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In this article a mathematical model of multi-tip field cathode is presented. The field emitters periodic system for rectangular lattice serves as a field cathode on a flat substrate. A flat anode is parallel to the substrate. A unit cell with the individual field emitter is considered to calculate the electrostatic potential distribution. The effect of the field emitter on the distribution of the electrostatic potential is simulated as the effect of a finite charged line that is located at the axis of the system. The variable separation method is used to solve the boundary-value problem. The three-dimensional analytical solution for the Laplace/Poisson equation is obtained in the Cartesian coordinate system. The potential distribution is represented as an Fourier expansion, and the expansion coefficients are found in an explicit form. Values of the emission characteristics are determined by FowlerNordheim equation. The effect of electrostatic shielding on the emission characteristics is presented. [ABSTRACT FROM AUTHOR]

The models proposed for the positive long air gap electrical discharge can be considered to be either engineering or physical in their approach. In this work, we make a general review of the available models and use two of them for a comparison with experimental data. Common underlying assumptions were found in most of the models analyzed. The comparison with the experimental data revealed that the results obtained from the models were a good representation of the physical situation when the leader potential distribution and the leader-corona region evolution were described with certain physical assumptions. [ABSTRACT FROM AUTHOR]

A three-dimensional (3-D), transient, nonisothermal model of all-vanadium redox flow batteries (VRFBs) is developed by rigorously accounting for the electrochemical reactions of four types of vanadium ions (V 2+ , V 3+ , VO 2+ , and VO 2 + ) and the resulting mass and heat transport processes. Particular emphasis is placed on analyzing various heat generation mechanisms, including irreversible and reversible heat generation due to vanadium redox reactions and joule heating arising from the solid electrode and electrolyte ionic resistances. The 3-D model is validated against voltage evolution curves measured under charging and discharging processes. The model predictions compare well with the experimental data over a wide range of state of charge (SOCs), and further reveal key electrochemical and transport phenomena inside VRFBs through multidimensional contours of solid electrode/electrolyte potentials, species concentrations, and temperatures. This full 3-D comprehensive VRFB model can be applied to realistic multicell stacks to determine the optimal design and operating conditions. [ABSTRACT FROM AUTHOR]

Abstract: We calculate one-loop contributions to the Kähler potential in 4D effective theory of 5D gauged supergravity (SUGRA) on with a generic form of the prepotential and arbitrary boundary terms. Our result is applicable to a wide class of 5D SUGRA models. The derivation is systematically performed by means of an superfield formalism based on the superconformal formulation of 5D SUGRA. As an illustrative example, we provide an explicit expression of the Kähler potential in the case of 5D flat spacetime. [Copyright &y& Elsevier]

Abstract: To study the coupled phenomena occurring in proton exchange membrane fuel cells, a two-phase, one-dimensional, non-isothermal model is developed. The model includes water phase change, proton transport in the membrane and electro-osmotic effect. The thinnest, but most complex layer in the membrane electrode assembly, catalyst layer, is considered an interfacial boundary between the gas diffusion layer and the membrane. Mass and heat transfer and electro-chemical reaction through the catalyst layer are formulated into equations, which are applied to boundary conditions for the gas diffusion layer and the membrane. Detail accounts of the boundary equations and the numerical solving procedure used in this work are given. The polarization curve is calculated at different oxygen pressures and compared with the experimental results. When the operating condition is changed along the polarization curve, the change of physicochemical variables in the membrane electrode assembly is studied. In particular, the over-potential diagram presents the usage of the electro-chemical energy at each layer of the membrane electrode assembly. As the fuel cell reaction becomes more limited by mass transfer, it is found that higher over-potential is uselessly concentrated on the cathode catalyst layer. The over-potential for the anode reaction was usually ignored in other studies, but the ratio of the anode over-potential to the cathode over-potential increases at a higher current condition. Water content is distributed more unevenly in the membrane, as the cell current is increased. That causes the proton conductivity of membrane to decrease and the water content to increase in the cathode side, which hampers O2 transfer. The effect of electro-osmotic property, one of important property of membrane, on cell performance is also studied. [Copyright &y& Elsevier]

Abstract: A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson–Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz–Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte. [Copyright &y& Elsevier]

Abstract: In this paper a free energy-based lattice Boltzmann (LB) approach for modeling and simulation of electrowetting is presented. First, based on the solution of the Poisson–Boltzmann (PB) equation, it is shown that the potential distribution inside a microsized droplet can always be assumed one-dimensional. Then, spreading and transporting of a microsized fluid droplet on a flat substrate, due to the electrowetting, are studied. By applying a voltage to the substrate, liquid–solid surface tension is locally decreased. To estimate the contact angle after applying the potential, new relations for surface tensions based on the free energy functional Minimization are proposed. The results are compared to the analytical and experimental results reported in the literature. A good agreement is found. [Copyright &y& Elsevier]

• A numerical model for direct formate fuel cells is developed. • Diffusion and migration as well as competitive adsorption are considered. • The effects of operating and design parameters are analyzed. • Distributions of concentrations, electrode potentials and local current densities are presented. In this work, a one-dimensional mathematical model of direct formate fuel cells is developed. The present model involves mass/charge transport and electrochemical reactions. Compared to the previous models, this model incorporates the ion migration and considers the anode catalyst layer thickness, so that this model is not only capable of predicting the polarization curves to evaluate the fuel cell performance, but also able to give more in-depth insights into the direct formate fuel cells, e.g., the concentration distributions of reactants/products, the distribution of local current density, and the distribution of electrode potential. In validation, the present model results agree well with the experimental data from the open literature. The voltage losses resulting from the anode, membrane and cathode, as well as the distribution of electrode potential are specified individually via using the present model. Moreover, the effects of the operating conditions, i.e., the feeding concentrations of reactants, and the structural design parameters, i.e., the thicknesses and porosities of diffusion layers and catalyst layers as well as the specific active surface area of catalyst layers, on the fuel cell performance are examined. Image, graphical abstract [ABSTRACT FROM AUTHOR]