scholarly journals Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190701 ◽  
Author(s):  
Luis Dorfmann ◽  
Ray W. Ogden
Keyword(s):  
Electric Field ◽  
Wave Speed ◽  
Cylindrical Tube ◽  
Radial Electric Field ◽  
Potential Difference ◽  
Axisymmetric Vibration ◽  
End Conditions ◽  
Circular Cylindrical Tube ◽  
Special Case ◽  
Tube Geometry

In two recent papers, conditions for which axisymmetric incremental bifurcation could arise for a circular cylindrical tube subject to axial extension and radial inflation in the presence of an axial load, internal pressure and a radial electric field were examined, the latter being effected by a potential difference between compliant electrodes on the inner and outer radial surfaces of the tube. The present paper takes this work further by considering the incremental deformations to be time-dependent. In particular, both the axisymmetric vibration of a tube of finite length with appropriate end conditions and the propagation of axisymmetric waves in a tube are investigated. General equations and boundary conditions governing the axisymmetric incremental motions are obtained and then, for purposes of numerical evaluation, specialized for a Gent electroelastic model. The resulting system of equations is solved numerically and the results highlight the dependence of the frequency of vibration and wave speed on the tube geometry, applied deformation and electrostatic potential. In particular, the bifurcation results obtained previously are recovered as a special case when the frequency vanishes. Specification of an incremental potential difference in the present work ensures that there is no incremental electric field exterior to the tube. Results are also illustrated for a neo-Hookean electroelastic model and compared with those previously obtained for the case in which no incremental potential difference (or charge) is specified and an external field is required.

scholarly journals Nonlinear electroelasticity: material properties, continuum theory and applications

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170311 ◽  
Author(s):  
Luis Dorfmann ◽  
Ray W. Ogden
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Material Characterization ◽  
Cylindrical Tube ◽  
Continuum Theory ◽  
Radial Electric Field ◽  
Short Account ◽  
Elastomeric Materials ◽  
History Of ◽  
Circular Cylindrical Tube

In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

scholarly journals Dynamics of liquid films on vertical fibres in a radial electric field

2014 ◽  
Vol 752 ◽  
pp. 66-89 ◽  
Author(s):  
Zijing Ding ◽  
Jinlong Xie ◽  
Teck Neng Wong ◽  
Rong Liu
Keyword(s):  
Electric Field ◽  
Wave Speed ◽  
Nonlinear Evolution ◽  
Radial Electric Field ◽  
Liquid Films ◽  
Asymptotic Model ◽  
Nonlinear Behaviour ◽  
Wave Instability ◽  
Long Wave ◽  
Evolution Study

AbstractThe long-wave behaviour of perfectly conducting liquid films flowing down a vertical fibre in a radial electric field was investigated by an asymptotic model. The validity of the asymptotic model was verified by the fully linearized problem, which showed that results were in good agreement in the long-wave region. The linear stability analysis indicated that, when the ratio (the radius of the outer cylindrical electrode over the radius of the liquid film) $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta <e$, the electric field enhanced the long-wave instability; when $\beta >e$, the electric field impeded the long-wave instability; when $\beta =e$, the electric field did not affect the long-wave instability. The nonlinear evolution study of the asymptotic model compared well with the linear theory when $\beta <e$. However, when $\beta =e$, the nonlinear evolution study showed that the electric field enhanced the instability which may cause the interface to become singular. When $\beta >e$, the nonlinear evolution studies showed that the influence of the electric field on the nonlinear behaviour of the interface was complex. The electric field either enhanced or impeded the interfacial instability. In addition, an interesting phenomenon was observed by the nonlinear evolution study that the electric field may cause an oscillation in the amplitude of permanent waves when $\beta \ge e$. Further study on steady travelling waves was conducted to reveal the influence of electric field on the wave speed. Results showed that the electric field either increased or decreased the wave speed as well as the wave amplitude and flow rate. In some situations, the wave speed may increase/decrease while its amplitude decreased/increased as the strength of the external electric field increased.

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

2011 ◽  
Vol 683 ◽  
pp. 27-56 ◽  
Author(s):  
Q. Wang ◽  
D. T. Papageorgiou
Keyword(s):  
Viscous Fluid ◽  
Electric Field ◽  
Electric Fields ◽  
Viscosity Ratio ◽  
Cylindrical Tube ◽  
Radial Electric Field ◽  
Boundary Element Methods ◽  
Annular Region ◽  
Two Fluids ◽  
Jet Breakup

AbstractThe nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

scholarly journals Investigation of turbulence rotation and radial electric field in the island divertor and plasma edge at W7-X

2019 ◽  
Vol 61 (5) ◽  
pp. 054003 ◽  
Author(s):  
A Krämer-Flecken ◽  
X Han ◽  
T Windisch ◽  
J Cosfeld ◽  
P Drews ◽  
...  
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Plasma Edge

scholarly journals Effect of CO Molecule Orientation on the Reduction of Cu-Based Nanoparticles

Nanomaterials ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 279
Author(s):  
Sergey Y. Sarvadii ◽  
Andrey K. Gatin ◽  
Vasiliy A. Kharitonov ◽  
Nadezhda V. Dokhlikova ◽  
Sergey A. Ozerin ◽  
...  
Keyword(s):  
Electric Field ◽  
External Electric Field ◽  
Adsorption Process ◽  
Co Adsorption ◽  
Reduction Rate ◽  
Sample Surface ◽  
Potential Difference ◽  
Precipitation Method ◽  
Scanning Tunneling ◽  
Tunneling Microscopy

The adsorption of CO on the surface of Cu-based nanoparticles was studied in the presence of an external electric field by means of scanning tunneling microscopy (STM) and spectroscopy (STS). Nanoparticles were synthesized on the surface of a graphite support by the impregnation–precipitation method. The chemical composition of the surface of the nanoparticles was determined as a mixture of Cu2O, Cu4O3 and CuO oxides. CO was adsorbed from the gas phase onto the surface of the nanoparticles. During the adsorption process, the potential differences ΔV = +1 or −1 V were applied to the vacuum gap between the sample and the grounded tip. Thus, the system of the STM tip and sample surface formed an asymmetric capacitor, inside which an inhomogeneous electric field existed. The CO adsorption process is accompanied by the partial reduction of nanoparticles. Due to the orientation of the CO molecule in the electric field, the reduction was weak in the case of a positive potential difference, while in the case of a negative potential difference, the reduction rate increased significantly. The ability to control the adsorption process of CO by means of an external electric field was demonstrated. The size of the nanoparticle was shown to be the key factor affecting the adsorption process, and particularly, the strength of the local electric field close to the nanoparticle surface.

Gas-ionizing shocks in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Wave Speed ◽  
Normal Velocity ◽  
Electrically Conducting ◽  
Shock Stability ◽  
The Face ◽  
Arbitrary Velocity ◽  
Flow Plane ◽  
The Magnetic Field

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

scholarly journals Electric potential differences across auroral generator interfaces

2013 ◽  
Vol 31 (2) ◽  
pp. 251-261 ◽  
Author(s):  
J. De Keyser ◽  
M. Echim
Keyword(s):  
Electric Field ◽  
High Altitude ◽  
Electric Fields ◽  
Electric Potential ◽  
Equilibrium Configuration ◽  
Potential Difference ◽  
Field Profile ◽  
Electric Potential Difference ◽  
Electric Field Profile

Abstract. Strong localized high-altitude auroral electric fields, such as those observed by Cluster, are often associated with magnetospheric interfaces. The type of high-altitude electric field profile (monopolar, bipolar, or more complicated) depends on the properties of the plasmas on either side of the interface, as well as on the total electric potential difference across the structure. The present paper explores the role of this cross-field electric potential difference in the situation where the interface is a tangential discontinuity. A self-consistent Vlasov description is used to determine the equilibrium configuration for different values of the transverse potential difference. A major observation is that there exist limits to the potential difference, beyond which no equilibrium configuration of the interface can be sustained. It is further demonstrated how the plasma densities and temperatures affect the type of electric field profile in the transition, with monopolar electric fields appearing primarily when the temperature contrast is large. These findings strongly support the observed association of monopolar fields with the plasma sheet boundary. The role of shear flow tangent to the interface is also examined.

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