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

      • A. Shatla, M. Landstorfer, H. Baltruschat, On the differential capacitance and potential of zero charge of Au (111) in some aprotic solvents, , published online on 16.04.2021, DOI 10.1002/celc.202100316 .

      • M. Landstorfer, B. Prifling, V. Schmidt, Mesh generation for periodic 3D microstructure models and computation of effective properties, Journal of Computational Physics, 431 (2021), pp. 110071/1--110071/20 (published online on 23.12.2020), DOI https://doi.org/10.1016/j.jcp.2020.110071 .
        Abstract
        Understanding and optimizing effective properties of porous functional materials, such as permeability or conductivity, is one of the main goals of materials science research with numerous applications. For this purpose, understanding the underlying 3D microstructure is crucial since it is well known that the materials? morphology has an significant impact on their effective properties. Because tomographic imaging is expensive in time and costs, stochastic microstructure modeling is a valuable tool for virtual materials testing, where a large number of realistic 3D microstructures can be generated and used as geometry input for spatially-resolved numerical simulations. Since the vast majority of numerical simulations is based on solving differential equations, it is essential to have fast and robust methods for generating high-quality volume meshes for the geometrically complex microstructure domains. The present paper introduces a novel method for generating volume-meshes with periodic boundary conditions based on an analytical representation of the 3D microstructure using spherical harmonics. Due to its generality, the present method is applicable to many scientific areas. In particular, we present some numerical examples with applications to battery research by making use of an already existing stochastic 3D microstructure model that has been calibrated to eight differently compacted cathodes.

      • M.G. Hennessy, A. Münch, B. Wagner, Phase separation in swelling and deswelling hydrogels with a free boundary, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 101 (2020), pp. 032501/1--032501/14, DOI 10.1103/PhysRevE.101.032501 .
        Abstract
        We present a full kinetic model of a hydrogel that undergoes phase separation during swelling and deswelling. The model accounts for the interfacial energy of coexisting phases, finite strain of the polymer network, andsolvent transport across free boundaries. For the geometry of an initially dry layer bonded to a rigid substrate,the model predicts that forcing solvent into the gel at a fixed rate can induce a volume phase transition, whichgives rise to coexisting phases with different degrees of swelling, in systems where this cannot occur in the free-swelling case. While a nonzero shear modulus assists in the propagation of the transition front separating thesephases in the driven-swelling case, increasing it beyond a critical threshold suppresses its formation. Quenchinga swollen hydrogel induces spinodal decomposition, which produces several highly localized, highly swollenphases which coarsen and are then ejected from free boundary. The wealth of dynamic scenarios of this systemis discussed using phase-plane analysis and numerical solutions in a one-dimensional setting.

      • J. Fuhrmann, M. Landstorfer, R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance, Journal of The Electrochemical Society, 167 (2020), pp. 106512/1--106512/15, DOI 10.1149/1945-7111/ab9cca .
        Abstract
        We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter $d^facet to 0$ we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit $L^Debye << d^facet$ , an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.

      • O. Klein, D. Davino, C. Visone, On forward and inverse uncertainty quantification for models involving hysteresis operators, Mathematical Modelling of Natural Phenomena, 15 (2020), pp. 53/1--53/19, DOI https://doi.org/10.1051/mmnp/2020009 .
        Abstract
        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.

      Preprints, Reports, Technical Reports

      • R. Shiri, L. Schmeller, R. Seemann, D. Peschka, B. Wagner, On the spinodal dewetting of thin liquid bilayers, Preprint no. 2861, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2861 .
        Abstract, PDF (12 MByte)
        We investigate the spinodal dewetting of a thin liquid polystyrene (PS) film on a liquid polymethylmethacrylate (PMMA) subtrate. Following the evolution of the corrugations of the PS film via in situ measurements by atomic force microscopy (AFM) and those of the PS-PMMA interface via ex situ imaging, we provide a direct and detailed comparison of the experimentally determined spinodal wavelengths with the predictions from linear stability analysis of a thin-film continuum model for the bilayer system. The impact of rough interfaces and fluctuations is studied theoretically by investigating the impact of different choices of initial data on the unstable wavelength and on the rupture time. The key factor is the mode selection by initial data perturbed with correlated colored noise in the linearly unstable regime, which becomes relevant only for liquid bilayers to such an extent. By numerically solving the mathematical model, we further address the impact of nonlinear effects on rupture times and on the morphological evolution of the interfaces in comparison with experimental results.

      • A.K. Barua, R. Chew, L. Shuwang, J. Lowengrub, A. Münch, B. Wagner, Sharp-interface problem of the Ohta--Kawasaki model for symmetric diblock copolymers, Preprint no. 2855, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2855 .
        Abstract, PDF (1087 kByte)
        The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.

      • A.H. Erhardt, S. Solem, Analysis and simulation of a modified cardiac cell model gives accurate predictions of the dynamics of the original one, Preprint no. 2848, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2848 .
        Abstract, PDF (4937 kByte)
        The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model - like early afterdepolarisations (EADs), which can be precursors to cardiac death - predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to wave break-up leading to cardiac death at the tissue level.

      • G. Arumgam, A.K. Dond, A.H. Erhardt, Global existence of solutions to Keller--Segel chemotaxis system with heterogeneous logistic source and nonlinear secretion, Preprint no. 2847, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2847 .
        Abstract, PDF (219 kByte)
        We study the following Keller-Segel chemotaxis system with logistic source and nonlinear secretion. For this system, we prove the global existence of solutions under suitable assumptions.

      • G.L. Celora, M.G. Hennessy, A. Münch, B. Wagner, S.L. Waters, A kinetic model of a polyelectrolyte gel undergoing phase separation, Preprint no. 2802, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2802 .
        Abstract, PDF (2799 kByte)
        In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multi-component transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.

      • M.G. Hennessy, G.L. Celora, A. Münch, S.L. Waters, B. Wagner, Asymptotic study of the electric double layer at the interface of a polyelectrolyte gel and solvent bath, Preprint no. 2751, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2751 .
        Abstract, PDF (2265 kByte)
        An asymptotic framework is developed to study electric double layers that form at the inter-face between a solvent bath and a polyelectrolyte gel that can undergo phase separation. The kinetic model for the gel accounts for the finite strain of polyelectrolyte chains, free energy ofinternal interfaces, and Stefan?Maxwell diffusion. By assuming that the thickness of the doublelayer is small compared to the typical size of the gel, matched asymptotic expansions are used toderive electroneutral models with consistent jump conditions across the gel-bath interface in two-dimensional plane-strain as well as fully three-dimensional settings. The asymptotic frameworkis then applied to cylindrical gels that undergo volume phase transitions. The analysis indicatesthat Maxwell stresses are responsible for generating large compressive hoop stresses in the double layer of the gel when it is in the collapsed state, potentially leading to localised mechanicalinstabilities that cannot occur when the gel is in the swollen state. When the energy cost of in-ternal interfaces is sufficiently weak, a sharp transition between electrically neutral and chargedregions of the gel can occur. This transition truncates the double layer and causes it to have finitethickness. Moreover, phase separation within the double layer can occur. Both of these featuresare suppressed if the energy cost of internal interfaces is sufficiently high. Thus, interfacial freeenergy plays a critical role in controlling the structure of the double layer in the gel.

      • G.L. Celora, M.G. Hennessy, A. Münch, S.L. Waters, B. Wagner, Spinodal decomposition and collapse of a polyelectrolyte gel, Preprint no. 2731, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2731 .
        Abstract, PDF (2259 kByte)
        The collapse of a polyelectrolyte gel in a (monovalent) salt solution is analysed using a new model that includes interfacial gradient energy to account for phase separation in the gel, finite elasticity and multicomponent transport. We carry out a linear stability analysis to determine the stable and unstable spatially homogeneous equilibrium states and how they phase separate into localized regions that eventually coarsen to a new stable state. We then investigate the problem of a collapsing gel as a response to increasing the salt concentration in the bath. A phase space analysis reveals that the collapse is obtained by a front moving through the gel that eventually ends in a new stable equilibrium. For some parameter ranges, these two routes to gel shrinking occur together.

      Talks, Poster

      • A. Erhardt, Online: ergänzen talk Juni, June 1, 2021.

      • M. Landstorfer, Modeling of concentration and electric field dependent susceptibilities in electrolytes (online talk), AA2 - Materials, Light, Devices, Freie Universität Berlin, Humboldt-Universität zu Berlin, WIAS Berlin, February 26, 2021.

      • R. Müller, Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance (online talk), 14th Virtual Congress WCCM & ECCOMAS 2020, January 11 - 15, 2021, January 11, 2021.

      • R. Müller, Online: Concentration. and field dependent suspeptibiliy of electrolytes, MODVAL 17, EPFL Valais Walis, Online, April 20 - July 22, 2021, Switzerland, April 22, 2021.

      • R. Müller, Online: Modeling electrode-electrolyte interfaces: The differential capacitance of polycrystalline surfaces and non-constant susceptibility, ESEE (12th European Symposium on Electrochemical Engineering, June 16, 2021.

      • R. Müller, Online: Modeling of ion transport by a Maxwell-Stefan approach and numerical results, 8ECM (European Congress of Mathematics, Vortrag im Minisymposium ``Multicomponent diffusion in porous media'', June 22, 2021.

      • B. Wagner, Online: BUF Special Issue IJAY SPP2171, May 3, 2021.

      • P.-É. Druet, The free energy of incompressible fluid mixtures: An asymptotic study (online talk), TES-Seminar on Energy-based Mathematical Methods and Thermodynamics, Technische Universität Berlin WIAS Berlin, January 21, 2021.

      • B. Wagner, Pattern formation in dewetting films (online talk), Workshop ``Mathematical Modeling and Scientific Computing: Focus on Complex Processes and Systems'' (Online Event), November 19 - 20, 2020, Technische Universität München, November 19, 2020.

      • B. Wagner, Phase-field models of the lithiation/delithiation cycle of thin-film electrodes (online talk), Oxford Battery Modelling Symposium (Online Event), March 16 - 17, 2020, University of Oxford, UK, March 16, 2020.

      • J. Fuhrmann, C. Guhlke, M. Landstorfer, A. Linke, Ch. Merdon, R. Müller, Quality preserving numerical methods for electroosmotic flow, Einstein Semester on Energy-based Mathematical Methods for Reactive Multiphase Flows: Kick-off Conference (Online Event), October 26 - 30, 2020.