Finite Permittivity Research Articles

Phase field model for electrically induced damage using microforce theory

In this paper, we present a consistent derivation of the phase field model for electrically induced damage. The derivation is based on Gurtin’s microstress and microforce theory and the Coleman–Noll procedure. The resulting model accounts for Ohmic currents, includes charge conservation law and allows for finite electric permittivity and conductivity distribution in the medium. Special attention is devoted to the case when the damaged region is a codimension-two object, i.e., a curve in three dimensions. It is shown that in this case the free energy of the model necessarily includes a high-order term, which ensures the well-posedness of the problem. A special problem setting is proposed to account for the prescribed charge distribution. Local features of the phase field distribution are illustrated with one-dimensional axisymmetric numerical experiments.

Constructing Hyperbolic Metamaterials with Arbitrary Medium

Recent advances in hyperbolic metamaterials have spurred many breakthroughs in the field of manipulating light propagation. However, the unusual electromagnetic properties also put extremely high demands on its compositional materials. Limited by the finite relative permittivity of the natural materials, the effective permittivity of the constructed hyperbolic metamaterials is also confined to a narrow range. Here, based on the proposed concept of structure-induced spoof surface plasmon, we prove that arbitrary materials can be selected to construct the hyperbolic metamaterials with independent relative effective permittivity components. Besides, the theoretical achievable ranges of the relative effective permittivity components are unlimited. As proofs of the method, three novel hyperbolic metamaterials are designed with their functionalities validated numerically and experimentally by specified directional propagation. To further illustrate the superiority of the method, an all-metal low-loss hyperbolic metamaterial filled with air is proposed and demonstrated. The proposed methodology effectively reduces the design requirement for hyperbolic metamaterials and provides new ideas for the scenarios where large permittivity coverage is needed such as microwave and terahertz focus, super-resolution imaging, electromagnetic cloaking, and so on.

Effect of ion partitioning on the electrostatics of soft particles with a volumetrically charged core

In most studies of the electrostatics of soft particles, the permittivities of the shell and the electrolyte are assumed to be equal so the ion partitioning effect, arising from the permittivity difference between these two media, can be neglected. On the other hand, recent investigations have revealed that considering the volumetric charge and finite permittivity of the rigid core results in more realistic descriptions of the electrostatics of biological particles. Here, the simultaneous impact of ion partitioning and core volumetric charge on the electrostatics of spherical soft particles is studied using theoretical methods. The equations governing the general case are solved numerically, and analytical expressions are also derived using the Debye–Hückel linearization, which are found to be accurate even in the presence of large core charges. It is observed that, whenever there is a difference between the permittivities of two neighboring media, there is a noticeable change in the slope of the electrostatic potential profile at the interface, with the result that the electrostatic potential distribution of the system deviates from literature predictions. Based on these findings, it is strongly recommended to take the effect of ion partitioning into account when studying the electrostatics of soft particles, especially in the case of low-shell permittivity and concentrated electrolytes.

Nonlinear electrokinetic effects in insulator-based dielectrophoretic systems.

Insulator-based dielectrophoresis (iDEP) has emerged as a powerful tool for multiple biomicrofluidic operations, such as cell separation and concentration. The key feature for iDEP systems is the alteration of insulating microchannel geometries to create strong electric field gradients. Under AC electric fields, this strong electric field gradient can affect fluid flow by (at least) two nonlinear electrokinetic phenomena; (a) electrothermal flow due to Joule heating and (b) induced charge electroosmosis (ICEO) near the microchannel constrictions of small (but finite) permittivity and conductivity. This paper presents an experimental and theoretical study on the interplay of electrothermal and ICEO flows near microchannel constrictions with various geometries and fluid ionic strengths, which are crucial design factors for iDEP systems. Temperature rise and fluid velocities in 2D Gaussian-shaped constrictions were studied experimentally with supporting analytical estimations and numerical simulations. Additionally, we show qualitatively distinct recirculating flow patterns in 2D and 3D microchannel constrictions used for iDEP systems. Approximate analytical expressions for electrothermal and ICEO velocity scales are provided as a function of constriction geometry, bulk electrolyte concentration, and the applied electric field. Insights from this study will be useful in designing microfluidic systems for electrokinetic particle manipulation.

Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions

We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.

Effect of core charge density on the electrophoresis of a soft particle coated with polyelectrolyte layer

The electrophoresis of a charged soft particle with charged rigid core is considered under a weak imposed field condition. The rigid core of the soft particle is considered to have a finite dielectric permittivity and a fixed volume charge density. The electric potential distribution is determined by solving the Poisson-Boltzman equation out side the rigid core and a Poisson equation within the core along with continuity conditions on the core-shell interface. We have extended the analytic expression of Ohshima (Electrophoresis 27:526–533, 2006) for the electrophoretic mobility of a soft particle with a charged shell to include the effect of the volume charge density of the rigid core. Mobility based on the present expression matches exactly with the existing analytical solutions for a soft particle with an uncharged core. We have also made a comparison of our solution for mobility with an uncharged rigid core with the existing experimental results. The impact of the core charge density on the soft particle mobility is analyzed.

Super-transmission from a finite subwavelength arrangement of slits in a metal film.

A theory is presented for the transmission of transverse magnetic waves through a finite number of subwavelength slits in metal film. While a single slit achieves the single channel limit on resonance, multiple slits show super-transmission exceeding the single channel limit. The phenomenon of super-transmission is revealed as a result of cross-coupling of modes and confirmed by simulations. The influence of finite permittivity in the IR and microwave regime is included by perturbative corrections to the theory. The theory agrees quantitatively with past experiments and finite-difference time-domain simulations. By considering two or more modes in the slit region, our theory provides an approach to the analysis of cross-coupling among slits, which allows for super-transmission and features of a Fano resonance.

Influence of the finite size and effective permittivity of ions on the equilibrium double layer around colloidal particles in aqueous electrolyte solution

The equilibrium properties of the electrical double layer surrounding a charged spherical colloidal particle immersed in an aqueous electrolyte solution are examined taking into account the finite ion size. This study includes the representation of the steric interactions among ions using both the Bikerman and the Carnahan–Starling models, an account of all the effects related to the representation of hydrated ions as dielectric spheres (dependence of the electrolyte solution permittivity, on the local ion concentration, and appearance of the Born and the dielectrophoretic forces acting on the ions), and solution of the problem for both high and low surface charge values. We find that the Carnahan–Starling model together with effective ion permittivity related effects appears to be able to provide an interpretation to the electrokinetic potential vs. surface charge dependence in the case of colloidal particles suspended in aqueous electrolyte solutions. On the contrary, for electrode–electrolyte systems, both the Bikerman and the Carnahan–Starling models might be able to explain this dependence.

Theoretical investigation of 2D periodic nanoplasmon structures

The problem of diffraction of electromagnetic waves by 2D periodic metal gratings is solved with allowance for the finite permittivity of a metal in the optical band. The developed mathematical model is based on the solution of the vector integro-differential equation of diffraction by 3D dielectric bodies by means of the Galerkin method. It is noted that the dependence of the scattered field amplitude on the wavelength has a resonance character and that the resonance wavelengths can substantially exceed the dimensions of a grating cell. The application of the method of approximate boundary conditions for the calculation of gratings containing nanodimensional metal layers is justified. It is demonstrated that a grating with small reflection and transmission factors under the plasmon-resonance conditions can be created.

Induced‐charge electrophoresis of uncharged dielectric spherical Janus particles

We derive the equations governing the dipolophoretic motion of an electrically inhomogeneous Janus particle composed of two hemispheres with differing permittivities. The general formulation is valid for any electric forcing, including alternating current (AC) and makes no assumptions regarding the size of the electric double layer (EDL). The solution is thus valid even for nanoparticles where the particle radius can be of the same order as the EDL thickness. Semi-analytic and numerical solutions for the linear phoretic velocity and angular rotation of a single Janus particle suspended in an infinite medium are given in the limit of uniform direct current (DC) electric forcing. It is determined that particle mobility is a function of the permittivity in each hemisphere and the contrast between them as well as the EDL length. For a particle in which both hemispheres are characterized by a finite permittivity, we discover that maximum mobility and rotation is not obtained in the Helmholtz-Smoluchowski thin EDL limit but is rather a function of the permittivity and EDL properties.

Dipole interaction of the Quincke rotating particles

We study the behavior of particles having a finite electric permittivity and conductivity in a weakly conducting fluid under the action of the external electric field. We consider the case when the strength of the external electric field is above the threshold, and particles rotate due to the Quincke effect. We determine the magnitude of the dipole interaction of the Quincke rotating particles and the shift of frequency of the Quincke rotation caused by the dipole interaction between the particles. It is demonstrated that depending on the mutual orientation of the vectors of angular velocities of particles, vector-directed along the straight line between the centers of the particles and the external electric field strength vector, particles can attract or repel each other. In contrast to the case of nonrotating particles when the magnitude of the dipole interaction increases with the increase of the strength of the external electric field, the magnitude of the dipole interaction of the Quincke rotating particles either does not change or decreases with the increase of the strength of the external electric field depending on the strength of the external electric field and electrodynamic parameters of the particles.

Effect of wall permittivity on electroviscous flow through a contraction.

The electroviscous flow at low Reynolds number through a two-dimensional slit contraction with electric double-layer overlap is investigated numerically for cases where the permittivity of the wall material is significant in comparison with the permittivity of the liquid. The liquid-solid interface is assumed to have uniform surface-charge density. It is demonstrated that a finite wall permittivity has a marked effect on the distribution of ions in and around the contraction, with a significant build-up of counter-ions observed at the back-step. The development length of the flow increases substantially as the wall permittivity becomes significant, meaning that the electric double-layers require a longer distance to develop within the contraction. Consequently, there is a corresponding decrease in the hydrodynamic and electro-potential resistance caused by the contraction. The effect of wall-region width on the flow characteristics is also quantified, demonstrating that the development length increases with increasing wall-region width for widths up to 5 channel widths.

On the theory of polarization radiation in media with sharp boundaries

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity ɛ(ω) = ɛ′ + iɛ″ and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on the parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity (ɛ″ → ∞), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.

Dynamics of induction charging for multiple particle agglomerations with a thin conducting surface layer

In electrostatic applications, particles are typically stacked in an arbitrary array. In this paper, multiple particle agglomerations with a finite volume conductivity, surface conductivity and permittivity have been simulated. Upon exposure to the electric field, electric shielding can occur due to the proximity of other particles, which greatly reduces the maximum accumulated charge and affects the charging time. All results have been obtained using the COMSOL commercial software. The simulation results show that shielding the electric field from a given particle reduces its saturation charge and the rate of charge accumulation was mainly affected by the volume and surface conductivities.

Virtual conversion from metal object to dielectric object using metamaterials

We propose an illusion device which transforms a perfectly-electric-conducting (PEC) object into a virtual dielectric object with arbitrary material parameters. Such an illusion device has unconventional electromagnetic properties as verified by accurate numerical simulations. The presented illusion device is composed of inhomogeneous and anisotropic media with finite and positive permittivity and permeability components. Hence the designed device is possible to be realized using artificial metamaterials.

Illusion media: Generating virtual objects using realizable metamaterials

We propose a class of optical transformation media, illusion media, which render the enclosed object invisible and generate one or more virtual objects as desired. We apply the proposed media to design a microwave device, which transforms an actual object into two virtual objects. Such an illusion device exhibits unusual electromagnetic behavior as verified by full-wave simulations. Different from the published illusion devices which are composed of left-handed materials with simultaneously negative permittivity and permeability, the proposed illusion media have finite and positive permittivity and permeability. Hence the designed device could be realizable using artificial metamaterials.

Dynamic Induction Charging of Particles With Finite Conductivity

Despite the common belief that, in the process of induction charging, the actual charging time constant and the material-based relaxation time constant are equal, there is no proof that these parameters are related at all. The purpose of this paper is to determine the actual induction charging time constant for practical types of particles having both finite conductivity and permittivity. All investigations were based on numerical simulations done for idealized geometric models of the problem. The model was developed for the transient case and solved by using the COMSOL commercial software, which is based on the finite-element method. Spherical and rough particles with various contact areas with the ground electrode were considered. The surface conduction of the particle was neglected. The effect of the particle contact area, conductivity, and permittivity on the actual charging time constant was investigated, and the results were compared with that predicted by the classic relaxation time constant, as defined by the material properties. It was found that the actual time constant is not equal to the relaxation time constant but is directly affected by the value of the contact area between the particle and ground electrode.

Scattering theory approach to electrodynamic Casimir forces

We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Route to low-scattering cylindrical cloaks with finite permittivity and permeability

The method of coordinate transformation offers a way to realize perfect cloaks but provides less ability to characterize the performance of a multilayered cloak in practice. Here, we propose an analytical model to predict the performance of a multilayered cylindrical cloak, based on which, the cloak in practice can be optimized to diminish the intrinsic scatterings caused by discretization and simplification. Extremely low scattering or ``quasiperfect invisibility'' can be achieved with only a few layers of anisotropic metamaterials without following the transformation method. Meanwhile, the permittivity and permeability parameters of the layers are relatively small, which is a remarkable advantage of our approach.

Solving the problem of diffraction of an optical-band electromagnetic wave by metal nanostructured aperture arrays with the use of the method of impedance boundary conditions

The problem of diffraction of an optical wave by a 2D periodic metal aperture array with square, circular, and ring apertures is solved with allowance for the finite permittivity of a metal in the optical band. The correctness of the obtained results is verified through comparison with experimental data. It is shown that the transmission coefficient can be substantially greater than the corresponding value reached in the case of diffraction by a grating in a perfectly conducting screen.