Electrochemical Kinetic Equations Research Articles

Research on the thermo-electrochemical behavior during the electrodeposition process of lithium metal battery

Lithium metal batteries (LMBs) are promising renewable energy storage device with higher energy density. During charging/discharging, the electrodeposition or dendrite growth on surface of Li electrode and temperature influence thermo-electrochemical behaviors in LMBs greatly. Coupling electrochemical reaction kinetic equations and thermal relations in electrode, as well as diffusion migrating equations of Li+ ion in electrolyte is employed to investigate the effects of temperature, charging current density, volume fraction of active solid and Li concentration in positive electrode, as well as salt concentration in electrolyte on the entropy production relating to power consumption and Joule heat, as well as cell voltage and overpotential in positive electrode and negative electrode with protrusion surface during charging. More polarization reactions together with larger heat generation take place, and cause more entropy generation in area of protrusion. The voltage efficiency is defined to evaluate thermo-electrochemical behaviors in LMBs, and the higher voltage efficiency occurs with the decrease in charging current density. The 93.6% voltage efficiency can be obtained in the case with solid-phase volume fraction of 0.518 in positive electrode under charging current density of 43.608A/m2. All results from investigation will be beneficial to obtain better thermo-electrochemical behavior in Li metal batteries.

A predictive phase-field approach for cover cracking in corroded concrete elements

Steel bar corrosion is a crucial problem in reinforced concrete structures. Corrosion, being one of the most prevalent deterioration mechanism in concrete elements, has a significant impact on the structure's serviceability and durability, since the cross section of the steel reinforcement is reduced and the mechanical steel performances deteriorate. Additionally, residual material is created as a result of the steel oxidation process, and the volume occupied by the reinforcement grows, forcing the concrete cover to crack and spall. The carbonation-induced rebar corrosion and the subsequent cover cracking are simulated via the usage of a predictive model which combines the concrete carbonation process with the phase-field technique for brittle fractures. First, the carbon dioxide transport within the concrete is described using the Fick’s second diffusion law. Then, the corrosion process is estimated via the electrochemical kinetics equations providing the associated steel expansion. The steel deformation and strain are calculated with the Faraday Law. Finally, a phase field approach for brittle material is used to reproduce rupture in the concrete cover. The developed model is validated against examples available in literature and representative examples are illustrated, describing the capability of the proposed approach to replicate the cover cracking in concrete.

Thermal behavior of full-scale battery pack based on comprehensive heat-generation model

In this study, the heat generation and dissipation terms are classified for both irreversible and reversible heat. The irreversible heat is formulated according to the Joule-heating model with internal resistance in order to circumvent the calculation of electrochemical reactions that require significant computational loads. The internal resistance in the Joule-heating model is determined via electrochemical impedance spectroscopy (EIS). The EIS tests are conducted with state-of-charge (SOC) increments of 5%. To capture rapid changes in the internal resistance, the EIS tests are conducted with smaller intervals in the 0–10% and 90–100% SOC regions. Additionally, an analytical formulation of the resistance is derived from the electrochemical kinetic equations to explain the rapid changes. Analysis reveals that the rapid changes are due to the Li intercalation phenomenon in the electrodes. Thermal analyses are conducted according to the proposed model for Li-ion single cells, and the simulation results exhibits good agreement with the experimental data. Finally, a thermal analysis for a full-scale battery tray comprising 280 cylindrical cells is performed, and the applicability of the proposed model is confirmed by comparing the simulation results with the experimental findings.

Validation of H2O2-mediated pathway model for elucidating oxygen reduction mechanism: Experimental evidences and theoretical simulations

Oxygen reduction reaction (ORR) on an electrode is a multi-step process that involves both H2O and H2O2 as final products, and the mechanism focusing on the productions of them has yet to be elucidated. In this study, simplifying the multi-step process of ORR by means of rate-limiting step (RLS) led to a H2O2-mediated pathway model. This model accounts for the productions of H2O and H2O2 by the H2O2-mediated strategy existing in 2 × 2e pathway. The model links the overall reaction with RLS and serves to establish the electrochemical kinetic equations of sub-processes. A tending degree (RH2O2) quantifying the “tendency” toward H2O and H2O2 was proposed. Finally, a mathematic approach based on the H2O2-mediated strategy are formed and well account for two common ORR behaviors: i) H2O2 is inevitably produced on most of the ORR catalysts, including Pt-based catalysts, and ii) the tendency is regulable from external factors rather than merely determined by the intrinsic properties of catalysts. Furthermore, this model is fully validated by the kinetic simulations of the ORR behaviors in the rotating ring-disk electrode (RRDE) system. This study opens a way to advance the ORR applications by regulating the tendency, and may facilitate the comprehensive understanding of ORR mechanism.

Kinetics of Phase Interaction During Secondary Cast Iron Melting

The article deals with the kinetics of phase interaction during secondary cast iron melting in cupolas and electric furnaces. The calculation of mass transfer according to the equations of electrochemical kinetics is possible only for individual cases. As the task of secondary melting of cast iron is to achieve a certain composition of cast iron, it is advisable to program complex mass transfer processes in the form of a generalized function, including the transport coefficients and the driving force of mass transfer. It is proposed to introduce the notion of the visible mass transfer coefficient (k^v), which is the density of the mass flow of an element related to one percent of the element's concentration in cast iron. The interaction of phases in devices for secondary cast iron melting is analyzed according to the laws and periods of melting. A mathematical model of mass transfer during secondary cast iron melting has been developed. Studies were conducted using a laboratory gas cupola and a 700 kg/h gas cupola, and quantitative characteristics of mass transfer have been established.

Nonlinear State-Variable Method for Solving Physics-Based Li-Ion Cell Model with High-Frequency Inputs

A nonlinear state-variable method is presented and used to solve the pseudo-2D (P2D) Li-ion cell model under high-frequency input current and temperature signals. The physics-based governing equations are formulated into a nonlinear state variable method (NSVM), in which the mass transfer variables are evaluated using a 1st order exponential integrator approach at each discrete time point and the electrochemical kinetics (Butler-Volmer) equations are solved by either an iterative or an explicit method. This procedure provides an accurate, computationally efficient method to develop physics-based simulations of the performance of a dual-foil Li-ion cell during practical drive cycles.

Electrochemical accelerometer with DC response, experimental and theoretical study

Abstract The subject of the studies presented in the paper is the electrochemical accelerometer capable of detecting DC signal. The accelerometer comprises a four electrode electrochemical cell placed in water based solution of potassium iodide with a small amount of iodine. Two electrodes work as anodes and two others as cathodes. The specific density of the liquid decreases in the space close to the cathodes as a result of electrochemical reactions. If an external acceleration is applied, the spatial variations of the specific density result in convection. In turn, the convection modifies the interelectrode currents, allowing to determine the amplitude and the direction of the acceleration. The dependence of the electrode current on the DC input signal amplitude was studied both analytically and experimentally. The theoretical model of the operation is based on the convective diffusion equation for active I 3 − ions and the equation for electrochemical potential. The boundary conditions are based on the electrochemical kinetics equations simplified by applying the condition of high concentration of the background electrolyte. Despite the simplicity of the model, such approach brings the results that are in a good agreement with the experimental data.

Experimental investigation and numerical comparison of the performance of a proton exchange membrane fuel cell at different channel geometry

In this study, the performance of a PEM fuel cell is investigated experimentally and numerically by changing the geometry of the channels. At first an experimental setup is used and three different fuel cells with rectangular, elliptical and triangular serpentine channels are constructed. The active area of each cell is 25 cm2 that its weight is 1,300 g. The material of the gas diffusion layer is carbon clothes, the membrane is nafion 117 and the catalyst layer is a plane with 0.004 g cm−2 platinum. Then a complete three-dimensional model for fuel cell is used to investigate the effect of using this channels geometry on the performance. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components. The results show that the predicted polarization curves by using this model are in good agreement with the experimental results. Also the results show that when the geometry of channel is rectangular the performance of the cell is better than the triangular and elliptical channel.

Three-Dimensional Modeling and Development of the New Geometry PEM Fuel Cell

A complete three-dimensional and single phase computational fluid dynamics model for duct-shaped geometry proton exchange membrane (PEM) fuel cell was used to investigate the effect of using different connections between bipolar plate and gas diffusion layer on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore, no interfacial boundary condition is required at the internal boundaries between cell components. This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the two-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that the predicted polarization curves using this model are in good agreement with the experimental results. Also the results show that by increasing the number of connection between GDL and bipolar plate the performance of the fuel cell enhances and the current density at the cathode catalyst layer increases.

Numerical Investigation of Channel Geometry on the Performance of a Pem Fuel Cell

A complete three-dimensional and single phase model for proton exchange membrane (PEM) fuel cells was used to investigate the effect of using different channels geometry on the performances, current density and gas concentration. The proposed model was a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations were solved in a single domain; therefore no interfacial boundary condition was required at the internal boundaries between cell components. This computational fluid dynamics code was employed as the direct problem solver, which was used to simulate the three-dimensional mass, momentum, energy and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC. The results showed that the predicted polarization curves by using this model were in good agreement with the experimental results and a high performance was observed by using circle geometry for the channels of anode and cathode sides. Also, the results showed that the performance of the fuel cell improved when a rectangular channel was used.

Numerical Simulation and Experimental Comparison of Channel Geometry on Performance of a PEM Fuel Cell

A complete three-dimensional model for proton exchange membrane (PEM) fuel cells is used to investigate the effect of the channel depth on the performance of the straight flow field at different stoichiometries of air. Therefore, there is a complete cell model that includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore, no interfacial boundary condition is required at the internal boundaries between cell components. This computational fluid dynamics code is used as the direct problem solver, intended to simulate the three-dimensional mass, momentum and species transport phenomena, as well as the electron- and proton-transfer process taking place in a PEMFC. The results show that the predicted polarization curves are in good agreement with the experimental data, and a high performance was observed at the channel depth of 1 mm for the cathode and 1.5 mm for the anode. Furthermore, the results show that the increase of the stoichiometry of air can enhance the performance of the cell. Also, it is observed that the current density distribution is more uniform for channel depth 1 mm for anode and 1.5 mm for cathode and for channel depth 1.5 mm for anode and 1 mm for cathode than the other two designs, and by moving in the channel, mole fraction of oxygen decreases due to consumption.

The effect of material properties on the performance of a new geometry PEM fuel cell

In this paper a computational dynamics model for duct-shaped geometry proton exchange membrane (PEM) fuel cell was used to investigate the effect of changing gas diffusion layer and membrane properties on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components. This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the 2-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that by increasing the thickness and decreasing the porosity of GDL the performance of the cell enhances that it is different with planner PEM fuel cell. Also the results show that by increasing the thermal conductivity of the GDL and membrane, the overall cell performance increases.

Effect of gas diffusion layer and membrane properties in an annular proton exchange membrane fuel cell

A complete three-dimensional and single phase computational dynamics model for annular proton exchange membrane (PEM) fuel cell is used to investigate the effect of changing gas diffusion layer and membrane properties on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components. This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the two-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that by increasing the thickness and decreasing the porosity of GDL the performance of the cell enhances that it is different with planner PEM fuel cell. Also the results show that by decreasing the thickness of the membrane the performance of the cell increases.

A mathematical model of the current density distribution in electrochemical cells

An approach based on the equations of electrochemical kinetics for the estimation of the current density distribution in electrochemical cells is presented. This approach was employed for a theoretical explanation of the phenomena of the edge and corner effects. The effects of the geometry of the system, the kinetic parameters of the cathode reactions and the resistivity of the solution are also discussed. A procedure for a complete analysis of the current distribution in electrochemical cells is presented.

Performance improvement of proton exchange membrane fuel cell by using annular shaped geometry

A complete three-dimensional and single phase CFD model for a different geometry of proton exchange membrane (PEM) fuel cell is used to investigate the effect of using different connections between bipolar plate and gas diffusion layer on the performances, current density and gas concentration. The proposed model is a full cell model, which includes all the parts of the PEM fuel cell, flow channels, gas diffusion electrodes, catalyst layers and the membrane. Coupled transport and electrochemical kinetics equations are solved in a single domain; therefore no interfacial boundary condition is required at the internal boundaries between cell components.This computational fluid dynamics code is used as the direct problem solver, which is used to simulate the three-dimensional mass, momentum and species transport phenomena as well as the electron- and proton-transfer process taking place in a PEMFC that cannot be investigated experimentally. The results show that the predicted polarization curves by using this model are in good agreement with the experimental results. Also the results show that by increasing the number of connection between GDL and bipolar plate the performance of the fuel cell enhances.

Multi-scale solid oxide fuel cell materials modeling

Performance and degradation of fuel cell components are discussed in a multi-scale framework in this paper. Electrochemical reactions in a solid oxide fuel cell occur simultaneously as charge and gas pass through the anode, electrolyte, and cathode to produce electric power. Since fuel cells typically operate at high temperatures for long periods of time, performance degradation due to aging of the fuel cell materials should be examined. This phenomenon is treated in a multi-scale framework by considering how microstructure evolution affects the performance at the macro-scale. Mass and charge conservation equations and electrochemical kinetic equations are solved to predict the overall cell performance using the local properties calculated at the micro-scale. Separately, the microstructures assigned to the macroscopic integration points are evolved via the Cahn–Hilliard equation using an experimentally calibrated kinetic parameter. The effective properties of the evolving microstructure are obtained by homogenization and incorporated in the macro-scale calculation. The proposed model is applied to a solid oxide fuel cell system with a nickel/yttria stabilized zirconia (Ni/YSZ) cermet anode. Our model predicts performance degradation after extended hours of operation related to nickel particle coarsening and the resulting decrease in triple phase boundary (TPB) density of the anode material. The investigation of the microstructural effects on TPB density suggests that using Ni and YSZ particles of similar size may retard performance degradation due to anode aging.

Control oriented 1D electrochemical model of lithium ion battery

Lithium ion (Li-ion) batteries provide high energy and power density energy storage for diverse applications ranging from cell phones to hybrid electric vehicles (HEVs). For efficient and reliable systems integration, low order dynamic battery models are needed. This paper introduces a general method to generate numerically a fully observable/controllable state variable model from electrochemical kinetic, species and charge partial differential equations that govern the discharge/charge behavior of a Li-ion battery. Validated against a 313th order nonlinear CFD model of a 6 Ah HEV cell, a 12th order state variable model predicts terminal voltage to within 1% for pulse and constant current profiles at rates up to 50 C. The state equation is constructed in modal form with constant negative real eigenvalues distributed in frequency space from 0 to 10 Hz. Open circuit potential, electrode surface concentration/reaction distribution coupling and electrolyte concentration/ionic conductivity nonlinearities are explicitly approximated in the model output equation on a local, electrode-averaged and distributed basis, respectively. The balanced realization controllability/observability gramian indicates that the fast electrode surface concentration dynamics are more observable/controllable than the electrode bulk concentration dynamics (i.e. state of charge).

Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations: Part 16: Patch-adaptive strategy combined with the extended Numerov spatial discretisation

Electrochemical kinetic simulations by the patch-adaptive strategy outlined in the previous parts of this series of papers can be computationally expensive in the extreme cases of very thin boundary layers, moving fronts, or models defined over multiple spatial subintervals having disparate scales. The replacement of the second-order accurate conventional spatial discretisation (thus far used by the strategy) by the fourth-order accurate extended Numerov discretisation of Chawla [M.M. Chawla, J. Inst. Math. Appl. 22 (1978) 89], discussed in this work, allows one to reduce the computational costs. Numerical experiments with five representative examples of difficult-to-simulate kinetic models reveal that the reduction of the computational time, the number of spatial grid nodes needed, and spatial grid refinement levels, is particularly noticeable when a high spatial accuracy of the simulations is requested. At low accuracy demands the conventional spatial discretisation may be more efficient and more convenient to use. The patch-adaptive simulations by the extended Numerov scheme require spatial tolerance parameter TOLX values that are several times larger than the TOLX values that ensure a comparable accuracy by the conventional spatial discretisation.

Modeling of Convective Heat and Mass Transfer Characteristics of Anode-Supported Planar Solid Oxide Fuel Cells

Convective heat and mass transfer in a planar, trilayer, solid oxide fuel cell (SOFC) module is considered for a uniform supply of volatile species (80%H2+20%H2O vapor) and oxidant (20%O2+80%N2) to the electrolyte surface with a uniform electrochemical reaction rate. The coupled heat and mass transfer is modeled by steady incompressible fully developed laminar flow in the interconnect ducts of rectangular cross sections for both the anode-side fuel and cathode-side oxidant flows. The governing three-dimensional mass, momentum, energy, species transfer, and electrochemical kinetics equations are solved computationally. The homogeneous porous-layer flow, which is in thermal equilibrium with the solid matrix, is coupled with the electrochemical reaction rate to properly account for the flow-duct and anode/cathode interface heat/mass transfer. Parametric effects of the rectangular flow-duct cross-sectional aspect ratio and anode porous-layer thickness on the variations in temperature and mass/species distributions, flow friction factor, and convective heat transfer coefficient are presented. The thermal and hydrodynamic behavior is characterized for effective convective cooling performance, and interconnect channels of cross-sectional aspect ratio of ∼2-3 along with relative anode porous-layer thickness of ∼0.5-1.5 are seen to provide optimal thermal management and species mass transport benefits in the SOFC module.

Effects of a magnetic field on the anodic dissolution, passivation and transpassivation behaviour of iron in weakly alkaline solutions with or without halides

The effects of a 0.4 T horizontal magnetic field on the anodic dissolution, passivation and transpassivation behaviour of iron in bicarbonate solutions of various concentrations and in dilute bicarbonate solutions with or without halides are investigated by electrochemical polarisation measurements. The applied magnetic field does not affect the activation-controlled anodic current, the steady passive current and the transpassive current, but significantly affects the activation–passivation transition processes for iron in bicarbonate solutions without halides. The effects of magnetic field are strongly dependent on passivation mechanisms that result in different types of surface films and corresponding rate determining steps of film dissolution. There is a synergistic effect between the applied magnetic field and halides, chlorides or bromides, on attacking the passivation of iron in dilute bicarbonate solutions. The effects of the magnetic field are analysed based on the previously proposed electrochemical kinetics equations. The magnetic field affects the anodic polarisation behaviour through its enhancing effects on mass transport processes at the precipitation–dissolution type surface film/solution interfaces. The magnetic field shows little or no effects on continuous and steady passivation films where the oxidation rate is controlled by mass transport processes within surface films. Magnetoelectrochemistry measurements are suggested as a prospective method for researches on corrosion or passivation mechanisms.