Electrohydrostatic instability in electrically stressed dielectric fluids. Part 2

1975 ◽  
Vol 72 (1) ◽  
pp. 95-112 ◽  
Author(s):  
D. H. Michael ◽  
J. Norbury ◽  
M. E. O'Neill
Keyword(s):  
Electric Field ◽  
Point Of View ◽  
Dielectric Fluid ◽  
Sufficient Information ◽  
Physical Point ◽  
Dielectric Fluids ◽  
A Value ◽  
Asymmetric Equilibria ◽  
The Stability ◽  
Loading Parameter

The paper is the second part of a study of the failure of the insulation of a layer of dielectric fluid of arbitrary volume, occupying a hole in a solid dielectric sheet, when stressed by an applied electric field. In part 1 symmetric and asymmetric equilibria were found for the two-dimensional problem, using an approximation given by Taylor (1968) for the electric field, which is valid for large holes. In this paper axisymmetric equilibria are given for a circular hole, under the same conditions. In addition the points of bifurcation of asymmetric solutions have been found, and provide sufficient information to give the stability characteristics. It is found that when the volume-excess fraction δ exceeds a value of approximately −0·3 instability occurs in an asymmetric form reported earlier for large holes by Michael, O'Neill & Zuercher (1971) in the case δ = 0. For δ < −0·3 the nature of the instability changes to an axisymmetric form of failure associated with a maximum of the loading parameter.The analysis given shows that axisymmetric displacements of ‘sausage’ mode type, that is, symmetric about a centre-plane, are associated with small changes in the static pressure in the dielectric layer. Such modes have not previously been examined in this context, and in an appendix to this paper Michael & O'Neill give an analysis of them when δ = 0, valid for all hole sizes, by extending the small perturbation analysis of Michael, O'Neill & Zuercher. These modes however do not provide the most unstable displacements for any configuration, and do not therefore affect the stability from a physical point of view.

Domains and Types of Aeroelastic Instability of Slender Beam

2007 ◽  
Author(s):  
Jirˇi´ Na´prstek
Keyword(s):  
Stability Boundary ◽  
Stability Loss ◽  
Stability Domain ◽  
Theoretical Explanation ◽  
Point Of View ◽  
System Response ◽  
Physical Point ◽  
Model Response ◽  
Gyroscopic Forces ◽  
The Stability

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.

Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
B. M. Shankar ◽  
Jai Kumar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Prandtl Number ◽  
Traveling Wave ◽  
Effective Viscosity ◽  
Darcy Number ◽  
Wave Mode ◽  
Dielectric Fluid ◽  
Fluid Viscosity ◽  
The Stability

The stability of natural convection in a dielectric fluid-saturated vertical porous layer in the presence of a uniform horizontal AC electric field is investigated. The flow in the porous medium is governed by Brinkman–Wooding-extended-Darcy equation with fluid viscosity different from effective viscosity. The resulting generalized eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Grashof number Gc, the critical wave number ac, and the critical wave speed cc are computed for a wide range of Prandtl number Pr, Darcy number Da, the ratio of effective viscosity to the fluid viscosity Λ, and AC electric Rayleigh number Rea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to be independent of Rea. The interconnectedness of the Darcy number and the Prandtl number on the nature of modes of instability is clearly delineated and found that increasing in Da and Rea is to destabilize the system. The ratio of viscosities Λ shows stabilizing effect on the system at the stationary mode, but to the contrary, it exhibits a dual behavior once the instability is via traveling-wave mode. Besides, the value of Pr at which transition occurs from stationary to traveling-wave mode instability increases with decreasing Λ. The behavior of secondary flows is discussed in detail for values of physical parameters at which transition from stationary to traveling-wave mode takes place.

Electrohydrostatic instability in electrically stressed dielectric fluids. Part 1

1974 ◽  
Vol 66 (2) ◽  
pp. 289-308 ◽  
Author(s):  
D. H. Michael ◽  
J. Norbury ◽  
M. E. O'Neill
Keyword(s):  
Electric Field ◽  
Critical Field ◽  
Pressure Difference ◽  
Unit Length ◽  
Potential Difference ◽  
Dielectric Fluid ◽  
Dielectric Fluids ◽  
Electric Stress ◽  
Equilibrium Profiles ◽  
Conducting Fluids

A theoretical investigation is presented of the electrohydrostatic stability of a given volume of incompressible dielectric fluid when stressed by the application of a potential difference between bounding conducting fluids. It is assumed that the dielectric fluid is located in a channel of breadth 2 a and height 2h, with h/a [Lt ] 1, whose walls are semi-infinite solid dielectric sheets of thickness 2h. The dielectric fluid may have a volume which differs from that of the channel, so that the presence of menisci at the interfaces between conducting and non-conducting fluids is taken into account. By a suitable method for approximating the electric stress at the interfaces, the electrostatic potential difference across the dielectric is determined as a function of the pressure difference across the interfaces for prescribed values of the discrepancy of the volume of the dielectric from the volume of the channel per unit length, and criteria are obtained for determining the critical electric field which precipitates the instability of the system. The variation of the critical electric field with the dimensionless volume excess 2δ is also found and it is shown that, for δ < −0·5, instability is associated with a symmetric mode of disturbance in which the critical field occurs at the maximum in a plot of potential difference vs. pressure difference. For δ > −0·5, instability arises from an asymmetric disturbance with the critical field occurring at a bifurcation point in the potential difference/pressure difference plane. Bifurcations are shown to occur only when the equilibrium profiles of the interfaces have extrema at the edges of the channel.

scholarly journals Effect of Horizontal AC Electric Field on the Stability of Natural Convection in a Vertical Dielectric Fluid Layer

2016 ◽  
Vol 9 (6) ◽  
pp. 3073-3086 ◽  
Author(s):  
B. M. Shankar ◽  
J. Kumar ◽  
I. S. Shivakumara ◽  
S. B. Naveen Kumar ◽  
◽  
...  
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Dielectric Fluid ◽  
Ac Electric Field ◽  
The Stability

A rotating spherical liquid drop in an electric field

1972 ◽  
Vol 56 (2) ◽  
pp. 305-312 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Electric Field ◽  
Equilibrium Shape ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Axis Of Rotation ◽  
Field Parallel ◽  
Electric Field Parallel ◽  
Fluid Drop ◽  
The Stability ◽  
Small Deformations

It is shown that the equilibrium shape of an incompressible dielectric fluid drop rotating with constant angular velocity in the presence of a uniform external electric field of appropriate magnitude along the axis of rotation is spherical. For an inviscid fluid drop, the stability of this spherical configuration to small deformations is investigated by means of Chandrasekhar's virial method. We find that a rotating drop in the presence of an electric field parallel to the axis of rotation is, in some respects, more stable than when either only the electric field or only rotation is present. This is due to the fact that the application of an electric field parallel to the axis of a rotating drop, or of rotation parallel to an electric field in which a drop is immersed, shifts the instability mechanism to another normal mode.

Effect of an electric field on the stability of binary dielectric fluid mixtures

2020 ◽  
Vol 152 (23) ◽  
pp. 234901
Author(s):  
Jonathan M. Martin ◽  
Kris T. Delaney ◽  
Glenn H. Fredrickson
Keyword(s):  
Electric Field ◽  
Dielectric Fluid ◽  
Fluid Mixtures ◽  
The Stability

scholarly journals Some Considerations on the Issue of Economic and Social Sustainability

2021 ◽  
Vol 13 (2) ◽  
pp. 97
Author(s):  
Giovanni Antonio COSSIGA
Keyword(s):  
Economic System ◽  
Global Economy ◽  
Point Of View ◽  
Economic Systems ◽  
Core Inflation ◽  
The Core ◽  
A Value ◽  
Global Economic Growth ◽  
The Stability ◽  
Development Course

To be implemented and analyzed, according to the good rules of relationship with nature, sustainability must be equipped with a theoretical scheme able of helping to understand the dynamics of this relationship together with the opportunities offered to improve the development of the economic system. Essentially, it&rsquo;s about acknowledging that, just like physics, also the economy is subject to some general and abstract laws. This is the case of the core inflation value, defined by Central Banks as a value close to 2%. So, if the economy moves along the track indicated by this value, we have confirmation that growth is regularly developing. This core inflation value is implicitly defined without a clear specification. We can therefore admit that it&rsquo;s an ideal value like the great universal constants, which reports about an economic system that develops according to the rules of natural compatibility. According to this point of view, the core inflation close to 2% is essentially a utopia, because it can only be achieved if the global economic growth moves in full accordance with the nature around us. It follows that even if we can verify on field the realization of a base value close to 2%, actually we are not in the best conditions, especially if the global economy is suffering from deflation as today. The deflation, that is the tendency of prices to fall, is part of the complex messages sent by the nature and economic systems to signal that the economy is not doing well and has become unstable. Both inflation and deflation are messages that never contribute to the economic development course, but they are born and evolving in parallel with the appearance of the economic cycle in daily activity. In summary, a mechanism that has the responsibility, by imposing pauses on the system, to reduce the instability of the systems and to facilitate the return to the natural development condition. A correction system based on the economic conjuncture that obviously distinguishes the stability by the way that the economy grows and develops in a linear and constant inclination depending on differentials.

Field-assisted ionization theory for microscopists

1994 ◽  
Vol 52 ◽  
pp. 820-821
Author(s):  
Patrick P. Camus
Keyword(s):  
Electric Field ◽  
Electron Tunneling ◽  
Ionization Probability ◽  
Critical Distance ◽  
Tunneling Probability ◽  
Field Ionization ◽  
Radius Of Curvature ◽  
Field Evaporation ◽  
A Value ◽  
Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

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