To gain deeper insights into battery production and improvement potentials, various simulation techniques can be employed. Here, the focus is on both the manufacturing process and the operational behavior of batteries. Most continuum simulation techniques require the specification of several thermophysical properties—such as viscosity, thermal conductivity, phase equilibrium, heat capacity, speed of sound, and density—as functions of temperature, pressure, and composition. Mostly, these properties are approximated using models based on strongly simplifying assumptions.
Our research group is developing a software package—MicTherm—to compute thermophysical properties using molecular thermodynamic models. Importantly, these molecular thermodynamics models require relatively few experimental data for the model parametrization and can be extrapolated to extreme conditions. Furthermore, these models are particularly effective in calculating mixture properties based solely on pure component parameters. Molecular thermodynamics models are based on molecular-based equations of state (EOS), such as PC-SAFT and SAFT-VR Mie, which originate from fundamental Helmholtz energy formulations. These EOS treat different molecular interactions and molecular architecture features as separate contributions, enabling accurate descriptions of static properties. We have tested the extrapolation capabilities of different molecular-based EOS models and identified some artifacts in models, but were also able to identify a model with excellent extrapolation behavior throughout [1], namely the SAFT-VR Mie EOS.
To extend the capability of these models for describing interfacial and transport properties, we incorporate auxiliary methods such as density gradient theory and entropy scaling, respectively. Recently, we developed an entropy scaling framework that can be coupled with practically any molecular-based EOS [2] and has excellent predictive capabilities. Very recently, we extended entropy scaling, for the first time, for modeling diffusion coefficients in mixtures [3], which is of central importance in batteries. This entropy scaling model is able to describe different diffusion coefficients, i.e. self-diffusion coefficients and mutual diffusion coefficients, in a thermodynamically consentient way.
In previous work, MicTherm was integrated into different simulation engines for modeling thermophysical properties of fluids in continuum models. One representative collaboration demonstrated the benefits of this coupling in elastohydrodynamic lubrication (EHL) simulations for modeling tribological systems [3]. Most recently, we have successfully coupled MicTherm with computational fluid dynamics (CFD) simulations using OpenFOAM. Therefore, the molecular thermodynamics models were integrated as an external thermophysical property library. Compared to conventional CFD approaches regarding the modeling of the thermophysical fluid properties—such as using interpolations from experimental data or assuming constant properties and ignoring their temperature and pressure dependency—our method enables the integration of robust molecular thermodynamics models in CFD simulations. This coupling bridges three length scales, namely atomistic quantum properties of individual molecules, the ensemble level of a multitude of molecules, and the continuum fluid flow dynamics.
In the first stage of our current work, we validated the coupled simulation approach by comparing it to standard interpolation methods based on literature data. During coupled simulations, the substance properties are calculated using the molecular thermodynamics models for each grid cell in the CFD simulation at each iteration step. The results showed good agreement with conventional methods, confirming its reliability and correctness of the implementation. However, this validation only demonstrated parity with existing approaches, not the full potential of our method. Our next steps involve simulating more complex systems, such as metastable phases, for which experimental data are rarely or not at all available. We will also focus on improving the computational performance and scalability. In future work, we will transfer the coupling technique for integrating the molecular thermodynamics models in other continuum simulation models and engines.
Xueqi Zhang and Simon Stephan
University of Kaiserslautern-Landau (RPTU)
March 2025
[1] S. Schmitt, H. Hasse, S. Stephan: Measurements and equation of state modeling of the density of five 1-alcohols (C6-C10) at pressures up to 120 Mpa, J. Chem. Eng. Data 69-9 (2024) 2967-2983.
[2] S. Schmitt, H. Hasse, S. Stephan: Entropy scaling framework for transport properties using molecular-based equations of state, J. Mol. Liq. 395 (2024) 123811.
[3] S. Schmitt, H. Hasse, S. Stephan: Entropy scaling for diffusion coefficients in fluid mixtures, Nat. Commun. 16 (2025) 2611.
[4] P. Wingertszahn, S. Schmitt, S. Thielen, M. Oehler, B. Magyar, O. Koch, H. Hasse, S. Stephan: Measurement, modelling, and application of lubricant properties at extreme pressures, Tribologie und Schmierungstechnik 70 (2023) 5-12.