Publications

Some of the current members of the research group "Thermodynamic Modeling and Analysis of Phase Transitions" were members of a former group or of RG 1 respectively. Therefore, the corresponding publications can found on the web pages of these groups:

  • former Young Scientists' Group "Modeling of Damage Processes"
  • former Leibniz Group "Mathematical Models for Lithium-Ion Batteries"
  • Research group 1 "Partial Differential Equations"
    • Articles in Refereed Journals

      • W. Dreyer, P. Friz, P. Gajewski, C. Guhlke, M. Maurelli, Stochastic many-particle model for LFP electrodes, Continuum Mechanics and Thermodynamics, 30 (2018), pp. 593--628, DOI 10.1007/s00161-018-0629-7 .
        Abstract
        In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltagecharge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.

      • M. Landstorfer, On the dissociation degree of ionic solutions considering solvation effects, Electrochemistry Communications, 92 (2018), pp. 56--59, DOI 10.20347/WIAS.PREPRINT.2443 .
        Abstract
        In this work the impact of solvation effects on the dissociation degree of strong electrolytes and salts is discussed. The investigation is based on a thermodynamic model which is capable to predict qualitatively and quantitatively the double layer capacity of various electrolytes. A remarkable relationship between capacity maxima, partial molar volume of ions in solution, and solvation numbers, provides an experimental access to determine the number of solvent molecules bound to a specific ion in solution. This shows that the Stern layer is actually a saturated solution of 1 mol L-1 solvated ions, and we point out some fundamental similarities of this state to a saturated bulk solution. Our finding challenges the assumption of complete dissociation, even for moderate electrolyte concentrations, whereby we introduce an undissociated ion-pair in solution. We re-derive the equilibrium conditions for a two-step dissociation reaction, including solvation effects, which leads to a new relation to determine the dissociation degree. A comparison to Ostwald's dilution law clearly shows the shortcomings when solvation effects are neglected and we emphasize that complete dissociation is questionable beyond 0.5 mol L-1 for aqueous, mono-valent electrolytes.

      • T. Ahnert, A. Münch, B. Niethammer, B. Wagner, Stability of concentrated suspensions under Couette and Poiseuille flow, Journal of Engineering Mathematics, (2018), published online on 21.02.2018, DOI 10.1007/s10665-018-9954-x .
        Abstract
        The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the two-phase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed.

      • T. Ahnert, A. Münch, B. Wagner, Models for the two-phase flow of concentrated suspensions, European Journal of Applied Mathematics, (2018), published online on 04.06.2018, DOI 10.1017/S095679251800030X .
        Abstract
        A new two-phase model is derived that make use of a constitutive law combining non-Brownian suspension with granular rheology, that was recently proposed by Boyer et al. [PRL, 107(18),188301 (2011)]. It is shown that for the simple channel flow geometry, the stress model naturally exhibits a Bingham type flow property with an unyielded finite-size zone in the center of the channel. As the volume fraction of the solid phase is increased, the various transitions in the flow fields are discussed using phase space methods for a boundary value problem, that is derived from the full model. The predictions of this analysis is then compared to the direct finite-element numerical solutions of the full model.

      • G. Kitavtsev, A. Münch, B. Wagner, Thin film models for an active gel, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, published online on 19.12.2018, DOI 10.1098/rspa.2017.0828 .

      • W. Dreyer, C. Guhlke, R. Müller, Bulk-surface electro-thermodynamics and applications to electrochemistry, Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 20 (2018), pp. 939/1--939/44, DOI 10.3390/e20120939 .
        Abstract
        We propose a modeling framework for magnetizable, polarizable, elastic, viscous, heat conducting, reactive mixtures in contact with interfaces. To this end we first introduce bulk and surface balance equations that contain several constitutive quantities. For further modeling the constitutive quantities, we formulate constitutive principles. They are based on an axiomatic introduction of the entropy principle and the postulation of Galilean symmetry. We apply the proposed formalism to derive constitutive relations in a rather abstract setting. For illustration of the developed procedure, we state an explicit isothermal material model for liquid electrolyte metal electrode interfaces in terms of free energy densities in the bulk and on the surface. Finally we give a survey of recent advancements in the understanding of electrochemical interfaces that were based on this model.

      Preprints, Reports, Technical Reports

      • M. Landstorfer, A discussion of the reaction rate and the cell voltage of an intercalation electrode during discharge, Preprint no. 2563, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2563 .
        Abstract, PDF (2144 kByte)
        In this work we discuss the modeling procedure and validation of a non-porous intercalation half-cell during galvanostatic discharge. The modeling is based on continuum thermodynamics with non-equilibrium processes in the active intercalation particle, the electrolyte, and the common interface where the intercalation reaction occurs. This yields balance equations for the transport of charge and intercalated lithium in the intercalation compound, a surface reaction rate at the interface, and transport equations in the electrolyte for the concentration of lithium ions and the electrostatic potential. An expression for the measured cell voltage is then rigorously derived for a half cell with metallic lithium as counter electrode. The model is then in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients of the active phase and the electrolyte, conductivity of both phases, and the exchange current density, with numerical solutions of the underlying PDE system. The current density as well as all non-equilibrium parameters are scaled with respect to the 1-C current density of the intercalation electrode and the C-rate of discharge. Further we derive an expression for the capacity of the intercalation cell, which allows us to compute numerically the cell voltage as function of the capacity and the C-rate. Within a hierarchy of approximations of the non-equilibrium processes we provide computations of the cell voltage for various values of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies and (surface) thermodynamic consistency.

      • M.G. Hennessy, A. Münch, B. Wagner, Surface induced phase separation of a swelling hydrogel, Preprint no. 2562, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2562 .
        Abstract, PDF (697 kByte)
        We present a formulation of the free boundary problem for a hydrogel that accounts for the interfacial free energy and finite strain due to the large deformation of the polymer network during solvent transport across the free boundary. For the geometry of an initially dry layer fixed at a rigid substrate, our model predicts a phase transition when a critical value of the solvent concentration has been reached near the free boundary. A one-dimensional case study shows that depending on the flux rate at the free boundary an initial saturation front is followed by spinodal decomposition of the hydrogel and the formation of an interfacial front that moves through the layer. Moreover, increasing the shear modulus of the elastic network delays or even suppresses phase separation.

      • O. Klein, D. Davino, C. Visone, On forward and inverse uncertainty quantification for models involving hysteresis operators, Preprint no. 2561, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2561 .
        Abstract, PDF (1190 kByte)
        Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied.

      • M. Landstorfer, A Redlich--Kister type free energy model for Li-intercalation compounds with variable lattice occupation numbers, Preprint no. 2560, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2560 .
        Abstract, PDF (1667 kByte)
        One of the central quantities of a lithium ion intercalation compound is the open circuit potential, the voltage a battery material delivers in thermodynamic equilibrium. This voltage is related to the chemical potential of lithium in the insertion material and in general a non-linear function of the mole fraction of intercalated lithium. Experimental data shows further that it is specific for various materials. The open circuit voltage is a central ingredient for mathematical models of whole battery cells, which are used to investigate and simulate the charge and discharge behavior and to interpret experimental data on non-equilibrium processes. However, since no overall predictive theoretical method presently exists for the open circuit voltage, it is commonly fitted to experimental data. Simple polynomial fitting approaches are widely used, but they lack any thermodynamic interpretation. More recently systematically and thermodynamically motivated approaches are used to model the open circuit potential. We provide here an explicit free energy density which accounts for variable occupation numbers of Li on the intercalation lattice as well as Redlich--Kister-type enthalpy contributions. The derived chemical potential is validated by experimental data of Liy(Ni1/3Mn1/3Co1/3)O2 and we show that only two parameters are sufficient to obtain an overall agreement of the non-linear open circuit potential within the experimental error.

      • P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Preprint no. 2549, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2549 .
        Abstract, PDF (2938 kByte)
        In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization.

      • D. Peschka, M. Thomas, T. Ahnert, A. Münch, B. Wagner, Gradient structures for flows of concentrated suspensions, Preprint no. 2543, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2543 .
        Abstract, PDF (6456 kByte)
        In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth two-homogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows

      • W. Dreyer, C. Guhlke, R. Müller, The impact of solvation and dissociation on the transport parameters of liquid electrolytes: Continuum modeling and numerical study, Preprint no. 2539, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2539 .
        Abstract, PDF (1472 kByte)
        Electro-thermodynamics provides a consistent framework to derive continuum models for electrochemical systems. For the application to a specific experimental system, the general model must be equipped with two additional ingredients: a free energy model to calculate the chemical potentials and a kinetic model for the kinetic coefficients. Suitable free energy models for liquid electrolytes incorporating ion-solvent interaction, finite ion sizes and solvation already exist and have been validated against experimental measurements. In this work, we focus on the modeling of the mobility coefficients based on Maxwell--Stefan setting and incorporate them into the general electro-thermodynamic framework. Moreover, we discuss the impact of model parameter on conductivity, transference numbers and salt diffusion coefficient. In particular, the focus is set on the solvation of ions and incomplete dissociation of a non-dilute electrolyte.

      • D. Peschka, S. Haefner, K. Jacobs, A. Münch, B. Wagner, Signatures of slip in dewetting polymer films, Preprint no. 2538, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2538 .
        Abstract, PDF (7811 kByte)
        Thin liquid polymer films on hydrophobic substrates are susceptable to rupture and formation of holes, which in turn initiate a complex dewetting process that eventually evolves into characteristic stationary droplet patterns. Experimental and theoretical studies suggest that the specific type of droplet pattern largely depends on the nature of the polymer-substrate boundary condition. To follow the morphological evolution numerically over long time scales and for the multiple length scales involved has so far been a major challenge. In this study a highly adaptive finite-element based numerical scheme is presented that allows for large-scale simulations to follow the evolution of the dewetting process deep into the nonlinear regime of the model equations, capturing the complex dynamics including shedding of droplets. In addition, the numerical results predict the previouly unknown shedding of satellite droplets during the destabilisation of liquid ridges, that form during the late stages of the dewetting process. While the formation of satellite droplets is well-known in the context of elongating fluid filaments and jets, we show here that for dewetting liquid ridges this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip.

      • M. Landstorfer, The dielectric constant of liquid electrolytes obtained from periodic homogenization theory, Preprint no. 2531, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2531 .
        Abstract, PDF (6771 kByte)
        The dielectric constant of an electrolytic solution is known to decrease with increasing salt concentration. This effect, frequently called dielectric decrement, is experimentally found for many salts and solvents and shows an almost linear decrease up to a certain salt concentration. However, the actual origin of this concentration dependence is yet unclear, and many different theoretical approaches investigate this effect. Here I present an investigation based on microscopic Maxwell equations and periodic homogenization theory. The microscopic perception of anions and cations forming a pseudo lattice in the liquid solution is exploited by multi-scale asymptotic expansions, where the inverse Avogadro number arises as small scaling parameter. This leads to a homogenized Poisson equation on the continuum scale with an effective or homogenized dielectric constant that accounts for microscopic field effects in the pseudo lattice. Incomplete dissociation is further considered at higher salt concentrations due to solvation effects. The numerically computed homogenized dielectric constant is then compared to experimental data of NaCl and shows a remarkable qualitative and quantitative agreement in the concentration range of (0 - 5)mol L.

      • J. Fuhrmann, C. Guhlke, B. Matejczyk, R. Müller, Transport of solvated ions in nanopores: Asymptotic models and numerical study, Preprint no. 2526, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2526 .
        Abstract, PDF (1233 kByte)
        Improved Poisson--Nernst--Planck systems taking into account finite ion size and solvation effects provide a more accurate model of electric double layers compared to the classical setting. We introduce and discuss several variants of such improved models. %Based on spatially fully resolved numerical models We study the effect of improved modeling in large aspect ratio nanopores. Moreover, we derive approximate asymptotic models for the improved Poisson--Nernst--Planck systems which can be reduced to one-dimensional systems. In a numerical study, we compare simulation results obtained from solution of the asymptotic 1D-models with those obtained by discretization of the full resolution models.

      • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Models and numerical methods for electrolyte flows, Preprint no. 2525, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2525 .
        Abstract, PDF (1807 kByte)
        The most common mathematical models for electrolyte flows are based on the dilute solution assumption, leading to a coupled system of the Nernst--Planck--Poisson drift-diffusion equations for ion transport and the Stokes resp. Navier--Stokes equations for fluid flow. This contribution discusses historical and recent model developments beyond the dilute solution assumption and focuses on the effects of finite ion sizes and solvation. A novel numerical solution approach is presented and verified here which aims at preserving on the discrete level consistency with basic thermodynamic principles and structural properties like independence of flow velocities from gradient contributions to external forces.

      Talks, Poster

      • P.-É. Druet, Analysis of mass transfer, Navier--Stokes equations for multicomponent fluids subject to a volume constraint, Berliner Oberseminar ``Nichtlineare partielle Differentialgleichungen'' (Langenbach-Seminar), WIAS, Berlin, November 28, 2018.

      • P.-É. Druet, Introduction to the DFG-Project: Analysis of improved Nernst-Planck-Poisson models for incompressible electrolytes, WIAS Days 2018, February 22 - 23, 2018, Berlin, February 23, 2018.

      • M. Landstorfer, Continuum thermodynamic modelling of electrolytes, BMBF Kickoff Meeting LuCaMag, Bonn, November 7, 2018.

      • M. Landstorfer, Homogenization methods for electrochemical systems, DFG Workshop Numerical Optimization of the PEM Fuel Cell Bipolar Plate, Universität Ulm, March 20, 2018.

      • M. Landstorfer, Modeling and simulation of porous battery electrodes with multi-scale homogenization techniques, 69th Annual Meeting of the International Society of Electrochmistry (ISE), September 2 - 7, 2018, Bologna, Italy, September 6, 2018.

      • M. Landstorfer, Modellbasierte Abschätzung der Lebensdauer von gealterten Li-Batterien für die 2nd-Life Anwendung als stationärer Stromspeicher, BMBF-Statusseminar zur Förderrichtlinie Mathematik, Bonn, November 19 - 20, 2018.

      • M. Landstorfer, Modellbasierte Abschätzung der Lebensdauer von gealterten Li-Batterien für die 2nd-Life Anwendung als stationärer Stromspeicher, BMBF-Statusseminar zur Förderrichtlinie Mathematik, November 19 - 20, 2018, Bonn, November 20, 2018.

      • M. Landstorfer, Modellierung und Upscaling, WIAS (AG 4), BMBF Workshop zu MaLLi2, November 12 - 13, 2018, Ellwangen, November 12, 2018.

      • M. Landstorfer, Modelling and simulation of porous battery electrodes with multi-scale homogenisation techniques, 6th European Conference on Computational Mechanics, 7th European Conference on Computational Fluid Dynamics (ECCM-ECFD 2018), June 11 - 15, 2018, Glasgow, UK, June 14, 2018.

      • M. Landstorfer, Modelling and simulation of porous battery electrodes with multi-scale homogenisation techniques, Solid State Electrochemistry Symposium, November 12 - 14, 2018, Helmut-Schmidt-Universität, Hamburg, November 13, 2018.

      • M. Landstorfer, Modelling and simulation of porous electrodes with multi-scale homogenization technique, ModVal 2018, 15th Symposium on Modeling and Experimental Validation of Electrochemical Energy Devices, Aarau, Switzerland, April 12 - 13, 2018.

      • M. Landstorfer, Modelling battery electrodes with homogenization techniques, Kick-Off-Meeting zu BMBF-Projekt MALLi^2, Universität Ulm, March 21, 2018.

      • M. Landstorfer, Thermodynamic modeling of electrolytes and their boundary conditions to electrodes, AMaSiS 2018: Applied Mathematics and Simulation for Semiconductors, October 8 - 10, 2018, WIAS, Berlin, October 9, 2018.

      • R. Müller, J. Fuhrmann, C. Guhlke, B. Matejczyk , Dimension reduction of improved Nernst-Planck models for charged nanopores, Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view (ABPDE III), France, August 28 - 31, 2018.

      • R. Müller, Dynamics of electrochemical interfaces, Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view (ABPDE III), August 28 - 31, 2018, Universität Lille I, France, August 30, 2018.

      • R. Müller, Modeling and simulation of electrolyte transport in nanopores, Center for Computational Engineering, RWTH Aachen, May 8, 2018.

      • M. Thomas, D. Peschka, B. Wagner, V. Mehrmann, M. Rosenau, Modeling and analysis of suspension flows, MATH+ Center Days 2018, October 31 - November 2, 2018, Zuse-Institut Berlin (ZIB), Berlin, October 31, 2018.

      • B. Wagner, Modeling microstructures for light harvesting surfaces, ECMI 2018, 20th European Conference on Mathematics for Industry, June 18 - 22, 2018, Budapest, Hungary, June 21, 2018.

      • B. Wagner, Modeling microstructures for light harvesting surfaces, European Women in Mathematics (EWM) General Meeting 2018, Minisymposium ``Mathematics in Industry'', Karl-Franzens-Universität Graz, Austria, September 7, 2018.

      • B. Wagner, Modelling, aymptotic analysis and numerical simulation of thin-film dynamics on solid and liquid substrates, Workshop ``Dynamic Wetting of Flexible, Adaptive and Switchable Substrates'', May 16 - 18, 2018, Universität Münster, Center for Nonlinear Sciences, May 17, 2018.

      • B. Wagner, Multi-scale problems of material design in sustainable energies, SIAM Conference on Nonlinear Waves and Coherent Structures, June 11 - 14, 2018, Anaheim, USA, June 13, 2018.

      • B. Wagner, Multiple scales in thin liquid films, UCLA Guest Lecture, University of California, Department of Mathematics, Los Angeles, USA, January 25, 2018.

      • B. Wagner, Multiscale modelling of suspensions and how it fits into the UL context, University of Limerick, Department Mathematics & Statistics, Ireland, June 7, 2018.

      • B. Wagner, Signatures of slip in thin film flows, SIAM Conference on Nonlinear Waves and Coherent Structures, June 11 - 14, 2018, Anaheim, USA, June 13, 2018.

      • B. Wagner, Thin film models for an active gel, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics, March 19 - 23, 2018, Technische Universität München, March 22, 2018.

      • B. Wagner, Yield stress in concentrated suspensions, Mathematical Nanosystems Workshop, January 17 - 18, 2018, CNSI at UCLA, Los Angeles, USA, January 18, 2018.

      • J. Fuhrmann, A. Linke, Ch. Merdon, C. Guhlke, R. Müller, Models and numerical methods for electroosmotic flow including finite ion size effects, Workshop on Ion Exchange Membranes for Energy Applications (EMEA2018), Bad Zwischenahn, June 26 - 28, 2018.

      • J. Fuhrmann, A. Linke, Ch. Merdon, C. Guhlke, R. Müller, Models and numerical methods for electroosmotic flow including finite ion size effects, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), Berlin, October 8 - 10, 2018.

      • O. Klein, On uncertainty quantification for models involving hysteresis operators, MURPHYS-HSFS-2018: Interdisciplinary Workshop on Multiple Scale Systems, Systems with Hysteresis and Trends in Dynamical Systems, May 28 - June 1, 2018, Centre de Recerca Matemàtica (CRM), Barcelona, Spain, May 31, 2018.

      External Preprints

      • J. Fuhrmann, C. Guhlke, Ch. Mehrdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Preprint no. arXiv:1901.06941 pp. 15, Cornell University, 2019.