The bursting of soap-bubbles in a uniform electric field

1925 ◽  
Vol 22 (5) ◽  
pp. 728-730 ◽  
Author(s):  
C. T. R. Wilson ◽  
G. I. Taylor
Keyword(s):  
Electric Field ◽  
Water Drop ◽  
The Other ◽  
Uniform Electric Field ◽  
Geometrical Shape ◽  
Soap Bubble ◽  
Charged Drop ◽  
Mathematical Discussion ◽  
Mathematical Expressions ◽  
The Stability

The stability of a charged raindrop has been discussed mathematically by Lord Rayleigh. The case of an uncharged drop in a uniform electric field is perhaps of more meteorological importance but a mathematical discussion of the conditions for stability turns out to be very much more difficult in this case, owing to the fact that the drop ceases to be spherical before it bursts. Moreover it does not seem possible to express its geometrical shape by means of any simple mathematical expressions. On the other hand, by using a soap bubble instead of a water drop it was found possible to carry out experiments under well-defined conditions in this case, whereas experiments with Rayleigh's charged drop would be difficult.

The stability of a water drop oscillating with finite amplitude in an electric field

1971 ◽  
Vol 50 (3) ◽  
pp. 417-430 ◽  
Author(s):  
P. R. Brazier-Smith
Keyword(s):  
Electric Field ◽  
Water Drop ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Step Function ◽  
Uniform Electric Field ◽  
Spheroidal Shape ◽  
Spheroidal Drop ◽  
The Stability ◽  
Approximate Equations

By assuming that an uncharged drop situated in a uniform electric fieldEretains a spheroidal shape while oscillating about its equilibrium configuration, two approximate equations of motion are derived for the deformation ratio γ expressed as the ratioa/bof the major and minor axis of the drop. Solutions of these equations of motion indicate that the stability of a drop of undistorted radiusRand surface tensionTdepends uponE(R/T)½and the initial displacement of γ from its equilibrium value. The predictions of the two equations are compared to assess the accuracy of the spheroidal assumption as applied to such a dynamical situation. The analysis is used to determine the stability criterion of a drop subject to a step function field. Finally, the limit of validity of the spheroidal assumption is discussed in terms of Rayleigh's criterion for the stability of charged spherical drops. By applying Rayleigh's criterion to the poles of a spheroidal drop, the stage at which the drop departs from spheroidal form to form conical jets was approximately determined.

Particle-Particle Interactions on the Surface of a Drop Subjected to a Uniform Electric Field

2008 ◽  
Author(s):  
S. Nudurupati ◽  
M. Janjua ◽  
P. Singh ◽  
N. Aubry
Keyword(s):  
Electric Field ◽  
Immiscible Liquid ◽  
The Other ◽  
Uniform Electric Field ◽  
Particle Interactions ◽  
Drop Surface ◽  
Dielectrophoretic Force ◽  
Dipole Interactions ◽  
Electric Field Direction ◽  
Local Direction

We recently proposed a technique in which an externally applied uniform electric field was used to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Particles move along the drop surface to form a ring near the drop equator or collect at the poles depending on their dielectric constant relative to that of the two liquid involved. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is non-uniform, despite the fact that the applied electric field is uniform. This technique could be useful to concentrate particles at a drop surface within well-defined regions (poles and equator), and separate two types of particles at the surface of a drop. In this paper we show that in addition to the dielectrophoretic force the particles also interact with each other via the dipole-dipole interactions to form chains or move away from each other depending the local direction of the electric field. The regions in which the local electric field is normal to the drop surface, i.e., the poles, the particles move away from each other. On the other hand, near the equator, where the local direction of electric field is tangential to the drops surface, they form chains that are aligned parallel to the electric field direction.

scholarly journals Theoretical and experimental studies of charged drop formation in a uniform electric field.

1981 ◽  
Vol 14 (3) ◽  
pp. 178-182 ◽  
Author(s):  
TORU TAKAMATSU ◽  
YOSHIKI HASHIMOTO ◽  
MANABU YAMAGUCHI ◽  
TAKASHI KATAYAMA
Keyword(s):  
Electric Field ◽  
Experimental Studies ◽  
Uniform Electric Field ◽  
Drop Formation ◽  
Charged Drop

scholarly journals Modeling and Analysis of Peer-to-Peer Botnets

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Liping Feng ◽  
Xiaofeng Liao ◽  
Qi Han ◽  
Lipeng Song
Keyword(s):  
Numerical Simulations ◽  
Cost Effective ◽  
Peer To Peer ◽  
Internet Security ◽  
The Other ◽  
Dynamical Models ◽  
Modeling And Analysis ◽  
Mathematical Expressions ◽  
The Stability ◽  
The Relationship

Peer-to-Peer (P2P) botnets have emerged as one of the most serious threats to Internet security. To effectively eliminate P2P botnets, in this paper, the authors present two novel dynamical models to portray the process of formation of P2P botnets, one of which is called microlevel model, the other is called macrolevel model. Also, the stability of equilibria is investigated along with the analysis of how to prevent the P2P botnet. Furthermore, by analyzing the relationship between infection rate and the proportion of the hosts with countermeasures, we obtain the mathematical expressions of effective immune regions and depict their numerical simulations. Finally, numerical simulations verify the correctness of mathematical analysis. Our results can provide the guidance for security practitioners to defend and eliminate P2P botnet at a cost-effective way.

scholarly journals The interpretation of the results of Bucherer's experiments on e/m

1925 ◽  
Vol 107 (743) ◽  
pp. 544-560 ◽  
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Parallel Plate ◽  
High Speed ◽  
Uniform Magnetic Field ◽  
Mechanical Force ◽  
High Potential ◽  
The Other ◽  
Uniform Electric Field ◽  
Left Handed

Introduction .—In the ‘Physikalische Zeitschrift,’ 9 Jahrgang, No. 22 pp. 755-760, and again, in greater detail, in the 'Annalen der Physik,’ 1909 vol. 28, pp. 513-536, Prof. A. H. Bueherer gives an account of an experiment performed by him with the object of ascertaining which of the various mass formulæ attributed to the electron by theoretical physicists agrees best with experiment. The method is briefly as follows: a source of high speed electrons (a stick of radium fluoride) is fixed on the axis of a circular parallel plate con denser, one of whose plates is connected to earth, and the other to a source o: high potential so as to produce a sensibly uniform electric field in the region between. Perpendicular to the electric field is applied a uniform magnetic field whose effect is to diminish, or increase, the mechanical force on the electron according as the direction of its velocity forms a left-handed or a right-handed system with those of the two fields. Since the distance between the plates is very small compared with their radius, it follows that the velocity of projection of an electron cannot have at arbitrary value if it is to escape from the condenser. Given the direction of projection of an electron, its velocity must lie between two definite limits which depend upon the relative intensities of the two fields, and also upon the distant between the plates of the condenser.

UNCHARGED CONDUCTING TOROIDAL RING IN A UNIFORM ELECTRIC FIELD

1961 ◽  
Vol 39 (10) ◽  
pp. 1495-1500
Author(s):  
S. C. Loh
Keyword(s):  
Electric Field ◽  
Potential Function ◽  
Systematic Study ◽  
Theoretical Calculations ◽  
Numerical Results ◽  
Experimental Results ◽  
Uniform Electric Field ◽  
University Of Toronto ◽  
Mathematical Expressions ◽  
The University

Mathematical expressions for the potential function of an uncharged conducting toroidal ring placed in a uniform electric field are derived and expressed in terms of toroidal functions. Some numerical results were calculated by the IBM 650 computer at the University of Toronto and are included in the present paper. To verify the calculated results, a systematic study of an electrolytic tank was undertaken. It was found that the theoretical calculations agreed well with the experimental results.

Computation, Visualization, and Chemistry of Electric Field-Enhanced Production of Ceramic Precursor Powders

1992 ◽  
Vol 271 ◽  
Author(s):  
Michael T. Harris ◽  
Warren G. Sisson ◽  
Osman A. Basaran
Keyword(s):  
Electric Field ◽  
Parallel Plate ◽  
The Other ◽  
Computational Results ◽  
Cylindrical Electrode ◽  
Parallel Plate Capacitor ◽  
Ceramic Precursor ◽  
Enhanced Production ◽  
The Stability ◽  
Precursor Powders

ABSTRACTThe stability of a liquid emanating from a nozzle is profoundly affected by an electric field. This electric-field induced instability is used here to form ceramic precursor powders having well-controlled particle-size distribution and morphology. Moreover, a hybrid boundary element/finite element method is used to determine the shapes and stability of a drop hanging from a nozzle. The efficiency of two different electrode configurations is considered: in one configuration, the nozzle is attached to the top plate of a parallel-plate capacitor and in the other, the nozzle is surrounded by a concentric cylindrical electrode. The computational results show that such pendant drops lose stability at turning points with respect to field strength. The experimental and computational results reported here are of importance not only in the development of electrodispersion apparatus, but in fields as diverse as capillarity and separations.

Removal of Particles From the Surface of a Droplet

2008 ◽  
Author(s):  
N. Aubry ◽  
P. Singh ◽  
S. Nudurupati ◽  
M. Janjua
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Strong Electric Field ◽  
Dielectric Constants ◽  
The Other ◽  
Uniform Electric Field ◽  
Drop Deformation ◽  
Ambient Fluid ◽  
Dielectrophoretic Force ◽  
Different Types

We present a technique to concentrate particles on the surface of a drop, separate different types of particles, and remove them from the drop by subjecting the drop to a uniform electric field. The particles are moved under the action of the dielectrophoretic force which arises due to the non-uniformity of the electric field on the surface of the drop. Experiments show that depending on the dielectric constants of the fluids and the particles, particles aggregate either near the poles or near the equator of the drop. When particles aggregate near the poles and the dielectric constant of the drop is greater than that of the ambient fluid, the drop deformation is larger than that of a clean drop. In this case, under a sufficiently strong electric field the drop develops conical ends and particles concentrated at the poles eject out by a tip streaming mechanism, thus leaving the drop free of particles. On the other hand, when particles aggregate near the equator, it is shown that the drop can be broken into three major droplets, with the middle droplet carrying all particles and the two larger sized droplets on the sides being free of particles. The method also allows us to separate particles for which the sign of the Clausius-Mossotti factor is different, making particles of one type aggregate at the poles and of the second type aggregate at the equator. The former are removed from the drop by increasing the electric field strength, leaving only the latter inside the drop.

scholarly journals Capillary Electrophoresis and its Basic Principles in Historical Retrospect. Part 2. Electrophoresis of Ions: the Period from its Discovery in 1800 till Faraday’s Lines of Electric Force in the 1840s.

Substantia ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 97-120
Author(s):  
Ernst Kenndler
Keyword(s):  
Electric Field ◽  
Colloidal Particles ◽  
The Other ◽  
Uniform Electric Field ◽  
Dispersed Particles ◽  
Dissolved Ions ◽  
History Of ◽  
Historical Retrospect ◽  
Humphry Davy ◽  
Michael Faraday

This review is the first in a series that deals exclusively with electrophoresis of ions. Since in modern terminology "electrophoresis is the movement of dispersed particles relative to a fluid under the influence of a spatially uniform electric field”, electrophoresis is not limited to colloidal particles, it includes ions as well. The history of electrophoresis of ions therefore begins in 1800 at the same time as that of electrolysis, because the two phenomena are so inextricably linked “that one cannot happen without the other” (Faraday, 1834). Between 1800 and 1805 about half a dozen different theories of electrolytic decomposition and the movement of the particles - for which we coin the term electrophoretic current - were formulated, all contributing to the discourse, but lacking consistency and none fully convincing. They are discussed nonetheless because most of them fell into oblivion, even though they are interesting for historical reasons. However, from 1805/1806 the predominant theory, formulated by Theodor von Grotthuß and independently by Humphry Davy assumed that polarized molecules of water or dissolved ions form chains between the two electrodes. Only the terminal atoms of these chains were in direct contact with the electrodes and were liberated by galvanic action, but are immediately replaced by neighboring atoms of the same type. This decomposition and recombination of the molecules driven by electric forces which follow the “action at a distance” principle like in Coulomb´s law takes place over the entire chains; they represent the electrophoretic current. However, in 1833 Michael Faraday refuted all previous theories. Two of his groundbreaking findings were of particular importance for the electrophoresis of ions: one was that electricity consists of elementary units of charge. The ions thus carry one or a multiple of these units. The other was the revolutionary theory of the electric lines of force in early 1840s, and of what was later called the electric field. With these findings Faraday fundamentally changed the previously prevailing view of the electrophoresis of ions.

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