Cell-level Model Research Articles

Multiscale Modeling of Oxygen Interfacial Transport Resistance in Proton Exchange Membrane Fuel Cell Catalyst Layer

As lower catalyst loading is required to maintain cost efficiency for PEMFCs, O2 transport becomes pivotal due to the spontaneously increased pressure-independent transport resistance. While O2 transport occurs from nanoscale to macroscale, emerging evidence suggests that the interfacial region at atomistic level near catalyst surface dominates the total transport resistance. Extensive experimental efforts have been taken to understand the transport resistance contributions from each level. However, due to the complexity of the multiscale porous structure and the triple-phase interfaces in catalyst layer, coupled with the limited laboratory techniques for probing the interface at nanoscale in MEA, no conclusive correlation has been established across the scales. Mathematical modelling is a promising approach to connect nanoscale interactions with macroscopic phenomena in a computationally efficient manner. In this work, a multiscale modeling study is presented to understand the effect of platinum interfacial transport resistance on cell performance. The Pt interfaces are separately considered as exterior and interior to represent solid carbon and porous carbon situations. Ionomer and SO3 - coverage are considered for the exterior Pt interfaces, and interior Pt is correlated with pore water uptake in terms of Pt utilization, O2 transport, and proton transport. The interface-dependent properties are up-scaled to a 2D MEA cell-level model through a modified agglomerate model framework. The model reasonably predicts the MEA measurements using Pt/Vulcan and Pt/KB with varying interior Pt loading. The ionomer poisoning not only attributes to the site blocking from SO3 - (reducing ECSA) but also from the low O2 solubility at Pt-ionomer interface compared to the water-covered exterior Pt interface. As for the Pt loaded inside the high surface area carbon (HSC) pores, we found a similar O2 interfacial permeability with the Pt-ionomer interface. Possible explanation includes ionomer penetration, confined water structure inside nanopore that hinders the O2 diffusion, or the long diffusion pathway because of the tortuous pore network. We also performed parametric studies to understand how transport at different scales—interface, ionomer film, and agglomerate—affect the total transport resistance. Lastly, a HSC pore water uptake model was integrated into the cell-level model to address the effect of RH and pore size distribution. We examined the optimal HSC pore size distribution that can balance the Pt utilization, proton transport, and oxygen transport at given operation conditions. The model offers guidance for catalyst design by optimizing ink interaction and CL multiscale porous structure.

A Novel Multi-Stage Stochastic Estimation Algorithm for Estimating the Parameters of the Extended Single Particle Model of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are commonly used as energy storage for many applications due to LiBs’ high energy density, long cycle life, and reliable manufacturing processes. Hence, effective performance management of LiBs is important and is implemented via Battery Management Systems (BMS)[1]. A BMS also maximises the safety and lifetime of battery packs; and therefore, needs to estimate the internal battery states including State of Charge (SoC) and State of Safety (SoS). Accurate estimation of battery SoX can be realized with the use of an accurate battery model [2].From the different types of battery models, electrochemical models (EMs) are considered the most accurate type of cell-level model [2]. EMs are sets of coupled-partial differential equation systems, where each equation is derived from the physics occurring in the cell. Of the different EMs, the partial two-dimensional model (P2D) is considered the most accurate cell-level model. However, the P2D model is complex and has no analytical solution, thus requiring computationally expensive iterative solvers for implementation. This makes practical implementation of the P2D model on BMS platforms challenging. Hence, most approaches seen in the literature prefer the use of reduced order versions (ROM) of the P2D model, that require far less computational power for implementation [1].One such ROM is the extended Single Particle Model (eSPM) which differs from the P2D model in considering each electrode to be modelled by a single spherical particle and charge conservation in the electrolyte to follow a simplified linear relationship. These assumptions help the model be accurate up to a 2C operational current, and enable an analytical solution to be derived using direct solving of the eSPM equations [2]. Due to fast-forward computation and reasonable accuracy, we’ve chosen the eSPM model for parameter estimation (PE). For accurate measurements of the model parameters, expensive and invasive experimental techniques are typically required. Non-destructive PE methods have a growing interest in the literature as they are not only non-invasive but also enable real-time dynamic PE to be done on a BMS [3].PE of EMs can be categorized under two approaches: deterministic methods and stochastic methods. Deterministic methods require a form of gradient descent to be used, wherein partial derivatives of the parameters of the model need to be calculated. This approach tends to be computationally expensive and tends to converge to local minima instead of searching the parameter space thoroughly. Hence, stochastic approaches incorporate randomness, thus searching the entire parameter space for the global optima [3]. Multiple different stochastic approaches have been employed for PE of EMs [4]. In this work, we compare and contrast some of the commonly used approaches and propose a novel multi-stage approach based on a combination of different stochastic PE algorithms.The proposed algorithm (see Figure (1)) requires three sets of data as inputs: the cell chemistry, constant current discharge data and the parameter boundaries of the eSPM model. Using these definitions, the first stage of the algorithm estimates a parameter set that has a reasonable level of accuracy i.e. less than 4% root mean square error (RMSE). The second stage of the algorithm does region-by-region optimisation, where parameters sensitive to different regions of the discharge curve are varied until the overall error is reduced to less than 1% RMSE. The proposed approach significantly reduces the estimation processing time compared to the ‘brute-force’ approach and is flexible in selecting different algorithms for each stage.Thus, contributions of this paper are briefly explained as follows: A performance comparison of the proposed algorithm with different stochastic estimation algorithms including the genetic algorithm, the particle swarm optimisation algorithm and the simulated annealing algorithm.A fast and adaptable multi-stage PE algorithm for the LiB eSPM model, with average estimation speeds of less than fifteen minutes for a typical BMS processor, with accuracy of less than 1% RMSE error.Validation of the algorithm with dynamic drive-cycle test data. [1] L. Lu et al, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[2] S. Abada et al, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[3] E. Miguel et al, “Review of computational parameter estimation methods for electrochemical models,” Journal of Energy Storage, vol. 44. Elsevier Ltd, Dec. 15, 2021. doi: 10.1016/j.est.2021.103388.[4] A. Jokar et al, “An Inverse Method for Estimating the Electrochemical Parameters of Lithium-Ion Batteries,” J Electrochem Soc, vol. 163, no. 14, p. A2876, Oct. 2016, doi: 10.1149/2.0191614JES. Figure 1

A Digitalized Methodology for Co-Design Structural and Performance Optimization of Battery Modules

In this study, we present an innovative, fully automated, and digitalized methodology to optimize the energy efficiency and cost effectiveness of Li-ion battery modules. Advancing on from today’s optimization schemes that rely on user experience and other limitations, the mechanical and thermal designs are optimized simultaneously in this study by coupling 3D multi-physical behavior models to multi-objective heuristic optimization algorithms. Heat generation at various loading and ambient conditions are estimated with a physics-based, fractional-order battery cell-level model, which is extrapolated to a module that further accounts for the interconnected cells’ heat transfer phenomena. Several key performance indicators such as the surface temperature increase, the temperature variations on the cells, and heat uniformity within the module are recorded. For the air-cooled study case, the proposed coupled framework performs more than 250 module evaluations in a relatively short time for the whole available electro-thermal-mechanical design space, thereby ensuring global optimal results in the final design. The optimal module design proposed by this method is built in this work, and it is experimentally evaluated with a module composed of 12 series-connected Li-ion NMC/C 43Ah prismatic battery cells. The performance is validated at various conditions, which is achieved by accounting the thermal efficiency and pressure drop with regard to power consumption improvements. The validations presented in this study verify the applicability and overall efficiency of the proposed methodology, as well as paves the way toward better energy and cost-efficient battery systems.

State-of-Charge Implications of Thermal Runaway in Li-ion Cells and Modules

The thermal safety of lithium-ion (Li-ion) batteries for electric vehicles continues to remain a major concern. A comprehensive understanding of the thermal runaway (TR) mechanisms in Li-ion cells and modules due to intrinsic factors such as state-of-charge (SOC) and cell-to-cell arrangement under abuse scenarios such as external heating is critical toward the development of advanced battery thermal management systems. This study presents a hierarchical TR modeling framework to examine the TR behavior of Li-ion cells at various SOCs and probe its implications on the thermal runaway propagation (TRP) in a battery module. We perform accelerating rate calorimetry (ARC) experiments with 3.25 Ah cylindrical Li-ion cells at different SOCs and demonstrate the strong SOC dependence of TR characteristics such as the onset temperature, maximum cell temperature, and self-heating rate. The thermo-kinetic parameters extracted from the ARC experiments are used to develop a TR model that captures the SOC-induced TR response in Li-ion cells. The mechanistic information from the cell-level model is used to examine the pathways for TRP in a battery module consisting of cells with uniform and imbalanced SOCs, thereby demonstrating the underlying role of SOC variability on the resulting TRP under abuse conditions.

Fuel-Cell Performance and Stability during Liquid-Water Removal Cycles

Water management is crucial for achieving high-performance proton-exchange-membrane fuel cells (PEMFCs), as it helps keep the electrolyte hydrated while avoiding performance degradation and cell shutdown due to liquid-water accumulation. According to ex-situ measurements [1-3], accumulation of liquid water in gas-diffusion layers (GDLs) of PEMFCs is a transient process that can be accompanied with oscillations in capillary pressure and saturation. To understand how liquid-water accumulation and drainage impact PEMFC performance hysteresis and stability, a transient cell-level model that accounts for electrode structure and composition and is computationally efficient is needed. A number of volume-averaged models that describe the electrode structure through pore-size distribution have been developed in the past [4-7], but they are steady-state and thus cannot predict dynamic PEMFC performance. Existing transient models have also not been used to analyze cyclic liquid-water accumulation [8-10].In this work, a transient two-phase 2D PEMFC model is developed in the open-source fuel-cell modeling software OpenFCST [11] and applied to analyze PEMFC performance hysteresis and stability during liquid-water accumulation and drainage cycles. The model accounts for the electrode structure through a mixed-wettability pore-size-distribution framework and incorporates a novel dynamic boundary condition to describe the experimentally observed cyclic liquid-water accumulation. Results of the numerical simulations are compared to transient current-density and resistance data at two polarization scan rates and during voltage steps measured with an in-house single-channel cell at multiple operating conditions. This work demonstrates how high breakthrough pressure and rapid liquid-water removal from GDLs may cause highly unstable fuel-cell operation with strong hysteresis and oscillations in the polarization curve (such as those in the figure below) that closely resemble experimental reports [12]. Numerical simulations also reveal the existence of a scan rate that maximizes polarization hysteresis due to a match between the time scale of GDL flooding and of a complete voltage sweep. Fast-scan polarization sweeps are shown most suitable for detecting catalyst-layer flooding that depends on its wettability and occurs within single seconds in contrast to GDL flooding that takes hundreds of seconds. Overall, this work brings more attention to the transient analysis of fuel-cell performance under wet conditions.Figure: Polarization-curve oscillations caused by cyclic liquid-water removal from the cathode GDL. Similar fluctuations have been experimentally observed in [12]. Transient graphs show the dynamics of current density and cathode GDL saturation. Operating conditions are 60 °C, 90% RH, 1.5 atm; scan rate is 0.5 mV/s. References J. T. Gostick et al., J. Electrochem. Soc. 157.4 (2010) C. Quesnel et al., J. Phys. Chem. C 119.40 (2015) D. Ziegler, B.Sc. thesis, Hochschule Mannheim / University of Alberta (2020) A. Z. Weber et al., J. Electrochem. Soc. 151.10 (2004) M. Eikerling, J. Electrochem. Soc. 153.3 (2006) V. Mulone and K. Karan, Int. J. Hydrog. Energy 38.1 (2013) Zhou et al., J. Electrochem. Soc. 164.6 (2017) R. J. Balliet and J. Newman, J. Electrochem. Soc. 158.8 (2011) I. V. Zenyuk et al., J. Electrochem. Soc. 163.7 (2016) A. Goshtasbi et al., J. Electrochem. Soc. 166.7 (2019) M. Secanell et al. ECS Transactions 64.3 (2014) C. Ziegler and D. Gerteisen, J. Power Sources 188.1 (2009) Figure 1

A Proton exchange membrane water electrolysis cell model for analyzing the effects of liquid water supply characteristics on cell performance

Proton exchange membrane water electrolyzers (PEMWE) have significant potential for green, high-purity hydrogen production. This study proposes a pseudo-two-dimensional cell-level model that considers all the physical characteristics involved in water electrolysis (WE), such as electron transport in the electrodes, proton transport in the membrane electrode assembly (MEA), water transport between the anode and cathode, gas diffusion in the porous electrodes, two-phase transport in the porous electrodes, and flow channel (FC), including the channel pressure drop and heat conduction across the cell. Liquid water dispersion at the electrode/channel interface is proposed based on a geometrical analysis of the bubble patterns inside the anode channel. The model was validated against the experimental data. The simulation results showed the effects of the liquid water supply characteristics on the cell operation, demonstrating that uniform water, temperature, and pressure distributions on the cell are required for higher performance. Furthermore, efficiency maps with operating constraints under different conditions provide basic guidelines for determining the optimum point of PEMWE operation. The proposed model is appropriate for extensive analysis of physical phenomena inside the PEMWE and rapid simulation for cell optimization.

Continuum Modeling of Gas and Ions Transport in a High-Surface-Area Carbon (HSC) Nanopore

PEM fuel cell (PEMFC) is one of the promising energy conversion devices for emission-free transportation applications. It is beneficial in faster charging and better scalability compared to battery-powered vehicles, making PEMFC a viable option for heavy-duty vehicles which require higher efficiency and longer lifetimes. To economically compete with the combustion engine and improve commercialization, the PEMFC cathode desires optimization in enhancing the utilization of the expensive Pt catalyst. Integration of high-surface-area carbon (HSC) has shown to increase accessible Pt surface by diminishing ionomer poisoning as Pt particles can be loaded inside the nanoscale micropores (<5 nm) that ionomer cannot penetrate due to size restriction. However, separating Pt catalysts from ionomers requires a water pathway to deliver the proton to the interior catalyst surface, leading to RH-dependent electrochemical surface area (ECSA). In this work, we develop a steady-state, isothermal continuum model to study the gas and ions transport within HSC nanopores. The pore is represented as a straight cylindrical channel filled with water with an ionomer domain at the pore mouth serving as a proton reservoir. The ionomer phase contains H+, OH-, and background stationary SO3 - while the water phase only includes H+ and OH-. The Poisson-Nernst-Plank equations describe the flux of ions, and O2 transport is described by Fick’s law. Non-ideal behaviors including nanoconfinement effects and dielectric saturation are considered in the pore water phase, reflected by corrections in ion chemical potentials, diffusion coefficients of transport species, and dielectric constant. The electrical double layer (EDL) at the water-electrode interface is depicted as discrete finite domains applying the Gouy-Chapman-Stern (GCS) theory, with the oxygen reduction reaction (ORR) occurring at a finite reaction plane at the outer Helmholtz plane (OHP) through both acidic and alkaline reaction pathways. Donnan potential drop is solved at the ionomer-pore water interface and governs potential distribution in the pore water phase, further determining ionic concentrations at the catalyst surface and thus the kinetic region of polarization curves. The strong-adsorbed water adlayers due to nanoconfinement effects create a transport barrier for O2 approaching the catalyst surface, leading to higher mass transport resistance. A comparison between a flooded pore scenario (only a water phase exists in the pore) and a wetted pore scenario (the pore wall is covered by a water film while a gas phase also exists in the pore) shows that mass transport is hindered in the flooding pore as O2 dissolves in the pore water through a limited pore-ionomer interfacial area, while pore gas phase in the wetted pore serves as an extra O2 resource. This suggests that the management of HSC water uptake needs to avoid pore flooding while ensuring enough wettability to allow proton transport. The model is expected to couple with HSC pore size distribution measured from experiments and upscale to a cell-level model in future work.

Leveraging Molecular Dynamics to Improve Porous Electrode Theory Modeling Predictions of Lithium-Ion Battery Cells

Lithium-ion battery cell modeling using physics-based approaches such as porous electrode theory is a powerful tool for battery design and analysis. Performance metrics such as cell power and resistance can be quickly calculated in a pseudo-two-dimensional (P2D) framework and when coupled with thermal models, component level detail of heating and temperature rise can be evaluated1. For engineering of electric vehicle batteries, speed and fidelity of electrochemical models is paramount in a competitive landscape. Physics-based models allow for high fidelity but require detailed knowledge of the cell component material properties. Acquiring these material characteristics typically requires time-consuming and expensive experiments limiting the ability to quickly screen through cell designs. Therefore, engineering assumptions of the materials properties must be made based on prior tests or literature sources necessarily limiting model accuracy. One approach to improve model accuracy and circumvent costly experiments is to use atomistic modeling to calculate battery cell material properties such as kinetics, OCVs, and transport properties without the need of experiments2–4.In this contribution we use molecular dynamics to calculate electrolyte conductivity and lithium-ion diffusion coefficients for a commercial electrolyte. We first validate our MD modeling approach by reproducing experimental measures of electrolyte conductivity for several test systems. We then construct a porous electrode theory model using the computed electrolyte transport values for the commercial system. Using this model, cell resistance and power is calculated and compared to experimental values measured from small-format pouch cells using the same electrolyte. We show how the variability in the MD modeling impacts cell performance metrics and demonstrate the robustness of this approach to improve cell-level model accuracy.

Development of a Detailed 3D Finite Element Model for a Lithium-Ion Battery Subject to Abuse Loading

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Lithium-ion batteries (LIBs) have been used as the main power source for Electric vehicles (EVs) in recent years. The mechanical behavior of LIBs subject to crush loading is crucial in assessing and improving the impact safety of battery systems and EVs. In this work, a detailed 3D finite element model for a commercial vehicle battery was built, in order to better understand battery failure behavior under various loading conditions. The model included the major components of a prismatic battery jellyroll, i.e., cathodes, anodes, and separators. The models for these components were validated against the corresponding material coupon tests (e.g., tension and compression). Then the components were integrated into the cell level model for simulation of jellyroll loading and damage behavior under three types of compressive indenter loading: (1) Flat-end punch, (2) Hemispherical punch and (3) Round-edge wedge. The comparisons showed reasonable agreement between modeling and experiments. With the validated numerical model, parametric studies were further performed to analyze the effect of separator anisotropy, to highlight its important role in the overall structural response of LIBs.&lt;/div&gt;&lt;/div&gt;

Standardizing mechanical tests on li-ion batteries to develop a useful cell-level model under extreme mechanical loads

Mechanical characterization of Li-ion battery cells is becoming increasingly important as the community becomes more aware that the underlying mechanisms of battery failure and degradation involve the complex interplay between electrochemistry and mechanics. Various types of mechanical tests have been developed, and how the tests are performed varies among individual research groups. Till today, there are no widely accepted standards acting as guidelines for battery mechanical engineers. This paper is motivated by our deep concern that nowadays various mechanical models are being developed, some of which were based on a limited number of tests but have led to ambitious conclusions about the modeling effectiveness. Here, through our test data and simulation results, we reveal that many existing types of cell-level mechanical tests can only result in a narrow stress state and thus could not be used to validate one another. This paper will also perform a careful examination of each individual test and provide the users with our recommendations on the choice of mechanical tests, the role of each test, and how to perform them. We hope that this paper can initiate a wide discussion among the battery modeling community leading to a standardized testing procedure soon.

Cardiac electro-mechanical activity in a deforming human cardiac tissue: modeling, existence-uniqueness, finite element computation and application to multiple ischemic disease.

In this study, the cardiac electro-mechanical model in a deforming domain is taken with the addition of mechanical feedback and stretch-activated channel current coupled with the ten Tusscher human ventricular cell level model that results in a coupled PDE-ODE system. The existence and uniqueness of such a coupled system in a deforming domain is proved. At first, the existence of a solution is proved in the deformed domain. The local existence of the solution is proved using the regularization and the Faedo-Galerkin technique. Then, the global existence is proved using the energy estimates in appropriate Banach spaces, Gronwall lemma, and the compactness procedure. The existence of the solution in an undeformed domain is proved using the lower semi-continuity of the norms. Uniqueness is proved using Young's inequality, Gronwall lemma, and the Cauchy-Schwartz inequality. For the application purpose, this model is applied to understand the electro-mechanical activity in ischemic cardiac tissue. It also takes care of the development of active tension, conductive, convective, and ionic feedback. The Second Piola-Kirchoff stress tensor arising in Lagrangian mapping between reference and moving frames is taken as a combination of active, passive, and volumetric components. We investigated the effect of varying strength of hyperkalemia and hypoxia, in the ischemic subregions of human cardiac tissue with local multiple ischemic subregions, on the electro-mechanical activity of healthy and ischemic zones. This system is solved numerically using the [Formula: see text] finite element method in space and the implicit-explicit Euler method in time. Discontinuities arising with the modeled multiple ischemic regions are treated to the desired order of accuracy by a simple regularization technique using the interpolating polynomials. We examined the cardiac electro-mechanical activity for several cases in multiple hyperkalemic and hypoxic human cardiac tissue. We concluded that local multiple ischemic subregions severely affect the cardiac electro-mechanical activity more, in terms of action potential (v) and mechanical parameters, intracellular calcium ion concentration [Formula: see text], active tension ([Formula: see text]), stretch ([Formula: see text]) and stretch rate ([Formula: see text]), of a healthy cell in its vicinity, compared to a single Hyperkalemic or Hypoxic subregion. The four moderate hypoxically generated ischemic subregions affect the waveform of the stretch along the fiber and the stretch rate more than a single severe ischemic subregion.

Micro-macroscopic modeling of a lithium-ion battery by considering grain boundaries of active materials

Many important properties of electrode materials are profoundly sensitive to deviations from the crystalline perfection. Among them are grain boundaries, which play an important role on battery performance by altering the distributions of ions inside the particles and changing the corresponding stress level. This paper explores the mechanical and microstructural aspects of battery behavior by developing a cell-level model that incorporates grain boundary diffusion in the electrode particles for the anode and cathode. The developed model is compared against a grainless model at various operating conditions to understand how grain boundaries influence capacity and stress generation. The results from the model revealed that the location of the maximum stress might not necessarily occur at the separator interface at any given time as the particles with heterogeneous diffusion paths displayed gradual changes in flux profile, which has just been believed in practice. The grain structure geometry variability showed that less diffusive particles at the rear side endure more stress than high diffusive frontal particles. Also, the results show an appreciable effect of grain boundary diffusion on the voltage profile of the cell for the tested parameters and, overall, a significant reduction in the maximum induced stress in the cell. Stress behavior between the anode and cathode differ significantly and show that the effective diffusivity of a particle might matter much more significantly than its location in the cell. With heterogeneous particle shape modeling capabilities, this approach can be next-generation battery model that improves understanding of battery materials and electrodes.

Fully coupled simplified electrochemical and thermal model for series-parallel configured battery pack

Battery packs are often designed with multiple battery cells configured in series and/or parallel combinations to meet the energy and/or power requirements of target applications. Modeling of these battery packs is very complex, computationally challenging and requires extending a single cell model to multi-cell models including electrical connections between cells. Also, the cell-to-cell variations of capacity, resistance, and temperature in the pack are vital in the battery pack design and battery management system development. Therefore, a robust modeling platform with in-built physics and fully coupled models both at the cell and the pack level is developed. The modeling framework consists of Simplified Electrochemical and lumped Thermal Model (SEM-T) at the cell level and Equivalent-Circuit Model (ECM) for Ohmic calculations and natural Convective Thermal Model (CTM) for thermal distribution at the pack level. A 7S4P battery pack with 21700 NCA cylindrical cells is considered in this study and the model is validated with the experimental data sets at different c-rates and temperatures. The developed model is able to successfully predict the pack voltage, capacities, and temperatures. The proposed model is computationally efficient and can be easily adopted for on-board implementation in battery management system for safe and reliable operations.

A Coupled Electrochemical-Mechanical Pressure Model for Lithium Metal Batteries

The application of mechanical pressure is receiving interest for controlling the deposition morphology of Lithium metal (Li metal) anodes.1 Pressure has been observed to induce constrained Li growth and result in more uniform deposition, in contrast to the high surface-area, mossy Li deposits that are typically observed.2 The prevention of undesirable phenomena such as mossy or dendritic lithium can potentially result in significant increases in the cycle life of high-energy Li metal cells.3 Modeling and experimental investigations at electrode and cell levels have identified the modification of interfacial kinetics and plastic deformation of Li as key mechanisms leading to dense deposition.1,2,4 Further insights can be obtained by the study of these coupled electrochemical-mechanical effects during the dynamic evolution of the electrode-electrolyte interface, and its correlation with cell-level measurements, e.g. voltage evolution during extended cycling.5 This article proposes a multiscale-continuum model applicable to both Li metal anodes and full cells under pressure. In the first iteration, the effect of interfacial deformation on kinetics is studied at different external pressures using a two-dimensional mechanical model. This model will employ more recent constitutive equations for the mechanical response of Li metal.6 The modified parameters obtained thus are combined with a cell-level macrohomogenous pseudo two-dimensional (p2D) model for the cathode and separator, which relates the effect of the modified kinetics on voltage. The voltage response from this ‘pressure-aware p2D model’ is studied both for symmetric cells and full Li metal cells, with different mathematical coupling techniques evaluated by comparison against experimental cycling data from cells under pressure. Efficient solutions are also presented for the two-dimensional mechanical model, which are envisaged to aid the computationally fast evaluation of the cell-level model. The two-dimensional interface model serves as the basis for addition of localized transport models. This in turn will introduce the ability to simulate the dynamic evolution of the anode-electrolyte interface, with attendant improvements in connecting morphological evolution to the evolution of cell-level variables during practical operation. AcknowledgmentsThe authors are thankful for financial support by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy through the Advanced Battery Materials Research (BMR) Program (Battery500 Consortium).

Agent-based modeling and bifurcation analysis reveal mechanisms of macrophage polarization and phenotype pattern distribution

Macrophages play a key role in tissue regeneration by polarizing to different destinies and generating various phenotypes. Recognizing the underlying mechanisms is critical in designing therapeutic procedures targeting macrophage fate determination. Here, to investigate the macrophage polarization, a nonlinear mathematical model is proposed in which the effect of IL4, IFNγ and LPS, as external stimuli, on STAT1, STAT6, and NFκB is studied using bifurcation analysis. The existence of saddle-node bifurcations in these internal key regulators allows different combinations of steady state levels which are attributable to different fates. Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization. Next, in order to investigate the polarization of a population of macrophages, bifurcation analysis is employed aligned with agent-based approach and a two-layer model is proposed in which the information from single cells is exploited to model the behavior in tissue level. Also, in this model, a partial differential equation describes the diffusion of secreted cytokines in the medium. Finally, the model was validated against a set of experimental data. Taken together, we have here developed a cell and tissue level model of macrophage polarization behavior which can be used for designing therapeutic interventions.

Characteristics and Prospect of Skin Aging Cell Model

Aging is a necessary stage of the body, accompanied by the decline and abnormal state of skin, nerves, organs and viscera. Skin aging is one of the most remarkable organs in the aging process of the body, its research has become an unfailing hot spot. With the deepening of research and the exploration of aging mechanism, the research on cell level becomes more and more important. In order to facilitate the study of cell level mechanism and model selection, this paper summarizes the replication and characteristics of skin aging cell model, so as to simplify model selection and promote new skin cell model replication methods.

Simple and Complex Polymer Electrolyte Fuel Cell Stack Models: A Comparison

The High Temperature Polymer Electrolyte Fuel Cell (HT-PEFC) converts chemical energy to electricity and heat. Operating at around 160°C, the heart of a HT-PEFC is a phosphoric-acid-doped polybenzimidazole membrane, which exhibits good protonic conductivity. HT-PEFCs may readily operate with either hydrogen or reformate as fuel. As is the case with most fuel cells, HT-PEFCs are operated in stacks in order to increase the overall electric potential. However, there are few comprehensive models of HT-PEFC stack performance. The results of this research program are among the first to obtain performance calculations for HT-PEFC at the stack scale with experimental validation. HT-PEFC stacks designed at the Forschungszentrum Jülich are actively cooled with polyalkyline glycol liquid (oil) coolant, flowing in internal passages within the solid bi-polar plates, upon the surfaces of which a complex pattern consisting of straight and serpentine passages have been machined, in order to supply the air and fuel to the cell. Because of the elevated temperature, liquid water is not generally found in the gas channels or porous layers. Considerable experimental data have been previously gathered, in-house, for a 5-cell stack based on this design. Two high temperature polymer electrolyte fuel cell (HT-PEFC) models of a HT-PEFC stack are described in detail: (i) A detailed cell-level model where a set of conformal meshes are body-fitted to all the different parts of the stack. The code typically runs, in parallel, on 1000-2000 cores at the Jülich Supercomputer Centre; and, (ii) A coarse-grid stack model based on a ‘distributed resistance analogy’ whereby rate equations supplant local diffusion terms in selected locations and directions to reduce computational requirements. A multiply-shared space (MUSES) method is employed to obtain simultaneous solutions for concentration, heat and momentum for the different phases occupying the ‘same’ global space. Both (i) detailed and (ii) MUSES methods are implemented by instantiating 5 distinct meshes corresponding to (i) air, (ii) fuel, (iii) oil (fluid), and (iv) membrane electrode assembly, (v) bipolar plate (solid) regions, and obtaining solutions of the governing equations on these meshes. For both methods a solution is obtained simultaneously for the stack manifolds, cell manifolds (entrance regions) as well as the ‘core’ of the fuel cell stack. Thermal equilibrium between the 3 fluid phases is not presumed, a priori. In both methods, the electric field potential is expressed as the ideal (Nernst) potential less activation, ohmic, and transport losses. Individual cell potentiostatic boundary conditions are iteratively corrected until the desired overall galvanostatic condition is obtained for all cells in the stack. Both codes are developed in the modern open-source object-oriented library, OpenFOAM. The results of the two models are compared with each other in terms of local current density and species partial pressure distributions. Both models are then compared with experimental data. The results show that the coarse-grid stack model (ii) agrees well, both quantitatively and qualitatively, with the detailed model (i) and experimental results and calculations are performed in two orders of magnitude less computation time. However, neither the experimental results nor the stack model (ii) are able to resolve local extrema in the current density and species mole fraction values that are observed with the detailed model (i). These are due to complex flow regimes associated with the meandering channels and flow bypassing in the porous transport layers. Importantly, these lead to significant local extrema in the local current density and other parameters of significance. These are among the first fully-comprehensive physicochemicohydrodynamic models of a HT-PEFC stack which allows calculations to be performed simultaneously for all the fluid and solids in the manifolds, entrance regions and stack core, together with experimental validation.

The impact of cardiac tissue anisotropy on spiral wave superseding: A simulation study using ionic cell models

Several types of dangerous cardiac arrhythmias, such as paroxysmal tachycardia and fibrillation, are linked with the spiral waves of electrical excitation in the heart muscle. In many cases, these diseases must be cured immediately after their diagnosis. Low-voltage defibrillation and cardioversion are modern treatment methods. Electrotherapy is based on spiral wave superseding by a high-frequency pacing from an electrode. In the present work, we study the influence of the anisotropic myocardial structure and cell-level model on cardioversion results. We use long line and point electrodes. Intervals of effective stimulation periods are determined and compared for two ionic cell-level models. Of all the considered factors, the cell-level model appears to play the greatest role in the results.

Model-based lifetime prediction of an LFP/graphite lithium-ion battery in a stationary photovoltaic battery system

Battery degradation is a complex physicochemical process that strongly depends on operating conditions. We present a model-based analysis of lithium-ion battery degradation in a stationary photovoltaic battery system. We use a multi-scale multi-physics model of a graphite/lithium iron phosphate (LiFePO4, LFP) cell including solid electrolyte interphase (SEI) formation. The cell-level model is dynamically coupled to a system-level model consisting of photovoltaics (PV), inverter, load, grid interaction, and energy management system, fed with historic weather data. Simulations are carried out for two load scenarios, a single-family house and an office tract, over annual operation cycles with one-minute time resolution. As key result, we show that the charging process causes a peak in degradation rate due to electrochemical charge overpotentials. The main drivers for cell ageing are therefore not only a high state of charge (SOC), but the charging process leading towards high SOC. We also show that the load situation not only influences system parameters like self-sufficiency and self-consumption, but also has a significant impact on battery ageing. We assess reduced charge cut-off voltage as ageing mitigation strategy.

A Detailed-Electrochemistry Model of an LiFePO4/Graphite Lithium-Ion Cell Capturing Abuse and Aging Phenomena

Numerical simulations are an important corner stone for the development of lithium-ion batteries as they can save expenses in time and cost for a large number of series of experiments. Empirical models have the advantage of a fast development and a low computational effort, but their predictions are only valid within the range of experimental data used for fitting. In contrast, physically-based models allow a deeper understanding and increase the applicability to different scenarios and the credibility of the model predictions. We present a multi-scale modelling approach coupling a 1D thermal cell-level (macro-scale) model, a 1D electrode-pair level (micro-scale) model, and a 1D particle-level (nano-scale) model (Figure 1) 1. A particular feature of the model is detailed electrochemistry, capturing multi-step main and side reactions occurring during ageing or thermal runaway. The model is parametrized to commercial lithium iron phosphate cells. We assume solid electrolyte interphase (SEI) formation at the anode as dominant aging mechanism, which is known to be the main contributor to calendaric aging 2. By capturing the nonlinear feedback between electrochemistry and transport, the model is able to simulate cell behavior not only within recommended operating conditions, but also during cell abuse, for example, due to external short circuit, and during long-time operation. Simulations of short time (external short circuit) and long time (lifetime estimation) scenarios are presented (Figure 2,3). These different events are compared and interpreted, for example in terms of reaction limitation or transport limitation. The sensitivity and reassessment of the model parameter is discussed, and the model as a comprehensive copy of the real battery is verified. Thereby insights into the battery which are experimentally hard to obtain, like concentration and temperature gradients or the distribution of lithium in the active material (Figure 4), are more justified than before.