path of the gas molecules to the characteristic length scale of the device, is a convenient measure of the degree of rarefaction of the flow. In this paper, the effect of Knudsen number on supersonic microchannel flow characteristics is studied by varying the incoming flow pressure or the microchannel height. In addition, the microchannel height and the incoming flow pressure are varied simultaneously to investigate their effects on the flow characteristics. Meanwhile, the results show that until the diffuse reflection model is used throughout the microchannel, the temperature and the Mach number in the microchannel entrance may not be equal to free-stream values and therefore a discontinuity appear in the flow field.

scholarly journals The Ultimate Ballistic Drift Velocity in Carbon Nanotubes

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammad Taghi Ahmadi ◽  
Razali Ismail ◽  
Michael L. P. Tan ◽  
Vijay K. Arora
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Carrier Concentration ◽  
Drift Velocity ◽  
Mean Free Path ◽  
High Electric Field ◽  
Fermi Velocity ◽  
Zero Field ◽  
Saturation Velocity ◽  
The Mean

The carriers in a carbon nanotube (CNT), like in any quasi-1-dimensional (Q1D) nanostructure, have analog energy spectrum only in the quasifree direction; while the other two Cartesian directions are quantum-confined leading to a digital (quantized) energy spectrum. We report the salient features of the mobility and saturation velocity controlling the charge transport in a semiconducting single-walled CNT (SWCNT) channel. The ultimate drift velocity in SWCNT due to the high-electric-field streaming is based on the asymmetrical distribution function that converts randomness in zero-field to a stream-lined one in a very high electric field. Specifically, we show that a higher mobility in an SWCNT does not necessarily lead to a higher saturation velocity that is limited by the mean intrinsic velocity depending upon the band parameters. The intrinsic velocity is found to be appropriate thermal velocity in the nondegenerate regime, increasing with the temperature, but independent of carrier concentration. However, this intrinsic velocity is the Fermi velocity that is independent of temperature, but depends strongly on carrier concentration. The velocity that saturates in a high electric field can be lower than the intrinsic velocity due to onset of a quantum emission. In an SWCNT, the mobility may also become ballistic if the length of the channel is comparable or less than the mean free path.

scholarly journals Experimental and theoretical studies of the behaviour of slow electrons in air. II. Ionospheric and other applications

1949 ◽  
Vol 196 (1046) ◽  
pp. 427-435 ◽  
Keyword(s):  
Experimental Data ◽  
Free Electron ◽  
Laboratory Data ◽  
Wave Interaction ◽  
Theoretical Studies ◽  
Radio Waves ◽  
Electronic Motion ◽  
Slow Electrons ◽  
Experimental And Theoretical Studies

The significance, for ionospheric and other studies, of the experimental data given in part I is considered. It is shown how the data obtained from rocket soundings may be combined with the measurements of wave interaction in the ionosphere and the laboratory data given in part I, to estimate the height at which wave interaction occurs and the collisional frequency at that height. The following topics are also discussed: the theory of electronic motion in direct and alternating fields; the power communicated to a free electron in a gas by an alternating field; and the interaction of radio waves in the ionosphere.

Experimental investigation of the diffusion of slow electrons in nitrogen and hydrogen

1952 ◽  
Vol 215 (1123) ◽  
pp. 467-480 ◽  
Keyword(s):  
Experimental Investigation ◽  
Cross Sections ◽  
Mean Free Path ◽  
Uniform Electric Field ◽  
Tabular Form ◽  
Energy Coefficient ◽  
Slow Electrons ◽  
Physical Quantities ◽  
Unit Pressure ◽  
Gas Pressures

This paper presents the results of precise measurements of the diffusion of slow electrons in hydrogen and nitrogen in the presence of a uniform electric field. Such measurements lead directly to the value of Townsend’s energy coefficient ( k T ) as a function of Z/p (field strength/gas pressure). Since the drift velocity ( W ) of the electrons is also known (Nielsen & Bradbury 1936), the following physical quantities are deduced as functions of Z/p : mean free path of the electrons at unit pressure, mean energy lost by an electron per collision and the collisional cross-sections of the molecules. Measurements of the diffusion were obtained from two apparatuses which differed in dimensions and metal of the electrodes. The range of gas pressures employed was 3 to 14 mm of mercury. A table shows that the values of k T as a function of Z/p derived from these measurements agree (with one exception) to within 3%, and it is therefore considered that the measurements are trustworthy. The results are presented graphically and in tabular form.

On the motion induced in a gas confined in a small-scale gap due to instantaneous boundary heating

2007 ◽  
Vol 593 ◽  
pp. 453-462 ◽  
Author(s):  
A. MANELA ◽  
N. G. HADJICONSTANTINOU
Keyword(s):  
Early Time ◽  
Mean Free Path ◽  
Small Scale ◽  
Characteristic Time Scale ◽  
Relative Temperature ◽  
The Mean ◽  
Gas Molecules ◽  
Hydrodynamic Fields ◽  
Gap Width ◽  
Good Agreement

We analyse the time response of a gas confined in a small-scale gap (of the order of or smaller than the mean free path) to an instantaneous jump in the temperature of its boundaries. The problem is formulated for a collisionless gas in the case where the relative temperature jump at each wall is small and independent of the other. An analytic solution for the probability density function is obtained and the respective hydrodynamic fields are calculated. It is found that the characteristic time scale for arriving at the new equilibrium state is of the order of several acoustic time scales (the ratio of the gap width to the most probable molecular speed of gas molecules). The results are compared with direct Monte Carlo simulations of the Boltzmann equation and good agreement is found for non-dimensional times (scaled by the acoustic time) not exceeding the system Knudsen number. Thus, the present analysis describes the early-time behaviour of systems of arbitrary size and may be useful for prescribing the initial system behaviour in counterpart continuum-limit analyses.

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