Relevant bibliographies by topics / Butler-Volmer equation

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  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Butler-Volmer equation'

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Published: 4 June 2021
Last updated: 25 January 2023

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Journal articles on the topic "Butler-Volmer equation"

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Dreyer, Wolfgang, Clemens Guhlke, and Rüdiger Müller. "A new perspective on the electron transfer: recovering the Butler–Volmer equation in non-equilibrium thermodynamics." Physical Chemistry Chemical Physics 18, no. 36 (2016): 24966–83. http://dx.doi.org/10.1039/c6cp04142f.

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Butler–Volmer equations can be recovered from a complete non-equilibrium thermodynamic model by application of asymptotic analysis. Thereby we gain insight into the coupling of different physical phenomena and can derive Butler–Volmer equations for very different materials and electrochemical systems.
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Xu, Aoni, Chaofang Dong, Angjian Wu, Ruixue Li, Li Wang, Digby D. Macdonald, and Xiaogang Li. "Plasma-modified C-doped Co3O4 nanosheets for the oxygen evolution reaction designed by Butler–Volmer and first-principle calculations." Journal of Materials Chemistry A 7, no. 9 (2019): 4581–95. http://dx.doi.org/10.1039/c8ta11424b.

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Electrocatalysts serving in electrochemical cells differ from general chemical catalysts by way of their special double-layer structure and a rarely discussed interface potential drop as described by the Butler–Volmer (BV) equation.
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Baschuk, Jeffrey J., Andrew M. Rowe, and Xianguo Li. "Modeling and Simulation of PEM Fuel Cells With CO Poisoning." Journal of Energy Resources Technology 125, no. 2 (June 1, 2003): 94–100. http://dx.doi.org/10.1115/1.1538186.

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A polymer electrolyte membrane (PEM) fuel cell is analyzed by applying the conservation principle to the electrode backing, catalyst layers and polymer electrolyte. The conservation equations used are the conservation of species, momentum and energy, with the Nernst-Planck equation used for the electrolyte. Oxygen reduction at the cathode is modeled using the Butler-Volmer equation while the adsorption, desorption and electro-oxidation of hydrogen and CO at the anode are modeled by the Tafel-Volmer and “reactant-pair” mechanism, respectively. Temperature variations within the cell are minimized by decreasing current density or increasing temperature. An increase in pressure increases the cell voltage at low current density, but decreases the cell voltage at high current density. The electrochemical kinetics model used for the adsorption, desorption and electro-oxidation of hydrogen and CO is validated with published, experimental data.
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Mitic, Vojislav, Goran Lazovic, Dragan Djordjevic, Maja Stankovic, Vesna Paunovic, Nenad Krstic, and Jelena Manojlovic. "Butler-Volmer current equation and fractal nature correction in electrochemical energy." Thermal Science, no. 00 (2020): 232. http://dx.doi.org/10.2298/tsci200117232m.

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The Global Energy Crisis necessitated improving research into new, renewable and alternative energy sources. Due to that, our focus is on the area of some phenomena and applications where different synthetic methods and microstructure property optimization achieved significant improvement in the electro physical properties of output materials and components. This is especially important for higher energy efficiency and electricity production (batteries and battery systems, fuel cells, and hydrogen energy).The improvement of energy storage tank capacity is one of the most important development issues in the energy sphere too. It?s because of this very promising research and application area that we are expanding the knowledge on these phenomena through fractal nature analysis. So, the results obtained in the field of electrochemical energy sources, especially in electrolyte development, are taken into account the analysis of fractal nature optimization. Based on the research field of fractal material science, particularly electronic materials, we conducted research in microstructure fractal influence in the area of electrochemistry. We investigated the consolidation parameters of Fe2O3 redox processes. The influence of activation energy, fundamental thermodynamic parameters, and also the fractal correction of electrode surface area through complex fractal dimension with recognized grains and pores, and the Brownian motion of particles is introduced. Finally, the electrochemical Butler-Volmer equation fractalization is obtained. These results practically open new frontiers in electrochemical energy processes performed through the Arrhenius equation within electrolyte bulk and electrode relations and more complete and precise energy generation.
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Vijay, Periasamy, and Moses O. Tadé. "Improved approximation for the Butler-Volmer equation in fuel cell modelling." Computers & Chemical Engineering 102 (July 2017): 2–10. http://dx.doi.org/10.1016/j.compchemeng.2016.10.018.

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Dickinson, Edmund J. F., and Andrew J. Wain. "The Butler-Volmer equation in electrochemical theory: Origins, value, and practical application." Journal of Electroanalytical Chemistry 872 (September 2020): 114145. http://dx.doi.org/10.1016/j.jelechem.2020.114145.

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Magonski, Zbigniew, and Barbara Dziurdzia. "New proposal to the electrical representation of a solid oxide fuel cell." Microelectronics International 34, no. 3 (August 7, 2017): 140–48. http://dx.doi.org/10.1108/mi-12-2016-0092.

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Purpose The aim of this paper is to find the electrical representation of a solid oxide fuel cell (SOFC) that enables the application of typical exploitation characteristics of fuel cells for estimation of fuel cell parameters (for example, exchange current) and easy analysis of phenomena occurred during the fuel cell operation. Design/methodology/approach Three-layer structure of an SOFC, where a thin semi-conducting layer of electrolyte separates the anode from the cathode, shows a strong similarity to typical semiconductor devices built on the basis of P-N junctions, like diodes or transistors. Current–voltage (I-V) characteristics of a fuel cell can be described by the same mathematical functions as I-V plots of semiconductor devices. On the basis of this similarity and analysis of impedance spectra of a real fuel cell, two electrical representations of the SOFC have been created. Findings The simplified electrical representation of SOFC consists of a voltage source connected in series with a diode, which symbolizes a voltage drop on a cell cathode, and two resistors. This model is based on the similarity of Butler-Volmer to Shockley equation. The advanced representation comprises a voltage source connected in series with a bipolar transistor in close to saturation mode and two resistors. The base-emitter junction of the transistor represents voltage drop on the cell cathode, and the base-collector junction represents voltage drop on the cell anode. This model is based on the similarity of Butler-Volmer equation to Ebers-Moll equation. Originality/value The proposed approach based on the Shockley and Ebers-Moll formulas enables the more accurate estimation of the ion exchange current and other fuel cell parameters than the approach based on the Butler-Volmer and Tafel formulas. The usability of semiconductor models for analysis of SOFC operation was proved. The models were successively applied in a new design of a planar ceramic fuel cell, which features by reduced thermal capacity, short start-up time and limited number of metal components and which has become the basis for the SOFC stack design.
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Lin, Zhen, Chang Hui Wang, and Yu Liu. "Modeling and Analysis of Static Water Feed Solid Polymer Water Electrolysis Cell." Advanced Materials Research 236-238 (May 2011): 750–54. http://dx.doi.org/10.4028/www.scientific.net/amr.236-238.750.

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A simple model specific to static water feed solid polymer electrolyte (SPE) water electrolysis cell is constructed containing Butler-Volmer equation for calculating electrode over potentials, Nernst equation for calculating thermodynamic voltage and water balance equation for solving membrane water content. Based on the model, the water content distribution of the membrane is obtained, and the operating current density limitation is shown. It is indicated that the operating current density limitation of static water feed SPE electrolysis cell is obviously lower than that of normal SPE electrolysis cell.
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Fletcher, Stephen, and Thomas Stephen Varley. "Beyond the Butler–Volmer equation. Curved Tafel slopes from steady-state current–voltage curves." Physical Chemistry Chemical Physics 13, no. 12 (2011): 5359. http://dx.doi.org/10.1039/c0cp02471f.

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Alvarez-Ramirez, J., J. Vazquez-Arenas, M. González, and Y. Carrera-Tarela. "Non-Linear First-Harmonic Balance to Compute the Electrochemical Impedance of Butler-Volmer Equation." Journal of The Electrochemical Society 165, no. 9 (2018): H517—H523. http://dx.doi.org/10.1149/2.1091809jes.

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Dissertations / Theses on the topic "Butler-Volmer equation"

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Meng, Yao. "Hydrogen electrochemistry in room temperature ionic liquids." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:be24c6ea-c351-4855-ad9c-98e747ac87e4.

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This thesis primarily focuses on the electrochemical properties of the H2/H+ redox couple, at various metallic electrodes in room temperature ionic liquids. Initially, a comprehensive overview of room temperature ionic liquids, RTILs, compared to conventional organic solvents is presented which identifies their favourable properties and applications, followed by a second chapter describing the basic theory of electrochemistry. A third chapter presents the general experimental reagents, instruments and measurements used in this thesis. The results presented in this thesis are summarized in six further chapters and shown as follows. (1) Hydrogenolysis, hydrogen loaded palladium electrodes by electrolysis of H[NTf2] in a RTIL [C2mim][NTf2]. (2) Palladium nanoparticle-modified carbon nanotubes for electrochemical hydrogenolysis in RTILs. (3) Electrochemistry of hydrogen in the RTIL [C2mim][NTf2]: dissolved hydrogen lubricates diffusional transport. (4) The hydrogen evolution reaction in a room temperature ionic liquid: mechanism and electrocatalyst trends. (5) The formal potentials and electrode kinetics of the proton_hydrogen couple in various room temperature ionic liquids. (6) The electroreduction of benzoic acid: voltammetric observation of adsorbed hydrogen at a Platinum microelectrode in room temperature ionic liquids. The first two studies show electrochemically formed adsorbed H atoms at a metallic Pt or Pd surface can be used for clean, efficient, safe electrochemical hydrogenolysis of organic compounds in RTIL media. The next study shows the physicochemical changes of RTIL properties, arising from dissolved hydrogen gas. The last three studies looked at the electrochemical properties of H2/H+ redox couple at various metallic electrodes over a range of RTILs vs a stable Ag/Ag+ reference couple, using H[NTf2] and benzoic acid as proton sources. The kinetic and thermodynamic mechanisms of some reactions or processes are the same in RTILs as in conventional organic or aqueous solvents, but other remarkably different behaviours are presented. Most importantly significant constants are seen for platinum, gold and molybdenum electrodes in term of the mechanism of proton reduction to form hydrogen.
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Johansen, Jonathan Frederick. "Mathematical modelling of primary alkaline batteries." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16412/1/Jonathan_Johansen_Thesis.pdf.

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Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.
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Johansen, Jonathan Frederick. "Mathematical modelling of primary alkaline batteries." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16412/.

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Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.
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Conway, Eamon. "Mathematical modelling of ionic transport through Nanopores." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134168/1/Eamon_Conway_Thesis.pdf.

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The transport of ionic species through nanopores is important in determining the underlying behaviour of electrolytes on the nanoscale; the understanding of which has important applications in the development of bio-molecular sensors and nanofluidic diodes. Importantly, this thesis has developed a novel mathematical model of ionic transport through a nanopore that can be quantitatively compared to experimental results. In doing so, we have been able to further understand the mechanisms behind ionic transport and explain previously unexplained experimental results.
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Vágner, Petr. "Fyzikální analýza hlavních procesů v palivových článcích s pevnými oxidy a jejich matematická formulace." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340880.

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Solid oxide fuel cells (SOFC) are mainly used as large stationary elec- tricity sources, therefore an every little improvement in their performance leads to considerable savings. In order to understand the fundamentals of the SOFC operation, we have developed a new model describing the main physical processes. The thermodynamical model of SOFC, developed in this thesis, concerns the gas transport, the transport of the charged particles in- cluding the thermoelectric effect and the electrochemical reactions. Linear irreversible thermodynamics is the key modelling framework, in which the dusty gas model and the Butler-Volmer equations are used. A new relation between the electrochemical affinity and the overpotential is introduced into the Butler-Volmer equation. A weakly formulated statinonary system en- dowed with boundary conditions is solved with the finite element method in one dimensional approximation. 1
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Book chapters on the topic "Butler-Volmer equation"

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Schmickler, Wolfgang. "Selected experimental results for electron-transfer reactions." In Interfacial Electrochemistry. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195089325.003.0013.

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Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. The Butler-Volmer equation (5.10) predicts that for |η| > kT/e0 a plot of the logarithm of the current versus the applied potential (Tafel plot) should result in a straight line, whose slope is determined by the transfer coefficient α. Because of the dual role of the transfer coefficient (see Section 5.2), it is important to verify that the transfer coefficient obtained from a Tafel plot is independent of temperature. We shall see later that proton- and ion-transfer reactions often give straight lines in Tafel plots, too, but the apparent transfer coefficient obtained from these plots can depend on the temperature, indicating that these reactions do not obey the Butler-Volmer law. In order to test the temperature independence of the transfer coefficient, Curtiss et al. investigated the kinetics of the Fe2+/Fe3+ reaction on gold in a pressurized aqueous solution of perchloric acid over a temperature range from 25° to 75°C. In the absence of trace impurities of chloride ions, this reaction proceeds via an outer sphere mechanism with a low rate constant (k0 ≈ 10-5 cm s-1 at room temperature). Figure 8.1 shows the slope of their Tafel plots, d(lni)/dη, as a function of the inverse temperature 1/T. The Butler-Volmer equation predicts a straight line of slope αe0/k, which is indeed observed. Over the investigated temperature range both the transfer coefficient and the energy of activation are constant: α = 0.425 ± 0.01 and Eact = 0.59± 0.01 eV at equilibrium, confirming the validity of the Butler-Volmer equation in the region of low overpotentials, from which the Tafel slopes were obtained. The phenomenological derivation of the Butler-Volmer equation is based on a linear expansion of the Gibbs energy of activation with respect to the applied overpotential. At large overpotentials higher-order terms are expected to contribute, and a Tafel plot should no longer be linear.
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Schmickler, Wolfgang. "Metal deposition and dissolution." In Interfacial Electrochemistry. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195089325.003.0015.

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On a liquid metal electrode all surface sites are equivalent, and the deposition of a metal ion from the solution is conceptually simple: The ion loses a part of its solvation sheath, is transferred to the metal surface, and is discharged simultaneously; after a slight rearrangement of the surface atoms it is incorporated into the electrode. The details of the process are little understood, but it seems that the discharge step is generally rate determining, and the Butler-Volmer equation is obeyed if the concentration of the supporting electrolyte is sufficiently high. For example, the formation of lithium and sodium amalgams [1] in nonaqueous solvents according to: . . .Li + + e- ⇌ Li(Hg) Na+ = e- ⇌ Cd(Hg) . . . (10.1) obey the Butler-Volrner equation with transfer coefficients that depend on the solvent. On the other hand, the deposition of multivalent ions may involve several steps. Thus, the formation of zinc amalgam from aqueous solutions, with the overall reaction: . . . zn2+ + 2e- ⇌ Zn (Hg) . . . (10.2) occurs in two steps: First, Zn2+ is reduced to an intermediate Zn+ in an electron transfer step, and then the univalent ion is deposited [2]. In contrast, the surface of a solid metal offers various sites for metal deposition. Figure 10.1 shows a schematic diagram for a crystal surface with a quadratic lattice structure. A single atom sitting on a flat surface plane is denoted as an adatom; several such atoms can form an adatom cluster. A vacancy is formed by a single missing atom; several vacancies can be grouped to vacancy clusters. Steps are particularly important for crystal growth, with kink atoms, or atoms in the halfcrystal position, playing a special role. When a metal is deposited onto such a surface, the vacancies are soon filled. However, the addition of an atom in the kink position creates a new kink site; so at least on an infinite plane the number of kink sites does not change, and the current is maintained by incorporation into these sites. Similarly metal dissolution takes place predominantly at half-crystal positions, since the removal of a kink atom creates a new kink site.
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Schmickler, Wolfgang. "Proton- and ion-transfer reactions." In Interfacial Electrochemistry. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195089325.003.0014.

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We consider the transfer of an ion or proton from the solution to the surface of a metal electrode; often this is accompanied by a simultaneous discharge of the transferring particle, such as by a fast electron transfer. The particle on the surface may be an adsorbate as in the reaction: . . .Cl - (sol) ⇋ Clad + e- (metal) . . . (9.1) In this case the discharge can be partial; that is, the adsorbate can carry a partial charge, as discussed in Chapter 4. Alternatively the particle can be incorporated into the electrode as in the deposition of a metal ion on an electrode of the same composition, or in the formation of an alloy. An example of the latter is the formation of an amalgam such as: . . . Zn2++2e- ⇋ Zn(Hg) . . . (9.2) The reverse process is the transfer of a particle from the electrode surface to the solution; often the particle on the surface is uncharged or partially charged, and is ionized during the transfer. Ion- and proton-transfer reactions are almost always preceded or followed by other reaction steps. We first consider only the chargetransfer step itself. Ions and protons are much heavier than electrons. While electrons can easily tunnel through layers of solution 5 to 10 Å thick, protons can tunnel only over short distances, up to about 0.5 Å, and ions do not tunnel at all at room temperature. The transfer of an ion from the solution to a metal surface can be viewed as the breaking up of the solvation cage and subsequent deposition, the reverse process as the jumping of an ion from the surface into a preformed favorable solvent configuration. In simple cases the transfer of an ion obeys a slightly modified form of the Butler-Volmer equation. Consider the transfer of an ion from the solution to the electrode. As the ion approaches the electrode surface, it loses a part of its solvation sphere, and it displaces solvent molecules from the surface; consequently its Gibbs energy increases at first.
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Conference papers on the topic "Butler-Volmer equation"

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Niya, Seyed Mohammad Rezaei, and Mina Hoorfar. "Determination of Activation Losses in Proton Exchange Membrane Fuel Cells." In ASME 2014 12th International Conference on Fuel Cell Science, Engineering and Technology collocated with the ASME 2014 8th International Conference on Energy Sustainability. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fuelcell2014-6334.

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Activation overpotentials, due to the reaction kinetics at the surface of the electrodes are the dominant losses in low current densities in proton exchange membrane (PEM) fuel cells. Although the Butler-Volmer equation can be employed to model the reactions at the anode and cathode, there are still ambiguities regarding the estimation and modeling of the activation losses. In this paper, the Butler-Volmer equation for both the anode and cathode is simplified. It is shown that the anode activation overpotential can be modeled using the linearized Butler-Volmer equation. The cathode activation overpotential is determined using Tafel equation. The both equations are discussed to be very accurate in the entire range of fuel cell performance. The total activation overpotential is then determined.
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Li, Kaiyuan, King Jet Tseng, Feng Wei, and Boon-Hee Soong. "A Practical Lithium-ion Battery Model Based on the Butler-Volmer Equation." In 2018 International Power Electronics Conference (IPEC-Niigata 2018-ECCE Asia). IEEE, 2018. http://dx.doi.org/10.23919/ipec.2018.8507765.

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Baschuk, Jeffrey J., and Xianguo Li. "Modelling and Simulation of PEM Fuel Cells With CO Poisoning." In ASME 2002 Engineering Technology Conference on Energy. ASMEDC, 2002. http://dx.doi.org/10.1115/etce2002/cae-29012.

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A polymer electrolyte membrane (PEM) fuel cell has been analyzed by applying the conservation principle to the gas channels, electrode backings, catalyst layers and polymer electrolyte. The conservation equations used are conservation of species, momentum and energy and the Nernst-Planck equation in the electrolyte. Oxygen reduction at the cathode is modeled using the Butler-Volmer equation while the adsorption, desorption and electro-oxidation of hydrogen and CO at the anode are modeled by the Tafel-Volmer and “reactant-pair” mechanism, respectively. Comparison of the anode electrochemical kinetics model to experimental data indicates that CO adsorption kinetics are Temkin. One-dimensional simulation of a PEM fuel cell operating with reformate fuel gas indicates an optimum operating pressure. Preliminary two-dimensional simulation verifies the one-dimensional assumption for mass transfer but indicates that a two-dimensional analysis is necessary for the catalyst layer.
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Goyal, Arpit, Homayoon Sadeghi Pouya, and Eshmaiel Ganjian. "Assessment of the effectiveness of Butler-Volmer equation to predict corrosion rate in cathodically protected structures." In Fifth International Conference on Sustainable Construction Materials and Technologies. Coventry University and The University of Wisconsin Milwaukee Centre for By-products Utilization, 2019. http://dx.doi.org/10.18552/2019/idscmt5103.

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Nakagawa, Tadahiro, Naoki Shikazono, and Nobuhide Kasagi. "Numerical Simulation of Electrochemical Reaction in Reconstructed Three-Dimensional LSM/YSZ Composite Cathode." In ASME 2008 6th International Conference on Fuel Cell Science, Engineering and Technology. ASMEDC, 2008. http://dx.doi.org/10.1115/fuelcell2008-65027.

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In the present study, a novel computational scheme for the assessment of the activation polarization of LSM/YSZ composite cathodes is proposed. The scheme consists of modeling techniques of three-dimensional microstructures and an evaluation method of electrochemical characteristics. Two modeling techniques of microstructures are employed, i.e. the stochastic reconstruction (SR) method and the random packing model (RPM). In the SR method, the 3-D structure is reconstructed statistically from the two-point correlation function of the cross-sectional image of SEM-EDX. In RPM, on the other hand, spherical LSM and YSZ particles are randomly packed in the computational domain. This model is mainly used for the parametric survey, because control parameters used in the model have good correspondence to the parameters used in the actual cell manufacturing process. The lattice Boltzmann method coupled with the Butler-Volmer equation is employed for the detailed assessment of the electrochemical characteristics inside the constructed 3-D cathode microstructures. The oxygen diffusion and the electronic and ionic conductions are calculated simultaneously, and coupled with the charge transfer at the three-phase boundary (TPB) using the Butler-Volmer equation. As a result, potential, polarization and current density distributions are fully investigated. The results from the SR method reveal that the cathode sintered at 1150 °C shows the smaller overpotential than the cathodes sintered at 1200 and 1250 °C. The RPM results show that particle diameter and its standard deviation as well as volume fraction of species have large effects on the cathode performance.
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Kollmeyer, Phillip J., Anantharaghavan Shridar, and T. M. Jahns. "Modeling of low-temperature operation of a hybrid energy storage system with a Butler-Volmer equation based battery model." In 2016 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, 2016. http://dx.doi.org/10.1109/ecce.2016.7855262.

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Sprague, Isaac B., and Prashanta Dutta. "A Numerical Model to Simulate Diffuse Effects in Microfluidic Fuel Cells." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-38735.

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A 2D numerical model is developed for a laminar flow fuel cell considering ion transport and the electric double layer around the electrodes. The Frumkin-Butler-Volmer equation is used for the fuel cell kinetics. The finite volume method is used to form algebraic equations from governing partial differential equations. The numerical solution was obtained using Newton’s method and a block TDMA solver. The model accounts for the coupling of charged ion transport with the electric field and is able to fully resolve the diffuse regions of the electric double layer in both the stream-wise and cross-channel directions. Different operating phenomena, such as laminar flow separation and the development of the depletion boundary layers and electric double layers are obtained. These numerical results demonstrate the model’s ability to capture the complex behavior of a microfluidic fuel cell which has been ignored in previous 1D models.
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Wa¨lter, Bettina, and Peter Ehrhard. "Numerical Simulation of the Interplay of Electrical Double Layers, Electrode Reactions, and Pressure-Driven Flows in Microchannels." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62097.

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We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. The mathematical model for the numerical treatment relies on a first–principle description of the EDL and the electrical forces caused by the electrical field between internal electrodes. Hence, the so–called Debye–Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the Navier–Stokes equations for the flow field, species transport equations, based on the Nernst–Planck equation, and a model for the electrode reactions, based on the Butler–Volmer equation. The simulations are time–dependent and two–dimensional (plane) in nature and employ a finite–volume method. It is discussed, e.g., how the thickness of the EDL expands at the stagnation point of a forced flow, as the velocity (or Reynolds number) is increased. Furthermore, the effect of electrode reactions on the ionic strength and, hence, on the EDL and the electroosmotic flow, are discussed.
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Wa¨lter, Bettina, and Peter Ehrhard. "Numerical Simulation of Fluid Flows and Mixing in Microchannels Induced by Internal Electrodes." In ASME 2009 7th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2009. http://dx.doi.org/10.1115/icnmm2009-82016.

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Abstract:
We investigate the influence of internal electrodes onto the flow field, governed by electroosmosis and electrophoresis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances, they can be operated at lower voltages and still ensure strong electrical field strength. Even at lower voltages, electrode reactions influence the species concentration fields, and the crucial question arises, whether at the electrodes all species can be kept in dissolution or whether some species are released in gaseous form. The position and charge of multiple internal electrodes is a further focus of our investigations: wall-tangential electrical field components are responsible for pumping, wall-normal electrical field components are responsible for mixing. Hence, an optimized position and charge of all electrodes will lead to an optimized electrical field, designed to fulfill the desired tasks of the modular microchannel. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces caused by the electrical field between the internal electrodes. Hence, the so-called Debye-Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the continuity and Navier-Stokes equations for the flow field, species transport equations, based on the Nernst-Planck equation, and a charge transport equation. Further, a model for the electrode reactions, based on the Butler-Volmer equation, is in place. The simulations are time-dependent and two-dimensional in nature and employ a FVM.
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10

Choi, Bong Hwan, Do Hyung Choi, and Hun Kwan Park. "A Parametric Study on the Planar SOFC Performance Using the Three-Dimensional Transport Equations With Electrochemical Reaction." In ASME 2010 8th International Conference on Fuel Cell Science, Engineering and Technology. ASMEDC, 2010. http://dx.doi.org/10.1115/fuelcell2010-33290.

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Abstract:
A three-dimensional heat/fluid flow analysis procedure to predict the planar SOFC performance has been developed. The continuity, Navier-Stokes, energy and species equations, coupled with the electro-chemical relation models, are solved for the single periodic module of a unit cell which is composed of the anode/cathode channels, the porous electrodes, the electrolyte, and the interconnect. Using the FVM method of SIMPLE type, the local current density, which is proportional to the rate of chemical reaction, is determined iteratively by forcing the local current density and the mass-transfer rate at the reacting surface match. The Butler-Volmer equation is used to estimate the activation overpotential while the diffusion in the porous electrodes is simulated to accurately predict the concentration overpotential. Upon validation of the procedure, the average current density and voltage relation has been successfully obtained for the given structure. The cell characteristics, which include the local current density, temperature, and concentration distributions, are presented and discussed. The effects of various parameters, namely, the inlet temperature, the electrode thickness, and the channel/rib width, on the cell performance are carefully examined for different electric loads.
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