Effect Of Finite Conductivity Research Articles

Effect of finite conductivity on the nonlinear behaviour of an electrically charged viscoelastic liquid jet

In this paper a one-dimensional numerical study on the nonlinear behaviour of an electrically charged jet of Oldroyd-B viscoelastic, Taylor–Melcher leaky dielectric liquid is carried out. The effect of surface charge level, axial wavenumber and finite conductivity on the nonlinear evolution of the jet is investigated. Different structures including beads-on-a-string with/without satellite droplets, quasi-spikes and spikes are detected, and their domains in the plane of the non-dimensional axial wavenumber and the electrical Bond number are illustrated. The underlying mechanisms in the formation of the structures are examined. It is found that tangential electrostatic force plays a key role in the formation of a quasi-spike structure. Decreasing liquid conductivity may lead to a decrease in the size of satellite droplets or even the complete removal of them from a beads-on-a-string structure, induce the transition from a beads-on-a-string to a quasi-spike structure or postpone the appearance of a spike. On the other hand, finite conductivity has little influence on filament thinning in a beads-on-a-string structure, owing to the fact that the electrostatic forces are of secondary importance compared with the capillary force. The difference between the finite conductivity, large conductivity and other cases is elucidated. An experiment is carried out to observe spike structures.

The effects of a horizontal magnetic field on the Rayleigh–Taylor instability

The stability of a thin conductive liquid film flowing along a solid wall is an important problem that occurs in many proposed fusion device designs. In this paper we investigate the linear stability of an electrically conductive liquid film of finite thickness in the presence of a strong magnetic field. Inviscid flows of finite and infinite electric conductivity are considered. The magnetic field is found to decrease the unstable growth rate for both finite and infinite conductivity fluids but only narrows the unstable modes for infinite conductivity fluids. Our theory serves as an extension to the classical theory by Chandrasekhar (1961) [1] by considering the finite-thickness and finite-conductivity effects.

Small-amplitude shape oscillation and linear instability of an electrically charged viscoelastic liquid droplet

In this paper the small-amplitude oscillation and linear instability of an electrically charged liquid droplet suspended in a vacuum is studied. The liquid is assumed to be viscoelastic and leaky dielectric. The problem is linearized and a characteristic equation is derived. The complex frequency is solved numerically as a function of the relevant dimensionless parameters. The effects of surface charge and the electrical properties of the liquid on the oscillation and instability characteristics of the droplet are investigated for several cases of viscoelasticity and the quadrupole mode n=2. In the case of large or small elasticities, increasing the charge level leads to a decrease in the critical Ohnesorge number at which a supercritical bifurcation occurs and narrows down the interval of the Ohnesorge number for oscillation. For large viscosities, oscillation can be induced by elasticity when the relative stress relaxation time is between 0.004 and 10 approximately, and the electric field may diminish this upper limit to a certain extent. The existence of the electric field also gives rise to new aperiodic branches first appearing at large viscosities or elasticities with smaller damping rates. The effect of finite conductivity on the oscillation behavior of the droplet is rather complicated. Most significantly, when the electrical relaxation time is of the order of the capillary time or a little smaller, new supercritical and subcritical bifurcations with new intervals that favor the appearance of oscillation occur at moderate/relatively large viscosities or elasticities. In addition, it is found that the Rayleigh limit expressed in the form χ=n+2 where χ the electrical Bond number and n is the order of the mode is identical with that for a perfectly conducting, inviscid droplet. Above the Rayleigh limit, the viscoelastic droplet becomes unstable, and high-order modes may be dominant over the quadrupole one when the charge level is high enough.

The Magnetic Binary GJ 65: A Test of Magnetic Diffusivity Effects

Abstract GJ 65 is an M dwarf binary system consisting of the two flare stars BL Cet (GJ 65A) and UV Cet (GJ 65B). Two teams of investigators have recently reported total magnetic fluxes corresponding to fields of 4.5 and 5.2 kG for GJ 65A and 5.8 and 6.7 kG for GJ 65B: for each component, the magnetic results obtained by the two teams agree with each other to within 1σ. For the first time, we can directly compare the predictions of our magneto-convective models, based on fitting observed stellar parameters, with measured field strengths. We find that our models agree with the observed field strengths, provided the effects of finite conductivity are accounted for. Thus, GJ 65 provides us with an opportunity to use observations of field strengths to distinguish between the predictions of our models that assume perfect electrical conductivity and those that allow for finite conductivity.

Casimir energy between a sinusoidally corrugated sphere and a plate using proximity force approximation

The aim of this paper is to obtain the Casimir energy between a sinusoidally corrugated sphere and a plate. We first present a derivation of the sphere-plate Casimir force obtained by applying proximity force approximation, and afterwards, we obtain the effect of deformation on the Casimir interaction energy by considering the sphere to have different kinds of sinusoidal corrugations. We suppose a/r ≤ 0.00755 for the sake of proximity force approximation validity and an experimental accuracy goal of 1 % in the case of a sphere with the radius r at a minimal distance a from a plate. The effect of finite conductivity is taken into account for such short distances. Furthermore, we consider that mirrors are not perfect reflectors indeed which concludes in exact theoretical prediction. Thus, we consider the correction due to finite conductivity. We note that for open geometries, temperature dependence of the Casimir force is larger than that of closed geometries. We also investigate thermal corrections of the Casimir force.

Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect

Finite conductivity, surface energy and nonlocal effect can influence the electromechanical performance of micro/nano-electromechanical systems (MEMS/NEMS). However, these factors are yet ignored on stability analysis of MEMS/NEMS fabricated from functionally graded materials (FGM). In this paper, dynamic stability of double-sided NEMS fabricated from non-symmetric FGM is investigated incorporating finite conductivity, surface energy and nonlocal effect. The Gurtin–Murdoch model and Eringen's elasticity are employed to consider the surface energy and nonlocal effect, respectively. Effect of finite conductivity of FGM on electrostatic and Casimir attractions is incorporated via relative permittivity and plasma frequency of the material. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. Moreover, bifurcation analysis is conducted to investigate the stability of the fixed points of the nano-structure. The validity of the proposed model is examined by comparing the results of the present study with those reported in the literature. The impact of various parameters i.e. finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic instability of the NEMS are addressed.

Transported PDF Modeling of Ethanol Spray in Hot-Diluted Coflow Flame

This paper presents a numerical modeling study of one ethanol spray flame from the Delft Spray-in-Hot-Coflow (DSHC) database, which has been used to study Moderate or Intense Low-oxygen Dilution (MILD) combustion of liquid fuels (Correia Rodrigues et al. Combust. Flame 162(3), 759–773, 2015). A “Lagrangian-Lagrangian” approach is adopted where both the joint velocity-scalar Probability Density Function (PDF) for the continuous phase and the joint PDF of droplet properties are modeled and solved. The evolution of the gas phase composition is described by a Flamelet Generated Manifold (FGM) and the interaction by exchange with the mean (IEM) micro-mixing model. Effects of finite conductivity on droplet heating and evaporation are accounted for. The inlet boundary conditions starting in the dilute spray region are obtained from the available experimental data together with the results of a calculation of the spray including the dense region using ANSYS Fluent 15. A method is developed to determine a good estimation for the initial droplet temperature. The inclusion of the “1/3” rule for droplet evaporation and dispersion models is shown to be very important. The current modeling approach is capable of accurately predicting main properties, including mean velocity, droplet mean diameter and number density. The gas temperature is under-predicted in the region where the enthalpy loss due to droplet evaporation is important. The flame structure analysis reveals the existence of two heat release regions, respectively having the characteristics of a premixed and a diffusion flame. The experimental and modeled temperature PDFs are compared, highlighting the capabilities and limitations of the proposed model.

On the field-to-current conversion factors for lightning strike to tall objects considering the finitely conducting ground

In this paper, we have studied the accuracy of field-to-current conversion factors (FCCFs) presented by Baba and Rakov (2007) for currents inferred from electromagnetic field produced by lightning strike to tall objects, considering the perfectly and finitely conducting ground, respectively. For the perfectly conducting ground, the different FCCFs for the initial peak current at the object top, the short-circuit current peak, the largest peak current at the object top, and the peak current at the object bottom have different accuracy ranging from underestimation of 18% to overestimation of 10% for the reflection coefficients at the two ends of object ρt = − 0.5 and ρb = 1.0, and from underestimation of 25% to overestimation of 10% for ρt = − 0.5 and ρb = 0.7; and their accuracy decreases with the increase of current risetime RT. For the finite conductivity with 0.01 S/m and 0.001 S/m, FCCFs will cause many errors if we do not take into account the propagation effect along the finitely conducting ground, and their errors obviously increase with the decrease of the conductivity. For example, for ρt = − 0.5 and ρb = 1.0, the errors are about 20% when the conductivity is 0.01 S/m while the errors are about 55% when the conductivity is 0.001 S/m for lightning strike to the 168 m high object. Therefore, we revised FCCFs by considering the propagation effect of finite conductivity on the electromagnetic field radiated by lightning strike to tall objects and found that our revised FCCFs have much better accuracy for the lossy ground than that presented by Baba and Rakov (2007).

On the change of phase when both the phases have different thermal properties

The growth of a plane boundary advancing in the supercooled fluid is discussed. The assumption of difference in densities results in a connective motion of the fluid and the mass solidified per unit area per unit time will occupy, on solidification, a different volume from that originally occupied by the fluid. The effect of finite conductivity of the solid on the growth has been studied by taking the Prandtl number different from unity. It is shown that equivalence of interface temperature and surface temperature of the solid leads to the results discussed by Chambre (1).

Using Modified Couple Stress Theory for Modeling the Size-Dependent Pull-In Instability of Torsional Nano-Mirror under Casimir Force

It is well-established that mechanical response of nanostructures is size-dependent. In this article, the size-dependent pull-in instability of rotational nano-mirror is investigated using modified couple stress theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and Casimir forces into account. Effect of finite conductivity of material is included in the Casimir formulation. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle of the system are determined. The effect of Casimir forces on the size-dependent pull-in instability of the system is discussed. Furthermore, the minimum gap between the mirror and the ground to prevent stiction (due to Casimir force) is determined as a function of material length scale parameter. It is found that the proposed model is able to predict the experimental results more accurately than the previous classical models and reduces the gap between previous theories and experiments.

Lateral Casimir Force Between Two Sinusoidally Corrugated Eccentric Cylinders Using Proximity Force Approximation

This paper is devoted to the presentation of the lateral Casimir force between two sinusoidally corrugated eccentric cylinders. Despite that applying scattering matrix method explains the problem exactly, procedure of applying this method is somehow complicated specially at nonzero temperature. Using the proximity force approximation (PFA) helps to achieve the lateral Casimir force in a truly explicit manner. We assume the cylinders to be slightly eccentric with similar radiuses and separations much smaller than corrugations' wave length for the validity of PFA. For such short distances the effect of finite conductivity would be non negligible. In addition to the effect of finite conductivity, we investigate thermal corrections of the lateral Casimir force to reduce the inaccuracy of the result obtained by PFA. Assuming the Casimir force density between two parallel plates, the normal Casimir force between two cylinders is obtained. With the aid of additive summation of the Casimir energy between cylinders without corrugation, we obtain the lateral Casimir force between corrugated cylinders.

Rigorous MoM Analysis of Finite Conductivity Effects in RLSA Antennas

Although slot antennas are usually modeled as perfectly electric conductors, for accurate antenna design and optimization, ohmic loss effects cannot be neglected. This is especially true in millimeter and submillimeter-wave applications, and in low-cost technology for mass production, where highly conductive surfaces are out of budget. This paper presents a rigorous but efficient method-of-moments (MoM) formulation for the analysis of radial line slot array (RLSA) antennas, which includes the finite conductivity of metals. First, by using equivalence and reciprocity theorems, effective magnetic currents are defined on each slot aperture, instead of standard electric and magnetic equivalent currents. This choice halves the number of unknowns of the MoM linear system, still preserving the rigor of the electromagnetic formulation. Next, proper Green's functions accounting for the finite conductivity of metals are derived analytically and used in the MoM admittance matrix expressions. A numerical check of self and mutual admittances for a couple of slots etched in a nonperfectly conducting structure is provided against results from a finite-element method. Finally, a few RLSA realizations are analyzed to investigate the effect of ohmic losses in a practical antenna design.

Casimir Force on a Surface with Shallow Nanoscale Corrugations: Geometry and Finite Conductivity Effects

We measure the Casimir force between a gold sphere and a silicon plate with nanoscale, rectangular corrugations with a depth comparable to the separation between the surfaces. In the proximity force approximation (PFA), both the top and bottom surfaces of the corrugations contribute to the force, leading to a distance dependence that is distinct from a flat surface. The measured Casimir force is found to deviate from the PFA by up to 10%, in good agreement with calculations based on scattering theory that includes both geometry effects and the optical properties of the material.

Atomic reflection off conductor walls as a tool in cold atom traps

We explain why a system of cold 85Rb atoms at temperatures of the order T≈ 7.78× 10-5 K and below, but not too low to lie in the quantum reflection regime, should be automatically repelled from the surface of a conductor without the need of an evanescent field, as in a typical atom mirror, to counteract the van der Waals attraction. The repulsive potential arises naturally outside the conductor and is effective at distances from the conductor surface of about 400 nm, intermediate between the van der Waals and the Casimir-Polder regions of variation. We propose that such a field-free reflection capability should be useful as a component in cold atom traps. It should be practically free of undesirable field fluctuations and would be operative at distances for which surface roughness, dissipative effects and other finite conductivity effects should be negligibly small.

Calculation of spin wave mode response induced by a coplanar microwave line

The geometry and method of spin wave excitation in planar waveguide inductive resonance methods is very different from that used in resonant cavity experiments, and correct interpretation of results requires an analysis which takes into account a number of features associated with the use of broadband microwave experiments. We consider aspects of a theoretical description of the resonance modes in ferromagnetic multilayers measured by a broadband inductive technique in a coplanar waveguide geometry. The effects of finite conductivity of the magnetic sample and contributions to the measured response from finite wavelength spin waves excited in this geometry are discussed. We also include the screening action of the coplanar line on the spin wave dispersion in the theory. We show that for a proper description of intensities, the theoretical model for the spin wave excitation has to include not only the contribution to intensities from the microwave current in the central conductor as did previous theories but also contributions from reverse currents in the ground half-planes of the coplanar waveguide.

Influence on electron coherence from quantum electromagnetic fields in the presence of conducting plates

The influence of electromagnetic vacuum fluctuations in the presence of the perfectly conducting plate on electrons is studied with an interference experiment. The evolution of the reduced density matrix of the electron is derived by the method of influence functional. We find that the plate boundary anisotropically modifies vacuum fluctuations that in turn affect the electron coherence. The path plane of the interference is chosen either parallel or normal to the plate. In the vicinity of the plate, we show that the coherence between electrons due to the boundary is enhanced in the parallel configuration, but reduced in the normal case. The presence of the second parallel plate is found to boost these effects. The potential relation between the amplitude change and phase shift of interference fringes is pointed out. The finite conductivity effect on electron coherence is discussed.

Finite conductivity effects and apparent contact angle saturation in AC electrowetting

AbstractWe measured the electrowetting behavior of aqueous salt solutions. By varying the conductivity and the frequency of the applied AC voltage we determined the range of the validity perfect conductor assumption of the standard electrowetting theory for the case of AC voltage. We show that the contact angle reduction is dramatically reduced at high frequency and low salt concentration due to Ohmic losses with the liquid. A simple RC-equivalent circuit model explains the observations. It is demonstrated that finite conductivity effects are more pronounced for sessile droplets than for droplets confined between to parallel plates.

Transmission through single subwavelength apertures in thin metal films and effects of surface plasmons.

The existing analyses on extraordinary optical transmission through apertures on a metal screen have been carried out assuming perfect conductivity or by examining arrays of closely spaced holes with subwavelength dimensions. We present an electromagnetic analysis of a single hole (modeled by use of an array of distant holes) in a finitely conducting metal membrane, applying no approximations. We demonstrate that finite conductivity is not of remarkable importance with small hole-diameter-to-wavelength ratios in the absence of strong resonances. However, if the angle of incidence of a plane wave is such that surface plasmons are excited, substantial enhancement of the transmittance can be observed, and the effect of finite conductivity will no longer be negligible. Our analysis also reveals that transmission of small apertures in highly conducting membranes can be described by approximate analytical formulas if surface waves are not excited, but with poor conductors the full electromagnetic analysis should be applied.

Influence of lightning electric field components on the induced voltages on a power distribution line

This paper analyses the magnitudes of induced voltages and their waveshapes due to different components of lightning electric field on a 33 kV, 3 φ power distribution line. The effect of finite conductivity of ground on the components of lightning electric field and hence on the induced voltages are studied. It is observed that the initial negative pulse in the induced voltage at the overhead line termination when finite ground conductivity is assumed is due to the large radiation component of the horizontal electric field. It is also observed that the total induced voltage gets reduced at line terminations whereas it is increased at line mid point when finite conductivity for ground is assumed for the lightning striking location considered.

Improved energy model for membrane electroporation in biological cells subjected to electrical pulses.

A self-consistent model analysis of electroporation in biological cells has been carried out based on an improved energy model. The simple energy model used in the literature is somewhat incorrect and unphysical for a variety of reasons. Our model for the pore formation energy E(r) includes a dependence on pore population and density. It also allows for variable surface tension, incorporates the effects of finite conductivity on the electrostatic correction term, and is dynamic in nature. Self-consistent calculations, based on a coupled scheme involving the Smoluchowski equation and the improved energy model, are presented. It is shown that E(r) becomes self-adjusting with variations in its magnitude and profile, in response to pore population, and inhibits uncontrolled pore growth and expansion. This theory can be augmented to include pore-pore interactions to move beyond the independent pore picture.