Electric Potential Function Research Articles

Calculation of electro-osmotic flow development length in a rotating three-dimensional microchannel

The numerical modeling of an electroosmosis flow in a rectangular three-dimensional rotating microchannel has been studied. The study’s goal is to calculate the flow’s development length, and as a novelty, a correlation is proposed to estimate the development length. The flow was simulated for angular velocity (ω) ranges of 0–9 and electric potential (φ) ranges of 0.1–0.3. The results were imported into the curve fitting toolbox to determine a correlation for the development length. The correlation was obtained as a function of angular velocity, electric potential, and hydraulic diameter. The results show that increasing both ω and φ leads to an increase in flow development length, where for constant φ, increasing ω from 0 to 9 results in a 20%–30% increase in development length. Furthermore, increasing φ from 0.1 to 0.3 for a constant ω raises development length by 35%–50%. The velocity field and its parameters, such as ω and φ, were analyzed and discussed.

Impact of Coulomb scattering on argon plasma based thermionic converter performance

Particle-in-cell (PIC) simulations were performed to study the impact of Coulomb scattering on the performance of argon plasma based thermionic converters. Using a simplified model, studies from the 1970’s concluded that plasma resistance resulting from Coulomb collisions shifts the IV-curves of thermionic converters that use plasmas to mitigate space charge, thereby strongly limiting their electricity generation capability. In this work the impact of Coulomb collisions in such devices were studied as a function of the relative electrical potential between the electrodes, with higher fidelity than earlier models, using a fully kinetic approach (PIC-MCC with grid based electron–ion scattering). This approach overcomes the incorrect assumption in earlier models that the electron temperature is equal to the cathode temperature in all operating conditions. The fully self-consistent results presented here showed an increase in electron temperature with an increase in gap distance or electrode bias, which decreases the plasma resistivity. It was consequently found that earlier reports overestimated the negative impact of Coulomb collisions at the maximum power point, suggesting the practical usefulness of such devices is higher than previously believed. Electronic conversion efficiency higher than 15% was shown to be feasible at 1200 °C cathode temperature with reasonable electrode work-functions.

Combined effects of temperature-dependent properties and magnetic field on electro-osmotic mobility at arbitrary zeta potentials

ABSTRACT We analyze the thermo-electroosmotic mobility of power-law electrolyte solution under the action of a magnetic field in a wavy pattern micro-channel. The flow is driven by the combined effect of the pressure gradient and the electric potential applied externally in the axial direction. The variable properties such as the viscosity, zeta potential, electrical and thermal conductivity of electro-thermal flow are assumed to vary with temperature. The entire flow phenomena have been solved by employing the finite difference method. We have presented the variation of electroosmotic mobility with the effect of Joule heating and applied magnetic field. We have examined the coupling effects of axial velocity, thermal energy, and electric potential function for various values of the temperature-dependent properties. These temperature-dependent property variations lead to developing volumetric flow rates associated with the behavior of the power-law index. The Nusselt number is drastically influenced by the temperature-dependent zeta potential variation in comparison with the Newtonian and shear-thickening fluids. The numerical and analytical solutions are validated with the existing literature and obtained a good agreement.

Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity

This study models and examines the thermal vibration and buckling behaviours of a porous nanoplate made of functional grading of barium-titanate and cobalt-ferrite. The porosity in the nanoplate is modelled with uniform and symmetrical porosity distribution functions. In the constitutive equation of the nanoplate, the strains are assumed to originate from classical mechanics, thermal expansion, electroelastic and magnetostrictive properties, nonlocal elasticity, and strain gradient elasticity. The motion equations of magneto-electro-elastic (MEE) nanoplate is obtained by Hamilton's principle. The study investigated the effects of thermal stresses, magneto-electro-elastic coupling, externally applied electric and magnetic field potential, nonlocal properties (nonlocal and material size parameters), and porosity volume fraction and function of porosity variation across thickness in free vibration and buckling behaviour of the nanoplate. According to the analysis results, the dimensionless frequencies decrease as the barium-titanate ratio in the nanoplate increases, and the frequencies increase as the cobalt-ferrite ratio increases, depending on the material grading index. While temperature increased and porosity ratio decreased dimensionless frequencies, external magnetic potential increased dimensionless frequencies. On the other hand, the application of electric potential causes a slight increase in dimensionless frequencies compared to the effect of magnetic potential.

CENT2: Improved charge equilibration via neural network technique

The high computational cost of first-principles electronic structure methods together with the successful applications of machine learning (ML) techniques in atomistic simulations resulted in a surge of interest in ML-based interatomic potentials. Despite great progress in the field, there remain some challenges to be solved such as the best way of incorporating long-range interactions, as well as nonlocal charge transfer. The first generation of the charge equilibration via neural network technique (CENT) was a major step forward in concurrently taking into account both aforementioned points. Within structure prediction methods, it turned out to be a powerful tool in discovering novel polymorphs of ionic systems. On the other hand, the method is not expected to be appropriate for multicomponent systems with reference data sets in which some or all elements are subject to varying oxidation states. Here, we present the second generation of CENT, with multiple improvements to the original variant that lead to a more accurate treatment of electrostatic interactions. To do this, it aims at reproducing the electric potential function, which is directly related to the charge distribution, rather than only considering total energies. In addition, a charge-free term is added to correct for the difference between the reference energies and those obtained with the energy functional of CENT. Moreover, the Green's function within the Hartree energy is modified to substantially shield interactions from charges in the neighborhood of each point. Also, the charge density is split into ionic and electronic parts, which allows for a better approximation of the electron density. The utility of this method is examined for magnesium oxide clusters, and multiple comparisons with the first generation are made, demonstrating that much more physical electrostatic interactions can be expected from the second generation of CENT.

Dynamic analysis of piezoelectric materials with an elliptical hole under the action of shear horizontal waves

The dynamic mechanical properties of piezoelectric materials are of interest because of their brittle nature. Previous studies have mainly focused on cylindrical cavities or cracks. However, these are specific forms of elliptical cylindrical cavities. This study aims to develop a semi-analytical approach for analyzing the anti-plane dynamics of piezoelectric materials containing elliptical cavities by exploiting the geometrical generality of ellipses. The Helmholtz and Laplace equations were identified as governing equations by decoupling the displacement and electric potential functions. The wave function expansion method was employed to express the displacement and electric potential functions in the form of a Mathieu function series containing unknown coefficients in the elliptical coordinate system. The unknown coefficients were determined using the traction-free boundary and electric displacement continuous condition. Although the method of intercepting a finite-term series was used, the solutions are reliable because the wave function exhibits convergence. In addition, a parametric study was conducted. The results demonstrated the importance of using large axial ratios, small wave numbers, and large piezoelectric characteristic parameters in the dynamic analysis of piezoelectric materials with elliptical defects.

Electromagnetohydrodynamic peristaltic flow of a couple stress nanofluid through a vertical annulus in the presence of Hall currents and thermal radiation

This paper investigates the electric properties of gold nanoparticles mixed with a convection dielectric couple stress fluid inside a vertical cylindrical tube with moving endoscope in the presence of Hall currents and thermal radiation. Under the long wavelength approximation and the use of appropriate conversion relationships between fixed and moving frame coordinates, the exact solutions have been evaluated for temperature distribution, gold nanoparticles concentration, electrical potential function and nanofluid pressure, while analytical solution is found for the axial velocity using the homotopy analysis method. The results show that the presence of the electric field enhances the effects of Brownian motion parameter, thermophoresis parameter, radiation parameter, Hall currents and wave amplitude ratio on the axial nanofluid velocity, while it was found that its presence reduces the effects of couple stress parameter, thermophoresis diffusion constant and Brownian diffusion constant.

Generalized Multiscale Finite Element Method for piezoelectric problem in heterogeneous media

In this paper, we study multiscale methods for piezocomposites. We consider a model of static piezoelectric problem that consists of deformation with respect to components of displacements and a function of electric potential. This problem includes the equilibrium equations, the quasi-electrostatic equation for dielectrics, and a system of coupled constitutive relations for mechanical and electric fields. We consider a model problem that consists of coupled differential equations. The first equation describes the deformations and is given by the elasticity equation and includes the effect of the electric field. The second equation is for the electric field and has a contribution from the elasticity equation. In previous findings, numerical homogenization methods are proposed and used for piezocomposites. We consider the Generalized Multiscale Finite Element Method (GMsFEM), which is more general and is known to handle complex heterogeneities. The main idea of the GMsFEM is to develop additional degrees of freedom and can go beyond numerical homogenization. We consider both coupled and split basis functions. In the former, the multiscale basis functions are constructed by solving coupled local problems. In particular, coupled local problems are solved to generate snapshots. Furthermore, in the snapshot space, a local spectral decomposition is performed to identify multiscale basis functions. Our approaches share some common concepts with meshless methods as they solve the underlying problem on a coarse mesh, which does not conform heterogeneities and contrast. We discuss this issue in the paper. We show that with a few basis functions per coarse element, one can achieve a good approximation of the solution. Numerical results are presented.

Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.

Heat transfer analysis for EMHD peristalsis of ionic-nanofluids via curved channel with Joule dissipation and Hall effects.

The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell's model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid's velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of [Formula: see text].

Evaluation of kinetics and thermodynamics of a naturally hydrophobic coal flotation in the presence of frother and regulated with pH

ABSTRACT Zeta potential of coal particles and kinetics of flotation along with the maximum recovery after a long time of fractionated flotation of naturally hydrophobic coals, both as a function of pH, were investigated. Empirical relations between the 1st order rate constant of flotation and zeta potential as well as the maximum recovery and zeta potential were established. Since fractionated flotation has features similar to chemical reactions, thermodynamic relations between maximum recovery and zeta potential as well as between rate constant and zeta potential were found. It was determined that the 1st order rate constant depends on two constants: flotation equilibrium constant and activity coefficient of surface electrical potential. It also depends on two variables: surface electrical potential (approximated with zeta potential) and the rate constant of the particle-bubble aggregate (flotulas) disintegration being a function of surface electrical potential. The values of the flotation equilibrium constant, activity coefficient of surface electrical potential and reverse process rate constant were determined. These parameters (especially flotation constant and activity coefficient of surface electrical potential) can be used for comparison of different flotation systems. Also useful for comparison purpose are kinetico-thermodynamic limits (Rmax vs k1) and Arrheniusan-type (ln k 1 vs ξ) plots.

Higher-order electroelastic modelling of piezoelectric cylindrical nanoshell on elastic matrix

This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation. The piezoelectric layers are actuated with external applied voltage. The nanocore is assumed in-homogeneous in which the material properties are changed continuously and gradually along radial direction. Third-order shear deformation theory is used for the description of kinematic relations and electric potential distribution is assumed as combination of a linear function along thickness direction to show applied voltage and a longitudinal distribution. Electro-elastic size-dependent constitutive relations are developed based on nonlocal elasticity theory and generalized Hooke’s law. The principle of virtual work is used to derive governing equations in terms of four functions along the axial and the radial directions and longitudinal electric potential function. The numerical results including radial and longitudinal displacements are presented in terms of basic input parameters of the integrated cylindrical nanoshell such as initial electric potential, small scale parameter, length to radius ratio and two parameters of foundation. It is concluded that both displacements are increased with an increase in small-scale parameter and a decrease in applied electric potential.

Axisymmetric Thermal Stresses of a Piezoelectric Poroelastic Circular Solid Plate

Abstract This paper presents the steady-state thermoelasticity solution for a circular solid plate is made of an undrained porous piezoelectric hexagonal material symmetry of class 6 mm. The porosities of the plate vary through the thickness; thus, material properties, except Poisson's ratio, are assumed as exponential functions of axial variable z in cylindrical coordinates. Having axisymmetric general form, external thermal and electrical loads are acted on the plate and the piezothermoelastic behavior of the plate is investigated. Using a full analytical method based on Bessel Fourier's series and separation of variables, the governing partial differential equations are derived. A formulation is given for the displacements, electric potential, thermal stresses, and electric displacements resulting from prescribed the general form of thermal, mechanical, and electric boundary conditions. Finally, the application of the derived formulas is illustrated by an example for a cadmium selenide solid, the results of which are presented graphically. Also, the effects of material property indexes, the porosity, and Skempton coefficients are discussed on the displacements, thermal stresses, electrical potential function, and electric displacements.

Simulations of argon plasma decay in a thermionic converter

The dynamics of an argon plasma in the gap of a thermionic diode is investigated using particle-in-cell (PIC) simulations. The time-averaged diode current, as a function of the relative electrical potential between the electrodes, is studied while the plasma density depletes due to recombination on the electrode surfaces. Simulations were performed in both one and two dimensions, and significant differences were observed in the plasma decay between the two cases. Specifically, in two dimensions it was found that the electrostatic potential gradually changes as the plasma decays, while in one dimension fluctuations in the plasma led to large potential fluctuations which changed the plasma decay characteristics relative to the two-dimensional case. This creates significant differences in the time-averaged diode current. Furthermore, it was found that the maximum time-averaged current is collected when the diode voltage is set to the flat-band condition, where the cathode and anode vacuum biases are equal. This suggests a novel technique of measuring the difference in work functions between the cathode and anode in a thermionic converter.

Mathematical aspects of fluid–multiferroic solid interaction problems

In the paper, we consider a three‐dimensional model of fluid–solid interaction when a thermo‐electro‐magneto‐elastic body occupying a bounded region Ω+ is embedded in an inviscid fluid occupying an unbounded domain . In this case, we have a six‐dimensional thermo‐electro‐magneto‐elastic field (the displacement vector with three components, electric potential, magnetic potential, and temperature distribution function) in the domain Ω+, while we have a scalar acoustic pressure field in the unbounded domain Ω−. The physical kinematic and dynamic relations are described mathematically by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, we prove the uniqueness and existence theorems for the corresponding boundary‐transmission problems in appropriate Sobolev‐Slobodetskii and Hölder continuous function spaces.

Entropic and heat-transfer analysis of EMHD flows with temperature-dependent properties

This paper focusses on a theoretical analysis of the entropic generation and heat-transfer characteristics of electromagnetohydrodynamic (EMHD) flow in vertical hydrophobic microchannels. The flow viscosity, electrical conductivity, and thermal conductivity are assumed to be temperature variant. The fluid velocity and energy transfer equations associated with a system of coupled non-linear equations dealing with hydrophobic slip conditions are solved using a finite volume method associated with lubrication theory. The Debye–Hückel approximation is employed in an electrical double layer combined with the Poisson–Boltzmann equation to acquire an analytical solution for the electrical potential function. Slip velocities along with constant temperatures are provided to obtain numerical solutions for the case of a fully developed EMHD flow, in order to reveal the influence of fluid rheology. The results are presented for electromagnetic transport with variable viscosity over hydrophobic interfaces. Numerical and analytical validations are performed using the existing experimental results. In this study, we vizualize the significance of variable viscosity, electrical conductivity, and thermal conductivity on temperature distributions in the presence of a magnetic field. In this work, entropy generation is represented in terms of the Bejan number, which greatly impacts the normalized electroosmotic flow as well as the thermophysical parameters, leading to a minimization of the entropy-generation rate.

Method for production of aligned nanofibers and fiber elasticity measurement

A novel method for collection of electrospun polymer nanofibers is proposed. This method can be applied to extrusion of various polymers and deposition on various types of substrates or without use of a substrate at all. The fiber is forced to alternate in its deposit in between two different segments of a collector electrode by a pair of square electric potential functions in anti-phase applied to these two electrode segments. As the fiber oscillation frequency is equal to the potential function frequency, the fiber deposition rate in between these two collector segments can be controlled. If an electrically non-conductive material is placed in between the two segments of the collector electrode, aligned fibers are simply deposited on the surface of this material. The method is used to perform stiffness measurements of the fibers demonstrating Young's modulus of 200.1 MPa with a standard deviation of 30.7 MPa. The stiffness measurement does not require any specialized equipment and requires minimal sample preparation. A sample consists of known amount of aligned fibers collected between a pair of thin coaxial rods leading to a cylindrical bundle with known number of fibers. A tensile test is then performed to obtain stress-strain curve and to find the Young's modulus of the fiber material.

A New Approach for Study the Electrohydrodynamic Oscillatory Flow Through a Porous Medium in a Heating Compliant Channel

The governing equations of an electrohydrodynamic oscillatory flow were simplified, using appropriate nondimensional quantities and the conversion relationships between fixed and moving frame coordinates. The obtained system of equations is solved analytically by using the regular perturbation method with a small wave number. In this study, modified non-dimensional quantities were used that made fluid pressure in the resulting equations dependent on both axial and vertical coordinates. The current study is more realistic and general than the previous studies in which the fluid pressure is considered functional only in the axial coordinate. A new approach enabled the author to find an analytical form of fluid pressure while previous studies have not been able to find it but have found only the pressure gradient. Analytical expressions for the stream function, electrical potential function and temperature distribution are obtained. The results show that the electrical potential function decreases by the increase of the Prandtl number, secondary wave amplitude ratio and width of the channel.

Rational design of self-supported Cu@WC core-shell mesoporous nanowires for pH-universal hydrogen evolution reaction

Cu@WC core-shell nanowires, as the WC-based materials with Pt-like electronic configurations around the Fermi level, have been successfully fabricated via chemical oxidation and electro-reduction processes followed by magnetron sputtering of WC for pH-universal hydrogen evolution reaction (HER). The Cu@WC catalyst showed low overpotentials of 92, 119 and 173 mV at 10 mA cm−2 in acidic, alkaline and neutral conditions with high exchange current densities. The core-shell structure was verified to increase the WC’s carrier density with the interfacial, strongly delocalised electrons under the external electric potential and matched work functions between Cu and WC preserving the high level of Pt-like electrons in WC. The ΔGH* calculations demonstrated that the lattice mismatch between WC and Cu modifies the atomic and electronic structures of WC and weakens the hydrogen bond during absorption leading to enhanced HER performance. This work provides a deep insight into the WC-based core-shell catalysts for pH-universal HER.

Mixed boundary–transmission problems for composite layered elastic structures

We investigate mixed type boundary–transmission problems of the generalized thermo‐electro‐magneto‐elasticity theory for complex elastic anisotropic layered structures containing interfacial cracks. This type of problems is described mathematically by systems of partial differential equations with appropriate transmission and boundary conditions for six dimensional unknown physical field (three components of the displacement vector, electric potential function, magnetic potential function, and temperature distribution function). We apply the potential method and the theory of pseudodifferential equations and prove uniqueness and existence theorems of solutions to different type mixed boundary–transmission problems in appropriate Sobolev spaces. We analyze smoothness properties of solutions near the edges of interfacial cracks and near the curves where different type boundary conditions collide.