scholarly journals The diffusion of electrons through a slit

1914 ◽  
Vol 90 (615) ◽  
pp. 69-72 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Simple Form ◽  
Lateral Diffusion ◽  
Metal Plate ◽  
Electric Force ◽  
Narrow Strip ◽  
Air Gaps ◽  
Uniform Rate

In a paper on “The Motion of Electrons in Gases,” by Prof. Townsend and Mr. Tizard* it was shown how, by measuring the lateral diffusion of a stream of electrons in an electric field, it is possible to find k the factor by which the energy of agitation of the electrons exceeds that of the surrounding molecules. The ions come at a uniform rate through a slit S of width 2 a in a large metal plate A, and traverse a distance c in the direction of an electric force Z. The plane of the plate A may be taken as that of xy , the origin of co-ordinates being the centre of the slit which latter is taken parallel to the axis of y . The ions are received on three insulated electrodes, c 1 c 2 , C 3 , which were portions of a disc of diameter 7 cm., c 2 being a narrow strip 5 mm. wide, cut from the centre of the disc and insulated by narrow air gaps from the two electrodes, c 1 c 3 , on each side of it. The electric field between A and the electrodes C was maintained constant by a series of rings of diameter 7 cm., kept at uniformly decreasing potentials. In this case the differential equation giving the distribution n of electrons in the electric field is ∇ 2 n = 41 Z/ k . ∂ n /∂ z . If q is defined to be ∫ ndy , this equation becomes ∂ 2 q /∂ x 2 + ∂ 2 q /∂ z 2 = 41 Z/ k . ∂ q /∂ z . If n 1 n 2 , n 3 are the charges received by the electrodes c 1 , c 2 , c 3 , it is shown that the values of Z/ k can be found by determining the ratio R = n 2 /( n 1 + n 2 + n 3 ), i . e . the value of k corresponding to any Z can be found. Experiments had previously been performed in which a circular stream of ions was collected on concentric circular electrodes, and from the results it appeared that the term ∂ 2 n /∂ z 2 was small compared with the others. By neglecting this term, Prof. Townsend obtained a solution of the differential equation in a simple form and plotted a curve with co-ordinates R and Z/ k .

scholarly journals The effect of small traces of water vapour on the velocities of ions produced by Röntgen rays in air

1910 ◽  
Vol 84 (569) ◽  
pp. 173-181 ◽  
Keyword(s):  
Electric Field ◽  
Water Vapour ◽  
Lateral Diffusion ◽  
Negative Ions ◽  
Complete Removal ◽  
The Other ◽  
Electric Force ◽  
Dry Air ◽  
Positive Ions ◽  
Low Pressures

Some experiments by Prof. J. S. Townsend on the lateral diffusion of a narrow stream of ions moving in an electric field led to the conclusion that negative ions in perfectly dry air are much smaller than those in air containing a small quantity of moisture. It was consequently to be expected that the complete removal of water vapour would cause an increase in the velocity with which negative ions move under the influence of an electric field of force. At his suggestion the following investigation of the velocities of ions in air at low pressures was undertaken, and it was found that, while the complete removal of water vapour had only a small effect on the velocities of positive ions, yet the same cause increased the velocities of the negative ions by a factor varying between 2 and 30 for the range of pressures and electric forces used in the experiments. The method adopted was to let the ions travel between two gauzes under a known electric force for a time t and then to reverse the field. If v is the velocity of the ions and d is the distance between the gauzes, then ions starting from one gauze will reach the other if t ≮ d / v . If t is gradually decreased, it is possible to find, by means of an electrometer, when ions cease to reach the second gauze; when this happens v = d / t .

scholarly journals The motion of electrons in gases

1913 ◽  
Vol 88 (604) ◽  
pp. 336-347 ◽  
Keyword(s):  
Electric Field ◽  
Lateral Diffusion ◽  
Ultra Violet ◽  
Negative Ions ◽  
Central Line ◽  
Transverse Magnetic ◽  
Uniform Electric Field ◽  
Internal Diameter ◽  
Narrow Slit ◽  
Electric Force

1. The methods of investigating the motion of negative ions in gases at low pressure that have been explained in some previous papers may be extended to cases in which larger variations are made in the electric force and pressure. In order to find the kinetic energy of the motion of agitation of the ions, the velocity in the direction of an electric force, and the value of e / m for different forces and pressures, it is necessary to investigate experimentally two properties which are characteristic of the motion of electrons. These are the abnormal lateral diffusion of a stream of ions moving in a uniform electric field, and the deflection of the stream produced by a small transverse magnetic force. In the previous experiments the two phenomena were investigated separately and in each case with apparatus which gave satisfactory results when small electric forces were used and the pressures were limited to a certain range. In order to investigate the motion under larger forces an apparatus of more suitable dimensions was constructed, by means of which both the required sets of experiments may be made. 2. The negative ions were generated by the action of ultra-violet light on the plate A, fig. 1, and after traversing the distance from A to B some of the ions passed through a narrow slit S, 2 mm. wide and 15 mm. long, in the centre of the metal sheet B. The electric force was in the same direction on the two sides of B, so that the ions, after passing through the slit, continue their motion towards the plane electrodes C, which were parallel to the plane of B. The electrodes C were 4 cm. from B, and three flat rings, R 1 , R 2 , R 3 , 7 cm. internal diameter, were fixed at distances of 1, 2, and 3 cm. respectively from the plane of the electrode C. A separate connection for each ring and for the plates A and B was brought out through a large ebonite plug fitted in the brass cover of the apparatus, and was maintained at a potential proportional to the distance of the corresponding ring, or plate, from the electrodes C. The stream of ions that came through the slit moved in a uniform electric field and was received by the three insulated electrodes c 1 , c 2 , c 3 . These were portions of a disc 7 cm. in diameter, the central section c 2 being 4.5 mm. wide and separated from the two equal side plates c 1 and c 3 by air gaps 0.5 mm, wide. The narrow gaps between the electrodes were parallel to the direction of the slit in B. In the calculations it will be supposed that the electrode c 2 is 5 mm. wide, and that the side plates c 1 and c 3 come within 2.5 mm. of the central line.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

The ionization kinetics and electric field in the leader channel in long air gaps

1997 ◽  
Vol 30 (11) ◽  
pp. 1616-1624 ◽  
Author(s):  
N L Aleksandrov ◽  
E M Bazelyan ◽  
I V Kochetov ◽  
N A Dyatko
Keyword(s):  
Electric Field ◽  
Air Gaps

A perturbation solution to the problem of Wien dissociation in weak electrolytes

1978 ◽  
Vol 359 (1698) ◽  
pp. 303-317 ◽  
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Applied Electric Field ◽  
Pair Distribution Function ◽  
Infinite System ◽  
Perturbation Technique ◽  
Relative Increase ◽  
Ion Pair ◽  
Legendre Transform ◽  
Weak Electrolytes

The problem of Wien dissociation of a weak electrolyte in the presence of a uniform applied electric field, X , is analysed by using a perturbation technique. The partial differential equation for the ion-pair distribution function is first reduced to an infinite system of ordinary differential equations by taking the Legendre transform . Explicit expressions for the relative increase in the dissociation constant, K ( X )/ K (0), due to the applied electric field, are calculated to second order in the expansion parameter 2 βq , where β is proportional to X and q is the Bjerrum association distance. Further, by induction, the m th term of this expansion is derived. The infinite series obtained in this way for K ( X )/ K (0) is convergent for all values of βq , and when summed, agrees with a formula in terms of an ordinary Bessel function of order one, given by onasager (1934) whose derivation has been published in full.

Electric features of dislocations and electric force between dislocations

2020 ◽  
pp. 108128652096564
Author(s):  
Yuanjie Huang
Keyword(s):  
Electric Field ◽  
Dielectric Materials ◽  
Dislocation Motion ◽  
Vital Role ◽  
Dislocation Dynamics ◽  
Electric Force ◽  
Fundamental Knowledge ◽  
Large Dielectric Constant ◽  
Net Charges ◽  
First Time

Dislocations and dislocation dynamics are the cores of material plasticity. In this work, the electric features of dislocations were investigated theoretically. An intrinsic electric field around a single dislocation was revealed. In addition to the well-known Peach–Koehler force, it was established that an important intrinsic electric force exists between dislocations, which is uncovered here for the first time and has been neglected since the discovery of dislocations. The electric forces may be large and sometimes could exceed the Peach–Koehler force for metals and some dielectric materials with large dielectric constant. Therefore, the electric force is anticipated to play a vital role in dislocation dynamics and material plasticity. Moreover, an external electric field could exert an electric force on dislocations and a threshold electric field was subsequently discovered above which this force enables dislocations to glide. Interestingly, it was found that some dislocations move in one direction, but others move in reverse in an identical electric field, which is in agreement with experimental observations. Despite dislocation motion under an electric field, to one’s surprise, both edge and screw dislocations do not carry net charges by themselves, which may tackle the long-standing puzzle on the charges of dislocations. These findings may supply people with new fundamental knowledge on dislocations as well as dislocation dynamics, and may assist people in understanding related phenomena.

scholarly journals Tracking Lysosome Migration within Chinese Hamster Ovary (CHO) Cells Following Exposure to Nanosecond Pulsed Electric Fields

2018 ◽  
Vol 5 (4) ◽  
pp. 103
Author(s):  
Gary Thompson ◽  
Hope Beier ◽  
Bennett Ibey
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Mammalian Cells ◽  
Plasma Membranes ◽  
Chinese Hamster ◽  
Lateral Diffusion ◽  
Cell Swelling ◽  
Dependent Manner ◽  
Membrane Repair ◽  
Osmotic Swelling

Above a threshold electric field strength, 600 ns-duration pulsed electric field (nsPEF) exposure substantially porates and permeabilizes cellular plasma membranes in aqueous solution to many small ions. Repetitive exposures increase permeabilization to calcium ions (Ca2+) in a dosage-dependent manner. Such exposure conditions can create relatively long-lived pores that reseal after passive lateral diffusion of lipids should have closed the pores. One explanation for eventual pore resealing is active membrane repair, and an ubiquitous repair mechanism in mammalian cells is lysosome exocytosis. A previous study shows that intracellular lysosome movement halts upon a 16.2 kV/cm, 600-ns PEF exposure of a single train of 20 pulses at 5 Hz. In that study, lysosome stagnation qualitatively correlates with the presence of Ca2+ in the extracellular solution and with microtubule collapse. The present study tests the hypothesis that limitation of nsPEF-induced Ca2+ influx and colloid osmotic cell swelling permits unabated lysosome translocation in exposed cells. The results indicate that the efforts used herein to preclude Ca2+ influx and colloid osmotic swelling following nsPEF exposure did not prevent attenuation of lysosome translocation. Intracellular lysosome movement is inhibited by nsPEF exposure(s) in the presence of PEG 300-containing solution or by 20 pulses of nsPEF in the presence of extracellular calcium. The only cases with no significant decreases in lysosome movement are the sham and exposure to a single nsPEF in Ca2+-free solution.

Numerical Study for Effect of Staggered Wire Electrodes in a Electrostatic Precipitator

2019 ◽  
Author(s):  
Hoyeon Choi ◽  
Yong Gap Park ◽  
Man Yeong Ha
Keyword(s):  
Electric Field ◽  
Corona Discharge ◽  
Reference Frame ◽  
High Voltage ◽  
Current Density ◽  
Electrostatic Precipitator ◽  
Collection Efficiency ◽  
Electric Force ◽  
Wire Electrode ◽  
Particle Charging

Abstract In this paper, a numerical model was developed to describe the wire-plate electrostatic precipitator, commonly called electronic air cleaners. Electrostatic precipitator have been widely used to control particulate pollutants, which adversely affect human health. In this model, the complex interactions between fluid dynamics, electric fields and particle dynamics are considered. Therefore different approach methods are used in this study for each field, Eulerian reference frame was used for the fluid flow field and the electric field, Lagrangian reference frame used for the particles trajectories. In order to describe corona phenomena around high voltage electrode, electric field and ion current density field in electrostatic precipitator are numerically calculated using the iterative method for corona discharge model suggested by Kim (2010). The most important concept in electrostatic precipitator is the electric force applied to particles through the particle charging phenomena. The charge acquired by the particle in the corona region was obtained by combining the field charge, the diffusion charge and the time available for charging being the residence time of the particle in the corona region. In order to simulate more accurately, the charging model suggested by Lawless (1996) is used for the charging phenomena of particles by corona discharge because this model was designed to predict combination effect of diffusion charge and field charge. The diminution of particle concentration along the collection plate was derived from Deutsch’s theory, and migration velocity of the particle was developed from the condition that the magnitude of Coulomb force is equal to that of Stoke’s resistance force. This model is implemented by UDF in commercial software Fluent and validated with experimental and numerical results from literatures. CFD results had been compared with various experimental data obtained by Penney&Matick, Parasram and Kihm. Our results shows good agreement in terms of distributions of electric potential, current density, electrohydrodynamic flow pattern, and particle trajectories as well as corona current and collection efficiency. From this simulation, the effect of wire arrangement on electrostatic precipitator characteristics and particle charging are investigated. Both inline and staggered arrangements of wire electrode have been considered for fixed values of gas velocity equal to 2m/s. Applied voltage on wire electrode varies 6∼13kV and particle diameter is 4μm. For low voltage condition, staggered arrangement of wire electrode caused the turbulent effect so that collection efficiency increase more than inline arrangement. However, collection efficiency decrease in high voltage condition because electric force applied on particles passing between the wire electrodes is canceled out by both side wire electrodes.

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