BatCAT deliverable 2.2: Report on multiphysics modelling of battery production

101137725/BatCAT/WP2/D2.2 D2.2: Report on multiphysics modelling of battery production Grant agreement number: 101137725 Project acronym: BatCAT Project title: Battery Cell Assembly Twin Project website: http://batcat.info/ Project start date: 01.01.2024 Project duration: 42 months Call topic: HORIZON-CL5-2023-D2-01-03 Deliverable type1: Report (R) Related work package: WP2 Due date: 30.06.2025 Actual submission date: 29.06.2025 Responsible beneficiary: LOYOLA Dissemination level2: Public (PU) Version: Submitted on portal (29.06.2025) Abstract: This report presents a comprehensive overview of multiphysics modelling activities developed within the BatCAT project to simulate key stages of lithiumion battery (LIB) manufacturing. Our work addresses the project's objectives to enable more sustainable and efficient battery production processes through predictive modelling and digital twin approaches. Contributions span several partners and manufacturing steps, including modelling of SEI formation (DTU, IFPEN), electrolyte filling (ITWM), electrode calendering (LOYOLA), and battery operation simulations (POLITO, SIMULA, NMBU, UKRI). These efforts are supported by the development of new multiphysics models and coupling strategies (RPTU) that serve as a unifying framework. 1 Deliverable type: R = Report, P = Prototype, D = Demonstrator, O = Other. 2 Dissemination level: PU = Public, SEN = Sensitive. Public Version submitted on portal (29.06.2025) Page 2 of 51 At the core of this deliverable is the implementation of physics-informed multiscale methods that connect manufacturing process parameters to the evolving microstructure and functional properties of electrodes. These models aim to bridge the gap between materials behaviour, manufacturing conditions, and electrochemical performance, laying the groundwork for future integration into digital twin environments and higher TRL decision-making tools. Author list Beneficiary Name Contact e-mail ITWM Jochen Zausch [email protected] IFPEN Martin Petit martin.p[email protected] IFPEN Carlos Nieto carlos.n[email protected] LOYOLA Francisco Montero fpm[email protected] LOYOLA David Gonzalez dgrodr[email protected] POLITO Gianluca Boccardo [email protected] UKRI Michael Seaton [email protected] NMBU Martin Thomas Horsch martin.tho[email protected] DTU Ivano Eligio Castelli [email protected] RPTU Simon Stephan simon.[email protected] SIMULA Eirik Valseth [email protected] NMBU Amirhossein Aghabarari amir[email protected] POLITO Elisa Buccafusco elisa.buccafus[email protected] Reviewer list Beneficiary Name Contact e-mail HSKL Johanna Glutting [email protected] Document history Version Date Reason/comment Revised by Submitted on portal 29.06.2025 Submission date See author list for all who contributed Disclaimer Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Climate, Infrastructure and Environment Executive Agency (CINEA). Neither the EU nor the CINEA can be held responsible for them. BatCAT has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement no. 101137725. Public Version submitted on portal (29.06.2025) Page 3 of 51 Contents 1. Executive summary ...................................................................................................................................... 4 Description of the deliverable content and objectives .................................................................................... 4 2. Progress report (main activities) .................................................................................................................. 5 Promoting model-experimental linking ........................................................................................................... 5 Electrolyte wetting in LIBs ................................................................................................................................ 6 SEI Formation in Li/Na-ion batteries ................................................................................................................ 9 Calendering in LiB ........................................................................................................................................... 15 RFB operation ................................................................................................................................................. 28 New Multiphysics Models for Battery Production Modelling ....................................................................... 34 3. Conclusion .................................................................................................................................................. 43 Electrolyte Wetting in LiB ............................................................................................................................... 43 SEI Formation in Li/Na-ion batteries .............................................................................................................. 43 Calendering in LiB ........................................................................................................................................... 43 Operation in LiB .............................................................................................................................................. 44 Operation in RFB ............................................................................................................................................ 44 New Multiphysics Models for Battery Production Modelling ....................................................................... 44 4. References .................................................................................................................................................. 45 Redox Operation ............................................................................................................................................ 45 New Multiphysics Models for Battery Production Modeling ........................................................................ 45 5. Annex .......................................................................................................................................................... 46 Simulation tool for Electrolyte Wetting in LiB................................................................................................ 46 Simulation tool for SEI Formation in Li/Na-ion batteries ............................................................................... 46 Simulation tool for Calendering in LiB............................................................................................................ 48 Simulation tool for Operation in LiB............................................................................................................... 50 Simulation tool for Operation in RFB ............................................................................................................. 50 Simulation tool for New Multiphysics Models for Battery Production Modelling ........................................ 51 Public Version submitted on portal (29.06.2025) Page 4 of 51 1. Executive summary Description of the deliverable content and objectives This manuscript reports on our efforts towards the multiphysics modelling of battery production. It aligns with the broader predefined project objectives: “Improvements towards new greener and more sustainable manufacturing processes for LIBs” and more precisely “Developing a methodology that will be adapted to the manufacture process for new battery Technologies “, which essentially impacts the rest of the project. The work presented here reflects a collaborative effort across project partners, each addressing critical stages of the battery lifecycle through targeted simulation strategies: • DTU & IFPEN lead the modelling of solid electrolyte interphase (SEI) formation in Li/Na-ion batteries, contributing key insights into degradation and surface reactions. • ITWM focuses on electrolyte filling simulations, accounting for the interplay between pore structure, wetting, and capillarity in complex electrodes. • LOYOLA contributes with mesoscale mechanical modelling of the calendering process in LIBs, using lattice-particle methods to predict porosity, compaction, and structural evolution. • POLITO simulates Li-ion battery operation, capturing coupled thermal-electrochemical dynamics under realistic cycling. • SIMULA, NMBU, and UKRI explore redox-active system behavior and degradation under operational conditions, particularly for Na-based chemistries. • RPTU develops novel multiphysics coupling strategies and contributes to the framework architecture for generalized battery process modelling. We present the fundamental advances achieved by month 18 (M18) toward Key Objective KO2 of the BatCAT project, which focuses on developing multiscale, multiphysics modelling frameworks for LIB production. Our contributions also align with KO3 (digital twin implementation) and KO6 (scalability and manufacturability), supporting the project’s trajectory from low TRL (2–3) modelling tools toward pilot-line integration at TRL 5. By embedding predictive simulations into the process-design feedback loop, this modelling infrastructure lays the groundwork for data-informed manufacturing and quality control. In conclusion, WP2 establishes the fundamental physically-based models for the BatCAT overall objectives. A key aspect to succeed in the “Up-scaling of process models along the LIB cell manufacturing to machine models”, and in general to the BatCAT objectives of interoperability (WP3), knowledge integration (WP4) and Digial Twin technology (WP5) is the knowledge transfer across partners and WPs. This report outlines the methods and tools established so far, highlighting the importance of strong coordination and knowledge exchange across partners and WPs. As modelling activities mature, we aim to strengthen cross-partner collaboration — especially in connecting experimental data with virtual simulations — to enhance model validation and practical relevance. Public Version submitted on portal (29.06.2025) Page 5 of 51 2. Progress report (main activities) The models reported here represent a crucial and fundamental part of WP2 for developing robust digital tools integrating multiphysics and multiscale models for both production and life-time operation of batteries. To develop a truly flexible and chemistry-neutral modelling workflow, different chemistries and arrangements will be explored: Li-ion cells and redox flow batteries (RFB). WP2 has the main responsibility for KO2, “integrate multiphysics and multiscale modelling approaches, aiming at scalability and efficiency,” and also delivers substantial contributions toward WP3 (technical interoperability). The longer-term commitments associated to this deliverable D2.2 (WP2), as per the BatCAT_part-B.pdf document, follow the anticipated “strategy for exploitation that will be regularly assessed during the project lifetime to assure knowledge progression and industry adoption. It will strengthen competitiveness in battery digitalization by accelerating access to new technologies, adapting and improving technical infrastructure to support its scalability and transferability. For its implementation, the BatCAT exploitation strategy relies on a two-phase model: During project execution in phase I (M1-M30), a short-term exploitation plan will be maintained for project results which have an strong potential for industrial uptake (for phase II).” Further, the initially anticipated list of WP2-related key exploitable results (KER) identified still holds, including: Electronic, atomistic, mesoscopic, and continuum models for LIBs and Na-ion batteries (TRLs 4 to 5) Electronic, atomistic, mesoscopic, and continuum models for redox-flow batteries (TRLs 4 to 5) Next, we report the main activities carried out in the key battery manufacturing and battery operation processes. Additional simulation details in lithium-ion batteries (LIB) are given in the annex for calendering and solid electrolyte interphase (SEI) formation subsections. In these subsubsections we will describe the theoretical foundation of each process in the workflow and the numerical approach, summarizing the input and outputs where applicable. Promoting model-experimental linking To enhance the predictive capability and relevance of our modelling tools, we actively promote coordinated model–experiment integration across project partners and work packages. While our methodology is exemplified through the calendering stage of LIB production, the same principles apply across other manufacturing steps. For instance, LOYOLA’s simulated calendered microstructures can be directly utilized by POLITO as inputs for their operation-stage simulations. This promotes continuity and realism across modelling scales and physical processes. Meanwhile, experimental partners such as IFPEN and CEI (WP1) are equipped to perform calendering experiments exploring the effects of particle size, shape, and active material distribution on porosity and tortuosity. These physical parameters are also tunable within our virtual RVE generation framework, allowing for parallel studies that support robust model validation. Experimental testing using different electrode combinations—such as NMC622/graphite and LFP/graphite—and variations in sieve curves can be directly compared with our lattice-particle predictions of structural evolution. Public Version submitted on portal (29.06.2025) Page 6 of 51 As experimental characterization advances, techniques such as SEM and Micro-CT will support model validation by capturing microstructural changes before and after calendering. These methods enable the analysis of particle distribution, binder behavior, porosity, and tortuosity evolution—key parameters for aligning virtual RVEs with real electrode structures. These methods are also complemented by 3D imaging and crystallographic techniques such as EBSD, which reveal the internal structure and orientation of particles—especially relevant in materials like NMC cathodes. EBSD enables the analysis of grain boundaries and crystal orientation, both of which significantly affect ion transport and mechanical resilience during operation. Together, these coordinated efforts promote a robust experimental–modelling feedback loop. Modelling informs experimental focus; experimental results in turn validate and refine the simulation framework. This integration not only ensures accuracy and relevance but also strengthens the interoperability and value of modelling contributions across the BatCAT consortium. Electrolyte wetting in LIBs In Li-ion battery manufacturing, filling refers to the process of introducing the electrolyte liquid into the battery cell, while wetting is the subsequent process where the electrolyte is absorbed by the porous structures of the electrodes and separator. While the former happens on the order of minutes, the latter requires typically several hours. Since there is no proper inline characterization method for the wetting state, the required wetting time is typically based on experience and trial and error. We apply a simulation model gain more insights into the process and get a reasonable estimation of the wetting time. In this section, the basics of the mathematical model for the wetting simulation is outlined. During and after dispensing the liquid electrolyte into the cell (e.g. the pouch bag or the cylindrical/prismatic housing) the liquid is soaked up by the porous sheets (electrodes and separator) mainly due to capillary forces. Because of the low permeability and the large cell footprint (in particular in electromobility applications) this process takes a considerable amount of time in the order of hours. Therefore, sometimes the external pressure is varied with the aim to speed up the wetting. In any case, it is experimentally difficult to determine when the whole pore space is homogeneously filled, and the process can be stopped. With the help of a proper model, the wetting dynamics and the influencing factors on the saturation distribution shall be assessed. A relatively simple approach to describe the wetting dynamics is given by the Richards equation 0=𝜕𝜙 𝑠 𝜕𝑡 −∇⋅[𝐾𝑙(𝑠) 𝜇∇𝑝𝑐(𝑠)] which describes the spatial and temporal evolution of the electrolyte saturation 𝑠(𝑥,𝑡) within the porous sheets. In this approach the microstructure is not resolved. Its effect on the fluid flow is characterized by the porosity 𝜙 and the saturation-dependent permeability 𝐾𝑙(𝑠). The capillary forces are accounted for by the capillary pressure 𝑝𝑐(𝑠). As final material parameter, the electrolyte’s viscosity 𝜇 enters the equation. Using ITWM’s software FLUID this equation can be solved numerically in a three-dimensional domain shown in Figure 1. Public Version submitted on portal (29.06.2025) Page 7 of 51 Figure 1. Illustration of simulation domain. The arrows indicate the faces through which electrolyte can in principle enter the pores of the sheets. The other two faces (current collector foils) are impenetrable. The arrows indicate the sides through which electrolyte can in principle enter the pores of electrodes and separator. The large front and back sides, are impenetrable due to the current collector foil. The actual area used for the penetrating liquid depends on its distribution in the void space between sheet stack and cell housing. Figure 2 shows a result from a wetting simulation, where electrolyte enters from only three of the four possible sides. Figure 2. Left: Snapshot of the saturation distribution in a cell stack at 1000s after wetting started. Here, electrolyte enters through the bottom and left and right faces. Right: Global saturation state versus time. The marker indicates the time of the snapshot. The main result of the simulation is a three-dimensional solution field of the electrolyte saturation between 0 (pores empty) and 1 (pores fully saturated) (left snapshot). Taking the average yields the global saturation state as it developed with time. While the rise of the saturation grows as √𝑡 in one-dimensional cases in accordance with the well-known solution of Washburn’s eqn., the general 3d solution will be different. This was, the necessary wetting time can be computed based on the material parameters described above. The described approach based on the Richards equation neglects the influence of a gas phase. In many cases this might be adequate since typically the cell is filled at very low gas pressures. However, if the residual gas cannot escape the sheet stack during the wetting, it will reduce the achievable saturation. Additionally, by varying the gas pressure during and after the filling, the wetting dynamics will be influenced. For these cases Public Version submitted on portal (29.06.2025) Page 8 of 51 a more complex model based on a modified Navier-Stokes-Brinkmann equation can be used. In ITWM’s FLUID we use the model of Carrillo et al. [3]: 𝜌 𝜙(𝜕𝑡𝑢+𝛻⋅(𝑢×𝑢 𝜙))=−𝛻𝑝−𝜇𝐾−1𝑢+𝛻⋅𝜇(𝛻𝑢+𝛻𝑢𝑇)+𝐹𝑐(𝑠) 𝜕𝑡𝜙𝑠+𝛻⋅(𝑠𝑢)+𝛻⋅𝑢𝑟    =0 Here, 𝑢 denotes the flow velocity, the capillary forces are encoded in the force density 𝐹𝑐(𝑠), and 𝑢𝑟    is the socalled relative velocity. The latter two are given by some more involved expressions and we refer for further details to [ 3 ]. It is important to note that this model accounts for the compressibility of the gas phase so that a trapped gas volume will eventually oppose further wetting once the gas pressure is high enough. The graph in Figure 3 shows the simulated electrolyte content for a process where the external pressure is increased at a certain time. Figure 3.Global saturation state (solid line) in terms of electrolyte mass during the wetting process versus time. The dashed line shows the applied external pressure which exhibits a jump at 300s. The pressure jump directly affects the saturation evolution. Similar to the Richards approach, this model yields the time dependent 3d fields of the electrolyte saturation from which the global saturation level can be deduced. The shown approaches allow the study of the wetting process, the influence of the process conditions and enables an estimate of the required time for a homogeneous, full saturation. The models are implemented in ITWM’s CoRheoS Framework in C++ using a Finite Volume Method for spatial discretization. 3 Francisco J.Carrillo et al. Journal of Computational Physics: X 8 (2020) 100073. Public Version submitted on portal (29.06.2025) Page 9 of 51 SEI Formation in Li/Na-ion batteries In lithium-ion batteries (LIB), a primary contributor to its degradation is the formation of the solid electrolyte interphase (SEI). The SEI forms due to the reduction of the electrolyte by electrons from the anode. Once the SEI is formed, it slows down further reduction of the electrolyte, thereby acting as a passive layer. However, it continues to grow over time, ultimately contributing to battery failure. The solid electrolyte interphase (SEI) is typically regarded as a heterogeneous, multilayered structure - comprising of an inner inorganic layer adjacent to the anode/SEI interface and an outer organic layer near the SEI/electrolyte interface 4 . Figure 1. Schematic representation of the electrode/electrolyte interface and indication of where SEI growth reactions are expected to occur. (Reprinted (adapted) with permission from Ref. [1]. Copyright 2025 American Chemical Society.) Developing a comprehensive understanding of the formation of the multilayered structure within the SEI matrix remains a significant challenge. Our atomistic-level simulations will serve as a powerful tool for elucidating the degradation mechanisms of electrolyte solvents and probing the intricate interactions between the electrolyte and SEI layers. As a result of the growing interest in sodium-ion batteries (SIB) as promising alternatives to lithium, understanding the relative degradation behaviour is essential for assessing the long-term performance and safety of SIBs as compared to LIBs. In this study, we address this gap by examining the battery aging process under storage conditions (calendar aging) through a comparative analysis of the decomposition reaction kinetics of ethylene carbonate (EC) in lithium and 4 Bin Jassar, M.; Michel, C.; Abada, S.; De Bruin, T.; Tant, S.; Nieto-Draghi, C.; Steinmann, S. N. A Joint DFT-kMC Study To Model Ethylene Carbonate Decomposition Reactions: SEI Formation, Growth, and Capacity Loss during Calendar Aging of Li-Metal Batteries. ACS Applied Energy Materials 2023, 6, 6934–6945. DOI: 10.1021/acsaem.3c00372 Public Version submitted on portal (29.06.2025) Page 16 of 51 Figure 1. Images showing the calendering process 15 and 16 roller detail. During drying, electrodes are dried to remove excess solvents to ensure stability of electrode materials. Drying involves solvent evaporation. Solvent evaporation triggers binder hardening, once the solvent evaporates, the binder solidifies, forming a durable layer. Understanding binder behavior prevents premature failure and enhances durability. Modelling drying is essential because improper drying can lead to cracking, warping, or residual stress in materials. Simulations identify inefficiencies before production, saving materials and cost. The huge influence on the electrochemical performance, compared to other process steps, is due to drastic changes in the pore structure of the particulate coating of the electrodes. The changes achieved by calendaring are very different for anodes and cathodes, mainly because of the diverging material properties. Experimental techniques, such as Micro-CT Analysis, can bring light in comparing the pore connectivity and density changes post-calendering. This aims to assess the mechanical adjustments to ensure improved conductivity while maintaining sufficient ion transport channels. These observations can play a primary role to identify any reduction in porosity and evaluate whether compression has optimized ion pathways or introduced bottlenecks. Figure 2 shows (Above) carbon binder and active particle is in NMC622 17 and NMC622 18 and (below) Macropores and microporous CBD phases in NMC 622 generated separately by using a thresholding random field algorithm 19 . 15 Gimenez, Simulation of electrodes during calendaring, Powder Technol., 2019. 16 Meyer, Calendering process for electrode compaction, J. Mater. Process. Technol., 2017. 17 Boyce, Cracking predictions of lithium-ion battery electrodes, J. Power Sources, 2022. 18 Sun, Elucidating degradation mechanisms in battery electrodes, Energy Storage Mater.. 19 Ge, Design of microporous binder domains in cathodes, ACS Appl. Mater. Interfaces, 2023. Public Version submitted on portal (29.06.2025) Page 17 of 51 Figure 2. Segmented particles In Figure 2, an Iamage-based explicit model was built to simulate the calendering of electrodes. In this study, to save the computational time and realise the quasi-static study, the time-scaling method was employed, in which the time length of the loading period is reduced to a certain value. This aims to ensure a balance computation speed with simulation fidelity. The image shows the 3D imaging through Micro-CT conducted to map the pore structure and assess the spatial distribution of materials within the electrode. Micro-CT, particularly when combined with pre-calendering imaging, allows a direct comparison of the microstructure, showcasing reductions in porosity, improvements in density, and any potential bottlenecks introduced in terms of ion transport. In conclussion, these experimental results can enhance the understanding of microstructural changes during calendering and support simulations predicting electrode performance. In the literature we can find the implementation of Discrete Element Method (DEM) for calendering 20 , and also in abaqus findreference. Abaqus commercial software support DEM simulations, which are useful for modeling granular materials and discontinuous systems. DEM in Abaqus uses softsphere methodology, meaning particles can have small overlaps to represent deformations. It applies contact mechanics and Newtonian laws to determine particle interactions, making DEM suitable for electrode manufacturnig 20 Zhang, Investigation of stress in composite electrodes, Electrochim. Acta. Public Version submitted on portal (29.06.2025) Page 18 of 51 Microindentation force-displacement curves have been well predicted using DEM for JKR 21 and Edinburgh models 22 The tortuosity factor can represent the lithiumion transport feasibility in the electrolyte phase. It is an important property as it limits the maximum charge/discharge rate for battery electrodes. We will review it in more detail in later sections. Electrode multiscale deformation Figure 3 shows typical load-displacement compression curves, showing the multiscale nature of the deformation involved during calendering. In fig 3a, the magenta-shaded area corresponds to the plastic work (Wpl) done by the indenter during the loading, while the yellow-shaded one corresponds to the recovered elastic work (Wel) during the indenter unloading 23 and evolution of unit pressure with reduction for the calendered electrodes, the reduction is 5, 10, 15 and 19.5 𝜇m 24 . Figure 3. Load-displacement curve of a microindentation experiment and macroscale Electrode deformation (experimentally-based for compaction). Multiscale deformation is even more important during service, where abundant studies have recently reported the crucial role of crystal anisotropy in cracking. The compressibility of particle assemblies can be described by an exponential compaction equation first proposed by Heckel: 𝜀=𝜀min +(𝜀ini −𝜀min)𝑒−𝑃 𝛾𝐶 where 𝜀, is the electrode porosity, 𝜀ini and 𝜀min are the initial and minimum structure porosities, Meyer et al. 25 systematically investigated the calendering process of graphite anodes and nickel manganese cobalt oxide (NMC) cathodes. It was found that the material mechanical properties play a significant role in the compaction. The relation between the coating density and circumferential speed, applied line load was studied. An exponential equation was found to describe the compaction 21 Ngandjong, Calendering and its electrochemical impact via DEM, J. Power Sources, 2021. 22 Zhang, Investigation of stress in composite electrodes, Electrochim. Acta. 23 Primo, Calendering processability of NMC-based cathodes, Adv. Energy Mater., 2021. 24 Zhang, Investigation of stress in composite electrodes, Electrochim. Acta. 25 Meyer, Calendering process for electrode compaction, J. Mater. Process. Technol., 2017. Public Version submitted on portal (29.06.2025) Page 19 of 51 force and the measured porosity reduction. The model parameters quantify the different compaction resistances of the cathodes and anodes Our Modelling Strategy Our overall modelling strategy relies on the lattice-particle method, which we will describe in more detail in later sections. Broadly speaking, we aim to build computational tools for understanding anode/cathode manufacturing and performance. This involves identifying relationships between manufacturing processes, microstructure, and material properties. In battery production, calendering represents a key manufacturing step due to its strong influence on the final electrode microstructure. Our approach focuses on modelling calendering and its effects, as follows: • Calendering process modelling → prediction of microstructure evolution. • Microstructure prediction → evaluation of diffusivity, depending on porosity and tortuosity. • Microstructure during service → volumetric changes induce material degradation via microcracking of particles within the electrode. Classic contact Models: Hertz & JKR. The Hertz elastic solution 1882 relates contact force to the approach distance for two contacting spherical particles. It relies onThe equivalent Young’s Modulus and the equivalent radius . It allows for the estimation of the resulting contact area, pressure, and stress in the solid. The Hertz model can be extended to include viscoelasticity. While the original Hertz contact theory (1889) describes elastic deformation between two bodies, researchers have developed viscoelastic Hertzian models to account for energy dissipation and time-dependent material behavior. Multiple modifications of the Hertzian theory have been introduced since the 1950s such as tangential behaviours, viscoelastic and damping effects. A significant modification to the Herz model was proposed by Johnson, Kendall and Roberts in 1971 (JKR model) to consider the effect of particle adhesion by JKR. This model incorporates the effect of particle interpenetration at the microscale by introducing a surface energy per unit area of the two contacting particles. Recently, Ngandjong et al. 26 developed a calendering model to evaluate the relationships between calendering pressure, microstructure and electrochemical performance. In their DEM model, Hertizan theory and simplified Johnson-Kendall-Roberts (JKR) model were used to validate their experimentally measured force-displacement curves and pressure-porosity responses during calendering. A more sophisticated model (The Edinburgh model) 27 proposed for adhesion strength at contact in cohesive granular materials, has recently been applied to successfully predict the force-displacement curves during calendering 28 .This model incorporates contact adhesion, contact plastictiy and contact 26 Ngandjong, Calendering and its electrochemical impact via DEM, J. Power Sources, 2021. 27 Thakur, Micromechanical modeling of Si particle electrodes, J. Electrochem. Soc.. 28 Ge, DEM analysis of battery electrodes from X-ray tomography, Powder Technol., 2022. Public Version submitted on portal (29.06.2025) Page 20 of 51 friction. By fitting a number fitting of parameters, it was capable of predicting the experimental flow function in limestone powder. The choice of an appropriate empirical contact model is not trivial due to the number of contributing factors and to the limitted experimentally available data at the particle length scale. The forcedisplacement curve during calendering has been accurately predicted by at least two different empirical contact models implemented in DEM: the JKR 29 and EDPA models 30 . Additionally, the particle adhesion forces during electrode manufacturing are likely to be lower than the forces between particles during electrode service, given the large volumetric strains during lithiation/lithiation. Besides, other events may have a larger effect on deformation, such as particle fracture and multiscale deformation of crystals within particles. As for adhesion, lack of experimental literature and model parameters sensitivity studies. Often, arbitrarily chosen model parameters, to fit data. Elastic-plastic contact model A contact model with a stiffer elastic modulus up to load reversal, followed by a stiffer modulus after reversal, can lock in permanent deformation. This concept aligns with elastic-plastic contact mechanics, where materials exhibit different stiffness characteristics depending on loading conditions. This approach models the permanent deformation due to microstructural changes (see figure 4). Additionally, friction resistance 31 is a reason for the higher compaction resistance. A simple elastic contact model incorporating a shear modulus effectively introduces friction between particles in granular materials. By implementing a softer unloading elastic modulus, the model accounts for dissipative energy losses, capturing hysteresis effects during cyclic loading. This formulation provides a physically consistent representation of adhesion, friction, and irreversible deformation, making it highly applicable to cohesive granular systems, including powders, soft particle interactions, and geomechanical materials. Figure 4. Multiscale contact between particles. a) Contact model proposed by Walton and Braun in 1986. Sometimes this model has been referred to as Hysteretic Spring Model, and b) The idealized stages I, II, and III of micromechanical deformation upon the indentation of a polycrystalline ceramic that give rise to decreasing hardness with an increasing indentation area for indentations of dimension comparable with the grain size. 32 . 29 Ngandjong, Calendering and its electrochemical impact via DEM, J. Power Sources, 2021. 30 Ge, DEM analysis of battery electrodes from X-ray tomography, Powder Technol., 2022. 31 Meyer, Calendering process for electrode compaction, J. Mater. Process. Technol., 2017. 32 Stallard, Mechanical behavior of calendered NMC cathodes, J. Power Sources. Public Version submitted on portal (29.06.2025) Page 21 of 51 The following equations describe the linear system, which can be extended for including adhesion, in a similar but simplified version of the Edinbrugh model: 𝐹𝑛={−𝐾1𝛿𝑛,for loading (𝐾1𝛿𝑁<𝐾2(𝛿𝑛−𝛿0)) 𝐾2(𝛿𝑛−𝛿0), for unloading/reloading (𝛿𝑛>𝛿0) 0, for unloading (𝛿𝑛≤𝛿0) Walton and Braun, in 1986, were probably the first to introduce a normal force displacement (NFD) elasto-plastic bilinear spring model, based on an approximation of finite element analysis (FEA) results, to account for the plasticity at the contact for cohesionless solids. The first NFD contact model with elasto-plastic deformation and adhesion was introduced by Thornton and Ning in 1998. Physically-based adhesion model implementations for loading history are also possible. In 2008, Luding et al. further improved the piece-wise linear model by recognizing the loading history dependent nature of the unloading/reloading stiffness by making the unloading/reloading stiffness a function of the previously experienced maximum overlap. This has introduced an element of nonlinearity in unloading/reloading path. Lattice-particle model and further details Lattice models are a class of discrete models commonly used to describe fracture processes in brittle materials. The basis of the lattice model is the discretization of a continuum domain into a group of connected one-dimensional elements, conforming a network. The model proposed by Hrennikoff in 1941 is considered the prototype of the lattice model. Initially, it was applied in physics to study the fracture process of disordered media. Later on, with the improved computational capacity, lattice models have been extended to 3D and applied in different fields. For example, transport problems of chloride in concrete have been successfully analyzed The lattice-particle model is designed to simulate multiphysical phenomena in a microstructured domain, namely a representative volume element (RVE) composed by particles. This model accounts for the influence of local microstructural features, including particle geometry and distribution, on the macroscopic transport properties and mechanical behavior. The primary application is to predict ion diffusion and structural integrity in heterogeneous particle-based materials, particularly useful for understanding the electrodes performance during operation conditions and it is being extended to calendering. The methodology of the lattice-particle model encompasses two primary components: microstructure generation and the lattice-particle formulation (described in later sections). We use the lattice particle method. In the mechanical problem, the domain is discretized into a set of beam elements with linear elastic behavior. Thus, the resulting system is: 𝐊𝑚𝐮=𝐟 where 𝐊𝑚 is the global stiffness matrix, and 𝐟 the global force vector, The global element matrix, 𝐊𝑚,𝑒𝑔, is then obtained with the use of a transformation matrix 𝐓𝑒 that contains the direction cosines of the element with respect to the global coordinates system, such that Public Version submitted on portal (29.06.2025) Page 22 of 51 𝐊𝑚,𝑒𝑔=𝐓𝑒T𝐊𝑚,𝑒𝐓𝑒 Note: For clarity and readability of the document, additional model details are given in the annex section on: Element Formulation and Integration Scheme, Definition of the Element Properties and Coupled diffusive-mechanical model. RVE generation The LIB anode and cathode are multi-material, porous composites and their microstructure can significantly affect battery performance. For example, the LIB cathode microstructure consists of (i) the majority active material (AM) particle phase for lithium-ion storage, (ii) the carbon binder domain (CBD) that is used to facilitate electronic conduction and ensure mechanical rigidity, and (iii) interconnected, tortuous porosity (30-40 vol %) that is filled with the Li-ion-containing electrolyte. The porous phase governs ion transport. In the literature, calendered electrode structures have been virtually generated using a number of numerical algorithms 33 . The phases considered include: the AM NMC622 particles, the binder domain, the macroscopic porous phase and an additional microporous phase within the binder. This can be appreciated in Figure 2. We have generated the microstructure using a "take-and-place" approach to produce a representative volume element (RVE) that captures the heterogeneous nature of the material. The process begins by defining the four key phases of the microstructure: active material (AM), additives (conductive), binder, and pores. We present a list of each volume fraction parameter with its corresponding description: 𝑣𝑎𝑚 - Volume fraction of the active material. This defines the portion of the electrode occupied by electrochemically active particles, which are responsible for lithium storage. In the anode simulations, a value of 𝑣𝑎𝑚=0.95 was used. Active particles (APs) of 5, 10, and 20 𝜇m in diameter were employed, with corresponding fraction volumes of 0.5, 0.3, and 0.2, respectively. 𝑣𝑎𝑑 - Volume fraction of the additive material. This represents the volume fraction occupied by conductive additives, such as carbon black, which enhance the electrical conductivity of the electrode network. In the cathode simulations, 4 𝜇m additive particles were used with a total additive volume fraction of 0.05. 𝑣𝑏𝑖 - Volume fraction of the binder. Corresponds to the proportion of the electrode composed of polymeric binders like Polyvinylidene fluoride **PVDF**, providing mechanical cohesion between particles and ensuring adhesion to the current collector. A value of 𝑣𝑏𝑖=0.05 was applied in both the anode and cathode configurations. 𝑣𝑝 or 𝜀 - Porosity. Refers to the fraction of the electrode volume that is void (typically filled with 33 Ge, Design of microporous binder domains in cathodes, ACS Appl. Mater. Interfaces, 2023. Public Version submitted on portal (29.06.2025) Page 23 of 51 electrolyte), which is essential for ion transport. Simulations were performed for porosity values of 0.35, 0.45, and 0.55. The construction of the microstructure involves placing particles within a cubic domain (RVE) sequentially, starting with the largest to optimize packing density. Partial overlap between particles is accepted to reflect realistic microstructural features. Once the particles are placed, the microstructure undergoes voxelization and segmentation, enabling computational simulations. Each voxel is assigned to a material phase based on particle and binder placement. This methodology is suitable for both anode and cathode designs, ensuring compatibility across battery electrode architectures. Figure 5. Simulation workflow and virtual electrode characterization: calendering process (top), microstructure evolution from dried to calendered states (left to right), and computed changes in effective diffusivity and elastic modulus (bottom). Public Version submitted on portal (29.06.2025) Page 24 of 51 Virtual Characterization of Properties The image in Figure 5 illustrates the typical workflow of our model. The top diagram shows a schematic of the calendering process, where an initially porous electrode (thickness 𝑡0) is compressed by two rollers down to a final thickness 𝑡𝑓, with a compaction height ℎ. This mechanical compaction influences both the microstructure and the electrochemical performance of the electrode. Our model captures this process using a lattice-particle approach, which generates realistic microstructures at different stages: dried and calendered. The middle row displays these Representative Volume Elements (RVEs), showing how particles become more densely packed upon compression (e.g., 30% or 10% compaction). The virtual microstructure incorporates active material (graphite), conductive additives (carbon black), binder (PVDF), and pores, with a porosity 𝜀=0.5 before calendering. The bottom panels show the spatial distribution of key mechanical and transport properties derived from the microstructure: • Diffusivity: Increased connectivity leads to enhanced ionic transport, though overly compressed structures can introduce tortuous paths. • Elastic Modulus: The stiffer response in compressed regions reflects structural rearrangement and increased contact between particles. This virtual characterization enables us to assess the balance between improved conductivity and mechanical integrity, as altered by calendering parameters. The presented modeling framework integrates calendering mechanics, microstructure evolution, and electrochemical performance in a unified lattice-particle method. It enables: • Quantification of how calendering alters key properties such as porosity, tortuosity, diffusivity, and stiffness. • Evaluation of structure-property relationships at the mesoscale, enabling optimization of manufacturing parameters. • Virtual testing of electrode performance under different compaction levels and geometrical configurations. Future developments will focus on: • Calibration and validation of the model against experimental data (e.g., force-displacement curves, micro-CT images). • Refinement of damage and inelastic models to better capture mechanical degradation during and after calendering. • Coupling this model with full-field Finite Element Methods (FEM), such as in Abaqus, to simulate stress evolution and failure in realistic, heterogeneous microstructures. Next, we present additional properties to be calculated by our modelling strategy Compactation and Tortuosity This modelling framework allows the introduction of key parameters of the process (e.g., pressure). Thus, it can be used to identify operation ranges targeting specific electrode properties such as the effective conductivity or final thickness. Public Version submitted on portal (29.06.2025) Page 25 of 51 Further work is required in the calibration to match experimental measurements, similar to the forcedisplacement calendering curves presented earlier (figure 3). Tortuosity describes the complexity of ion transport paths in the porous microstructure of the electrode. It reflects how much longer ions have to travel compared to a straight line.In our latticeparticle model, tortuosity is not an input but emerges from the simulated microstructure. It is obtained from steady-state simulations of ion diffusion. Tortuosity depends on the microstructure, which in turn is affected by calendering. As porosity decreases, tortuosity typically increases. The tortuosity factor 𝜏 has a significant impact on the transport properties of porous structures. It can be defined as: 𝐷eff =𝐷0⋅𝜀𝜏 where Deff is the diffusivity of the porous structure, D is the intrinsic diffusivity of the porous phase material and 𝜀 is the porosity. An open source MATLAB application (TauFactor), based on numerically solving steady diffusive equations, can be used for tortuosity analysis. IFPEN can also characterize Electrode tortuosity turlough a Bruggeman correlation, while another BatCAT partner, POLITO, can import our predicted porous microstructure to simulate the discharge curves. Stress Evolution During (De)Lithiation During battery operation, the lithiation and delithiation processes induce significant volumetric changes in electrode particles. These changes lead to complex stress development within the microstructure. Lithiation generally causes particles to expand, generating compressive hydrostatic stresses in the particle core and tensile stresses at the particle surface. Conversely, delithiation leads to contraction, reversing the stress profile. This cyclic variation of tensile and compressive stresses can lead to mechanical degradation of the electrode, including the formation of cracks and eventual particle fracture. As shown in Boyce et al. 34 , finite element modeling of individual particles under (de)lithiation cycles reveals that: • During lithiation, tensile hoop stresses appear at the surface, which can drive crack initiation. • During delithiation, residual tensile stresses may remain, exacerbating damage over cycles. Stallard et al. 35 further show how the mechanical properties of cathode materials, including Young’s modulus and fracture toughness, critically influence the stress thresholds for cracking. The microstructural arrangement of particles also governs the way stress distributes across the material. In realistic electrode structures obtained from heterogeneous calendering (as produced by our lattice-particle simulations), the stress field becomes highly non-uniform. The contact network between particles, anisotropic compaction, and porosity gradients introduce local amplifications of stress. These complex stress fields can be further analyzed using finite element methods (FEM) in software such as Abaqus. By importing microstructures from our models into FEM environments, we can simulate stress evolution under operating conditions and predict where mechanical failure is 34 Boyce, Cracking predictions of lithium-ion battery electrodes, J. Power Sources, 2022. 35 Stallard, Mechanical behavior of calendered NMC cathodes, J. Power Sources. Public Version submitted on portal (29.06.2025) Page 32 of 51 are modelled individually and are only assumed to interact with water and sulphate beads via a truncated and shifted Morse potential to represent proton transfer effects [12]. The diffusivity of each component in the electrolytes depends on both their thermodynamic interactions (as outlined above) and the choice of DPD thermostat (dissipative force) parameters 𝛾. As such, it has been possible to obtain appropriate 𝛾 values to match both the self-diffusivity of water and the diffusivities of ionic species (vanadium, sulphate and protons) in water to experimentally-determined values [13]. These diffusivities have been measured by carrying out DL_POLY_5 simulations of water or ionic solutions and measuring temporal gradients of meansquared displacements (MSDs). A ‘standard DPD’ (Groot-Warren) interaction between carbon beads in the felt and all electrolyte beads [14] is proposed. The carbon felt will be represented as a surface made up of frozen carbon beads, which can be functionalised by embedding charges and including indentations similar to those observed experimentally after treatment. Figure 2 illustrates a schematic of the constructed model and its corresponding mesh resolution. The computational domain spans (from left to right): porous carbon felt electrode (the negative half-cell) →, Nafion membrane →, porous carbon felt electrode (the positive half-cell). Flow enters and exits each halfcell in the vertical (y) direction; the out-of-plane (z) width is taken as 10 cm to recover full-cell rates. Cell Geometry and Boundary conditions Component Dimension Negative & Positive Electrode 10 cm (height) × 0.4 cm (thickness) Porous Carbon Felt Electrode Effective volumetric porosity ϵ = 0.68 Fiber diameter = 10 μm Inter-fiber spacing ≈ 10 μm Membrane Thickness = 180 μm Inlets (both half-cells): A uniform inlet velocity corresponding to 1 mL s⁻¹ per half-cell is imposed across the electrode face (in the y direction) Outlets (both half-cells): A fixed hydraulic pressure of 300 kPa is applied at each outlet plane. Membrane–Electrode Interfaces: Continuity of fluid velocity and pressure is enforced. Vanadium species cannot permeate the membrane (N_Vanadium·n = 0), while the membrane’s fixed‐charge density fixes proton concentration at the membrane surfaces. Public Version submitted on portal (29.06.2025) Page 33 of 51 Figure 2. Mesh geometry for the continuum simulations of the RFB system using FEniCSx. Public Version submitted on portal (29.06.2025) Page 34 of 51 New Multiphysics Models for Battery Production Modelling Several new multi-physics models were developed in M1-M18 that cover different aspects of battery production processes. In several cases, entirely new approaches had to be developed where established methods were either not sufficiently robust and/ or reliable. While the focus in D2.2 was on Li-ion battery production and RFB battery production, see subsections above, the new multiphysics models developed and described here can be applied for various battery chemistries – including those previously discussed. Therefore, these new multi-physics models are described here in a generic way. In each newly developed method, at least two physics models are coupled to improve battery production modelling aspects. Specifically, the following new multi-physics models were developed within BatCAT for enhancing battery production process modelling. • Fluid caloric property multi-physics model → drying of slurry; formation • Mixture diffusion coefficient model → drying of slurry; operation • Polar interaction model evaluation → mixing, coating, drying of slurry; filling • MCO Design of experiment for multi-physics transport property model parametrization→ coating, drying of slurry; filling • Multiphysics coupling of mesoscopic molecular models with continuum fluid simulations → mixing, coating, drying, calendaring, filling These new methods are briefly introduced in the following. They have been published in five peerreviewed publications [1-5]; one more being under review; and two more manuscripts are prepared for publication. Multi-physics Caloric Property model for Fluids for Battery Production In many battery production steps, caloric properties such as the heat capacity play a critical role, e.g. for the drying of the slurry. For the prediction of the heat capacity by molecular models, both intermolecular and intramolecular interactions need to be captured. For the latter, no reliable model was so far available that is suitable for fluids relevant for battery production processes. Such a model was newly developed and implemented here. It can be applied for >20,000 species. All parameters and an executable implementation is part of the manuscript presently being under review. Thermodynamic properties are typically calculated as derivatives of the Helmholtz energy of a fluid. This Helmholtz energy can be split into an ideal part (intramolecular interactions and energy storage) and a residual (intermolecular interactions) contribution as: . In a typical modern equation of state (PC-SAFT, CPA, GERG, ePC-SAFT, etc.) only the residual part is covered and parameters are fitted to PVT or phase-equilibrium data; the ideal part must be supplied separately. For organic battery solvents (Ethylene Carbonate, Propylene Carbonate, Ethyl Methyl Carbonate, Diethyl Carbonate, N-Methyl-2-Pyrrolidone, …) this ideal contribution is dominated by intramolecular vibrations e.g.: Public Version submitted on portal (29.06.2025) Page 35 of 51 Because the vibrational spectrum is highly temperature-dependent (low-frequency modes switch on between 250–450 K), any error in aid rapidly propagates to: • Battery thermal-runaway models, i.e. heat generation can be written as The reversible (entropic) term needs a correct electrolyte entropy, which in turn needs the vibrational aid. Under-estimating cp by 20 % can shift predicted cell temperature rise during a 10 C charge by > 5 K, enough to miss the threshold for SEI exotherms. • Process design in electrode manufacture – drying or solvent-exchange ovens must supply Q = m cp ΔT. For NMP or EC the vibrational share of cp adds approx. 1 kJ/(kg*K) at 350 K; leaving it out undersizes heaters by approx. 25%. Although ion–solvent interactions dominate the character of an electrolyte, the magnitude of every caloric property—heat capacity, enthalpy, entropy, speed of sound—is set first by the intramolecular vibrational contribution to the ideal Helmholtz energy contribution. Battery-level calculations that neglect or oversimplify this term propagate sizeable, temperature-dependent errors into thermalmanagement, safety and process-energy models—especially across the critical 20–80 °C operating window. In practice, the residual part of the equation of state merely fine-tunes values that the “ideal” vibrational term already defines. Therefore we developed a new ideal Helmholtz energy contribution model based on statistical mechanics and quantum mechanical ab initio data and coupled that new model with molecularbased equation of state models describing the residual part. We performed high throughput quantum mechanical calculations for approximately 21,500 species, determining the vibrational and rotational energy levels. To validate the model predictions, experimental isobaric heat capacity data from the literature was used for approx. 1,000 species. The results of that comparison are shown in Fig. 1 and 2. The model as an impressive accuracy of about 3% - being fully predictive. Figure 1: Parity plot of the ideal isobaric heat capacity experimental data (exp) from the Dortmund Data Bank and results from the physical intramolecular model from this work (model). Enlarged plot on left for clarity. The dashed line indicates 10% deviation. Data points are grouped and colored according to the chemical families (color bar). Public Version submitted on portal (29.06.2025) Page 36 of 51 Figure 2: Box plot of the AAD of the ideal isobaric heat capacity calculated for the substances grouped in the chemical families k. Results for the physical intermolecular model from this work in comparison to the reference data from the literature. Additionally, the first quartile Q1,k and third quartile Q3,k as well as 1.5 times the interquartile range IQRk are given. Multi-physics model for prediction of Mixture Diffusion Coefficients Mixture diffusion coefficients play a crucial role in several battery production process steps such as mixing, drying, and test operation. So far, there were no physical-based predictive models available that consistently describe the different diffusion coefficients in mixtures (i.e. self-diffusion and mutual diffusion coefficients – see Fig. 3). Such a method was newly developed here. It is based on a multi-physics approach coupling entropy scaling, the Chapman-Enskog theory, a molecular-based equation of state, and the Lennard-Jones model fluid. Based on that hybrid model, the different diffusion coefficients in mixtures can be predicted for complex real substance systems, see Fig. 4 and 5 for examples. Modeling diffusion coefficients of binary mixtures is crucial for battery production because it directly influences the performance, safety, and longevity of batteries. • Ion transport through the electrolyte is a key factor. The diffusion coefficient determines how fast ions migrate under a concentration gradient. Poor diffusion can lead to concentration gradients, slow charging/discharging, and reduced power output. • Designing better electrolytes requires understanding how different species interact. Modeling diffusion in binary mixtures helps to predict the behaviour of new electrolyte formulations without exhaustive experimentation – which reduces development time and cost. • Battery operation generates heat – the diffusion coefficient influences how concentration gradients respond to temperature. The modeling helps designing thermal control strategies and predict behaviour under stress or abuse conditions. Public Version submitted on portal (29.06.2025) Page 37 of 51 In summary, modeling diffusion in binary mixtures enables better material selection, safer operation, and more efficient battery design, all of which are critical for advancing battery technology and meeting industrial and consumer demands. Therefore we developed an entropy scaling model for the prediction of mixture diffusion coefficients in mixtures. With our framework all, e.g. in a binary mixture four, diffusion coefficients (namely the two self-diffusion coefficients as well as the mutual diffusion coefficients (Fickian and Maxwell-Stefan) can be predicted from the pure substances without any adjustable mixture parameter. This physical framework can be applied in the entire fluid region, i.e. it covers gases, liquids, and supercritical fluids, phase equilibria and even metastable states. The approach is based on three central ideas and concepts: • Diffusion coefficients in infinite dilution were treated as pseudo-pure components, exhibiting a monovariate scaling behavior, that can be treated by classical entropy scaling. • The pure component limits are modeled as functions of the configurational entropy. • Based on the information of the limiting cases, the concentration dependencies of the four diffusion coefficients is predicted using simple mixing rules. Figs. 4 and 5 show exemplaric results for some real substance test systems. The model predictions are in excellent agreement with the experimental data, which is impressive considering the fact that no parameters were adjusted. The model was published in Ref. [4], which also comprises an executable open source implementation. Figure 3: Schematic representation of the different diffusion coefficients in a binary mixture as a function of the mole fraction. Public Version submitted on portal (29.06.2025) Page 38 of 51 Figure 4: Self-diffusion coefficients of real substance mixture n-hexane + n-dodecane predicted by the entropy scaling model as a function of the mole fraction x2 at p = 0.1 MPa. Symbols are experimental data, and lines are model predictions. Figure 5: Fickian diffusion coefficients of real substance mixture n-hexane + n-dodecane predicted by the entropy scaling model as a function of the mole fraction x2 at p = 0.1 MPa. Symbols are experimental data, and lines are model predictions. Multiphysics Modeling of Polar Interactions using Molecular-Based Equations of State and Molecular Dynamics Simulations In battery production processes, several fluids are relevant that exhibit strong polar interactions, e.g. the electrolytes during the filling and formation. The modelling of the thermophysical properties of these polar fluids is very challenging. Polar interactions are usually modelled as a Helmholtz energy contribution model describing the effect of the polar interactions on the total Helmholtz energy. These polar contribution models are usually trained using molecular dynamics simulation data for polar model fluids. Several Helmholtz energy models for polar contributions are available today. It is unclear which of them is most suitable for modelling and simulation of battery production processes. Therefore, we developed a robust multi-physics methodology for the critical assessment of polar contribution models for battery production processes. The results were published in Refs. [1-3, 5]. The results are briefly summarized in the following. Public Version submitted on portal (29.06.2025) Page 39 of 51 Knowledge in multiphysics modeling of polar interactions using molecular-based equations of state (EoS) and molecular dynamics (MD) simulations is crucial for advancing battery production. It allows us to understand and optimize the behavior of electrolytes, which often involve complex polar solvents and ions. These simulations help reveal how ions move and interact in different solvent environments, affecting conductivity and overall battery performance. Figure 6: Characteristic curves of 2CLJD fluids with L/σ = 0.505 and different µ2/εσ3: a) and b) Zeno curve; c) and d) Amagat curve; e) and f) Boyle curve; g) and h) Charles curve. Results from MD simulations are represented by circles. Lines represent the EOS results. 50% transparent lines and symbols indicate the vaporliquid equilibrium. Thermal and mechanical stability of battery components also benefit from this modeling. Molecularbased EoS provide insights into how materials respond to temperature and pressure changes, helping Public Version submitted on portal (29.06.2025) Page 40 of 51 in the design of robust electrolytes and structural components. This ensures safe operation under varying real-world conditions. We used simple model fluids such as the Lennard-Jones plus point dipole (Stockmayer) fluid to investigate different dipole and quadrupole. The performance of the models was evaluated in a wide temperature and pressure range such that different battery production and operation conditions are covered. Fig. 6 shows exemplary results – here for Brown’s test. The model shown here yields a good but not perfect performance indicating the need for further refinement of polar interaction models for battery production processes. Design of Experiment for Transport Properties using Entropy Scaling For several battery production process steps, fluid transport properties are critical, e.g. the viscosity during the mixing, the thermal conductivity during the drying of the slurry, and diffusion coefficients during the formation. In many cases, a wide temperature range is relevant. Moreover, mostly mixtures occur. Therefore, robust predictive models are required. In a previous work of our group [15], we have developed a physically-based entropy scaling model that can be favourably coupled with molecular-based equations of state for predicting transport properties across wide state ranges and, in particular, for mixtures. The main benefit is the fact that only very few experimental data are required. In this work part, we developed a new method for the parametrization of entropy scaling transport property models for fluids for battery production processes based on minimal experimental data points. Impressively, only very few data points are required, e.g. up to five, if they are favourably chosen. The main question was: What are the ideal thermodynamic conditions for the experiments to be carried out such that the parametrization yields the optimal model. Therefore, we developed a new method here coupling design of experiments with our entropy scaling framework. This was done in collaboration with the BatCAT partners from the ITWM. Design of Experiment is the statistical backbone of evidence-based optimisation. Here we used model-based optimal experimental design (MbOED) to reduce experimental effort in parametrising an entropy scaling framework by determining the most favourable (computer) experimental state points. These are the state points that maximize the information content about the underlying process. The entropy scaling framework in conjunction with an equation of state (EoS) can be used to model transport properties i.e. shear viscosity, thermal conductivity, and diffusion coefficients. It also yields physical extrapolation results -- far outside of the pressure and temperature range considered in the parametrization comprising only 5 adjustable parameters. We tested the novel multi-physics approach using exemplary substances that are relevant for battery production, e.g. as cleaning solvents (n-butane, benzene, nitrogen and 1-octanol). The new method was applied to two different equations of state (PC-SAFT and SAFT-VR Mie); we used the MbOED to determine the most favourable datapoints for the model parametrisation. We used literature data to validate the results. Fig. 8 shows exemplary results. This gives important insights where the optimal experiments should be carried out for the parametrization of transport property models for battery production modelling. Public Version submitted on portal (29.06.2025) Page 41 of 51 Figure 7: Design of Experiment results for n-butane using the entropy scaling framework with the SAFT -VR Mie EoS (top) and the PC-SAFT EoS (bottom). Symbols represent the suggested statepoints from MbOED for different numbers of parameters used in the entropy scaling model. Multi-physics Coupling of Equations of State and Computational Fluid Dynamics In many battery production processes, macroscopic fluid flow is critical, e.g. for the mixing, coating, and filling. For the simulation of these processes, usually continuum simulation methods are applied such that the macroscopic fluid behaviour is described in a computationally efficient way. In these simulations, a large number of thermophysical properties of the fluids are required, e.g. the heat capacity, thermal conductivity, surface tension, diffusion coefficient, density, phase equilibria etc. The accuracy of these thermophysical properties is critical such that reality of the battery production process is well captured. Here, we developed a new multi-physics method that directly couples molecular thermodynamics methods for the description of the fluid properties with continuum simulations. This was demonstrated using computational fluid dynamics (CFD) as implemented in the open source tool OpenFoam. For the molecular thermodynamics models, an in-house software from previous works from our group was used. In particular, the multi-physics models described in the sections above are implemented in this comprehensive toolbox and can be directly used now within the coupling to continuum simulations. For the molecular thermodynamics tools, a molecular-based equation of state was used in combination with the ideal term (see 1st subsection) and the entropy scaling model from our previous works (using the parametrizations obtained in 4th subsection. Public Version submitted on portal (29.06.2025) Page 48 of 51 To better account for formation modelling, some modification will be provided to the models such as the link between SEI formation and porosity clogging and also possibly a more versatile SEI formation in the formation phase. The simulation will begin from the end of the manufacturing when the cell is fully assembled with completely lithiated positive electrode and completely delithiated negative electrode. The formation cycle will be simulated and the final state of the cell will be used as the fresh cell state for operation modelling. Simulation tool for Calendering in LiB o Tool Used: Pekken3D (LOYOLA) o Description: Our approach focuses on modelling for simulating the calendering of electrodes in batteries. Fundamental methodology is given above, describing the modelling procedure, generation of the virtual microstructure, material properties employed and final desired properties (diffusivity, mechanical properties and final microstructure obtained). Further details of the model about constitutive laws, given below on: Element Formulation and Integration Scheme, Definition of the Element Properties and Coupled diffusive-mechanical model. Element Formulation and Integration Scheme The numerical implementation of the lattice-particle model 52 is based on the finite element framework. The diffusion problem is modeled as a network of one-dimensional flow elements and the mechanical problem is modeled by a set of normal and shear springs describing the particle interaction (as in the discrete element method). The interaction of particles 𝑖 and 𝑗 is modeled using the following mechanical stiffness. Note we include a diffusivity term: 𝐾𝐷,𝑖𝑗=𝐷𝑖𝑗𝐴𝑖𝑗 𝐿𝑖𝑗 , 𝐾𝑛,𝑖𝑗=𝛼1𝐸𝑖𝑗𝐴𝑖𝑗 𝐿𝑖𝑗 , 𝐾𝑠,𝑖𝑗=𝛼2𝐸𝑖𝑗𝐴𝑖𝑗 𝐿𝑖𝑗 The system is solved at each time step 𝑡𝑗 using an explicit central-difference integration scheme, following the approach described by Marin-Montin et al. This method is particularly suitable for lattice-particle models due to its low computational cost and straightforward implementation. The concentration rate at time 𝑡𝑛 is approximated by: 𝑐󰇗𝑛=𝑐𝑛+1−𝑐𝑛−1 2Δ𝑡 and the concentration update is given by: 𝑐𝑛+1=𝑐𝑛−1+2Δ𝑡 𝑐󰇗𝑛 For the initial time step (𝑛=1), a forward Euler step is used: 𝑐1=𝑐0+Δ𝑡 𝑐󰇗0, with 𝑐󰇗0=𝑀𝑑−1(𝑞0−𝐾𝑑𝑐0) Here: • 𝑀𝑑 is the capacity matrix, • 𝐾𝑑 is the diffusion matrix, 52 Marin-Montin, Lattice-particle model for ion diffusion in graphite, 2021. Public Version submitted on portal (29.06.2025) Page 49 of 51 • 𝑞𝑛 is the flux vector, • 𝑐𝑛 is the concentration vector at time step 𝑛. This explicit scheme allows efficient time integration of diffusion across complex microstructures, provided that the time step Δ𝑡 satisfies the stability condition. Definition of the Element Properties The element properties (𝐴𝑏𝑖, 𝐷𝑏𝑖, 𝐸𝑏𝑖) depend on the distance between the two interacting particles 𝐿𝑏𝑖 and their respective diameters 𝑑𝑏 and 𝑑𝑖. A meniscus length is defined to model the interaction of active particles and binder: 𝑙𝑎=𝐿𝑏𝑖−𝑑𝑖 2−𝑑𝑗 2 Three cases are identified: • Particle overlapping (𝑙𝑎<0): 𝐴𝑏𝑖=𝜋ℎ2, 𝐷𝑏𝑖=𝐷am, 𝐸𝑏𝑖=𝐸am • Particle binding (0≤𝑙𝑎≤𝑙th): 𝐴𝑏𝑖=𝜋 4min(𝑑𝑏2,𝑑𝑖2) 𝐷𝑏𝑖,𝐸𝑏𝑖 defined using serial coupling • No interaction (𝑙𝑎>𝑙th): No physical interaction Coupled diffusive-mechanical model The ionic diffusion problem is governed by Ficks second law: ∂𝑐 ∂𝑡+∇⋅𝐉=0 where 𝑐 is the ionic concentration and 𝐉 is the species flux, given by: 𝐉=−𝐃(∇𝑐−Ω𝑐 𝑅𝑇∇𝜎ℎ) Here: • 𝐃 is the ionic diffusion matrix, • Ω is the partial molar volume of the ion (Na+), • 𝑅 is the universal gas constant, • 𝑇 is the absolute temperature, • 𝜎ℎ is the hydrostatic stress. Public Version submitted on portal (29.06.2025) Page 50 of 51 The total strain tensor is composed of elastic, inelastic, and diffusion-induced strains: 𝛆=𝛆el +𝛆in +𝛆𝑑 with the diffusion strain given by: 𝛆𝑑=Ω 3(𝑐−𝑐0)𝐈 The constitutive mechanical response follows a continuum damage model: 𝛔=(1−𝑑)𝐃0 el:𝛆el where 𝐃0 el is the undamaged elasticity matrix and 𝑑∈[0,1] is the damage parameter. The damage variable is used to degrade both the elastic and diffusive properties and evolves with strain: 𝑑=𝑑(𝜀,𝜀0) This coupled formulation enables the simulation of mechanical degradation driven by ion diffusion, as well as the feedback of stress on transport. It forms the basis for future finite element implementation (e.g., in Abaqus) using microstructures generated from our lattice-particle simulations. Simulation tool for Operation in LiB Multiphysics simulations for electrochemical behavior and thermal aging during operation. o Tool Used: Simcenter Amesim (IFPEN), Comsol Multiphysics (POLITO) o Description: The PoliTO 3D model of lithium-ion battery (LIB) operation in ideal conditions (no side reactions occurring) is carried out using a custom simulation tool developed in Java, which interfaces directly with COMSOL Multiphysics via its API. This code automates the setup of the model by programmatically defining the geometry, physical interfaces, material properties, meshing, and solver configuration. COMSOL then solves the governing equations (Table 5) using the finite element method (FEM). To enable interoperability across partners, the model architecture is designed to load simulation parameters from external text files. These include geometric dimensions, material properties (e.g., diffusivities, conductivities), and operational settings such as discharge current or initial state-of-charge. This approach allows other partners to provide input data generated from their own tools or experimental campaigns, without needing to directly access or modify the COMSOL modelling framework. The modularity of the Java-based COMSOL implementation allows rapid adaptation to different cell materials or operating scenarios, making the tool suitable for virtual prototyping. Simulation tool for Operation in RFB Multiphysics system modeling for fluid dynamics and electrochemical kinetics. o Tool Used: FEniCSx (SIMULA/NMBU), DL_POLY_5, DL_MESO (UKRI), MicTherm (RPTU). o Description: Public Version submitted on portal (29.06.2025) Page 51 of 51 The modeling of the operation of the RFBs is accomplished by considering the underlying partial differential equations (PDEs) governing flow of solutes and electrochemistry. The model(s) are based on the paper of Shah et al. “A dynamic performance model for redox-flow batteries involving soluble species” [1] for a Vanadium RFB (VFRB). It details the coupled multi-physics phenomena—mass transport, charge transport, fluid dynamics, and electrochemical kinetics—providing a clear example of the foundational equations used to simulate the dynamic operation of RFBs. Its validation against experimental data and mesoscopic simulations further underscores its relevance. The tools used to accomplish these simulations include the FEniCSx finite element software framework, the molecular dynamics package DL_POLY_5 and the mesoscopic simulation package DL_MESO. Simulation tool for New Multiphysics Models for Battery Production Modelling o New thermophysical property models for more robust predictions of fluid properties for battery manufacturing. o Tool Used: in-house thermodynamics software (RPTU). Maybe molecular dynamics (ms2) (RPTU), MolMod database (RPTU), LAMMPS MD simulation engine. o Description: LAMMPS, which stands for Large-scale Atomic/Molecular Massively Parallel Simulator, is a classical molecular dynamics simulation engine developed by Sandia National Laboratories. It is designed to model particles at the atomic, mesoscopic, or continuum level and is particularly known for its ability to run efficiently on parallel computing architectures. LAMMPS supports a wide range of interaction potentials and materials, including metals, polymers, and biomolecules, and can handle various types of simulations such as equilibrium and nonequilibrium dynamics under different thermodynamic ensembles. Its modular structure makes it highly extensible, allowing users to implement custom features. LAMMPS is open-source and widely used in both academic research and industrial applications. We used our in-house software package designed to streamline the development and application of molecular equations of state and classical density gradient theory (DFT) and entropy scaling. It targets researchers in thermodynamics and fluid mechanics by providing a modular, extensible framework that supports sophisticated models like PCSAFT and classical DGT. These components are integrated, benchmarks performance against existing implementations were carried out, and validations for the framework through example applications were executed. This thermodynamics tool box makes it easier to implement and couple equations of state with for example entropy scaling calculations, enabling rapid prototyping, testing, and analysis of fluid-phase and interfacial phenomena. In particular, it can be coupled to other simulation engines via an application programming interface (API) for coupling and running multi-physics simulations.