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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

      • 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), 53, 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.

      • M. Landstorfer, A discussion of the cell voltage during discharge of an intercalation electrode for various C-rates based on non-equilibrium thermodynamics and numerical simulations, Journal of The Electrochemical Society, 167 (2020), pp. 013518/1--013518/19 (published online on 19.11.2019), DOI 10.1149/2.0182001JES .

      • M. Landstorfer, Mathematische Modellierung elektrokatalytischer Zellen, Mitteilungen der Deutschen Mathematiker-Vereinigung, 26 (2019), pp. 161--163.

      • D. Peschka, S. Haefner, L. Marquant, K. Jacobs, A. Münch, B. Wagner, Signatures of slip in dewetting polymer films, Proceedings of the National Academy of Sciences of the United States of America, 116 (2019), pp. 9275--9284, DOI 10.1073/pnas.1820487116 .

      • P. Vágner, C. Guhlke, V. Miloš, R. Müller, J. Fuhrmann, A continuum model for yttria-stabilised zirconia incorporating triple phase boundary, lattice structure and immobile oxide ions, Journal of Solid State Electrochemistry, 23 (2019), pp. 2907--2926, DOI 10.1007/s10008-019-04356-9 .
        Abstract
        A continuum model for yttria-stabilised zirconia (YSZ) in the framework of non-equilibrium thermodynamics is developed. Particular attention is given to i) modeling of the YSZ-metal-gas triple phase boundary, ii) incorporation of the lattice structure and immobile oxide ions within the free energy model and iii) surface reactions. A finite volume discretization method based on modified Scharfetter-Gummel fluxes is derived in order to perform numerical simulations.
        The model is used to study the impact of yttria and immobile oxide ions on the structure of the charged boundary layer and the double layer capacitance. Cyclic voltammograms of an air-half cell are simulated to study the effect of parameter variations on surface reactions, adsorption and anion diffusion.

      • H. Abels, J. Daube, Ch. Kraus, Pressure reconstruction for weak solutions of the two-phase incompressible Navier--Stokes equations with surface tension, Asymptotic Analysis, 113 (2019), pp. 51--86, DOI 10.3233/ASY-181507 .
        Abstract
        For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation.

      • P. Nestler, N. Schlömer, O. Klein, J. Sprekels, F. Tröltzsch, Optimal control of semiconductor melts by traveling magnetic fields, Vietnam Journal of Mathematics, 47 (2019), pp. 793--812, DOI 10.1007/s10013-019-00355-5 .
        Abstract
        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.

      • W. Dreyer, C. Guhlke, R. Müller, The impact of solvation and dissociation on the transport parameters of liquid electrolytes: Continuum modeling and numerical study, European Physical Journal Special Topics, 227 (2019), pp. 2515--2538, DOI 10.1140/epjst/e2019-800133-2 .
        Abstract
        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.

      • J. Fuhrmann, C. Guhlke, Ch. Merdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Electrochimica Acta, 317 (2019), pp. 778--785, DOI 10.1016/j.electacta.2019.05.051 .

      Contributions to Collected Editions

      • D. Peschka, M. Thomas, T. Ahnert, A. Münch, B. Wagner, Gradient structures for flows of concentrated suspensions, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 295--318, DOI 10.1007/978-3-030-33116-0 .
        Abstract
        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.

      • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Models and numerical methods for electrolyte flows, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 183--209.

      • J. Fuhrmann, C. Guhlke, A. Linke, Ch. Merdon, R. Müller, Voronoi finite volumes and pressure robust finite elements for electrolyte models with finite ion sizes, in: Numerical Geometry, Grid Generation and Scientific Computing. Proceedings of the 9th International Conference, NUMGRID 2018 / Voronoi 150, V.A. Garanzha, L. Kamenski, H. Si, eds., 131 of Lecture Notes in Computational Science and Engineering, Springer Nature Switzerland AG, Cham, 2019, pp. 73--83, DOI 10.1007/978-3-030-23436-2 .

      • O. Klein, On uncertainty quantification for models involving hysteresis operators, in: Extended Abstracts Spring 2018 -- Singularly Perturbed Systems, Multiscale Phenomena and Hysteresis: Theory and Applications, A. Korobeinikov, M. Caubergh, T. Lázaro, J. Sardanyés, eds., 11 of Research Perspectives CRM Barcelona, Birkhäuser, Cham, 2019, pp. 271--275, DOI 10.1007/978-3-030-25261-8 .

      Preprints, Reports, Technical Reports

      • M.G. Hennessy, G.L. Celora, A. Münch, S.L. Waters, B. Wagner, Asymptotic study of the electric double layer at the interface of apolyelectrolyte 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.

      • M. Landstorfer, B. Prifling, V. Schmidt, Mesh generation for periodic 3D microstructure models and computation of effective properties, Preprint no. 2738, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2738 .
        Abstract, PDF (12 MByte)
        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.

      • 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.

      • H. Abels, J. Daube, Ch. Kraus, D. Kröner, The sharp-interface limit for the Navier--Stokes--Korteweg equations, Preprint no. 2663, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2663 .
        Abstract, PDF (173 kByte)
        We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions.

      • D. Bothe, P.-É. Druet, Mass transport in multicomponent compressible fluids: Local and global well-posedness in classes of strong solutions for general class-one models, Preprint no. 2658, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2658 .
        Abstract, PDF (509 kByte)
        We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell- Stefan closure approach. Mechanical forces result into one single convective mixture velocity, the barycentric one, which obeys the Navier-Stokes equations. The thermodynamic pressure is defined by the Gibbs-Duhem equation. Chemical potentials and pressure are derived from a thermodynamic potential, the Helmholtz free energy, with a bulk density allowed to be a general convex function of the mass densities of the constituents. The resulting PDEs are of mixed parabolic-hyperbolic type. We prove two theoretical results concerning the well-posedness of the model in classes of strong solutions: 1. The solution always exists and is unique for short-times and 2. If the initial data are sufficiently near to an equilibrium solution, the well-posedness is valid on arbitrary large, but finite time intervals. Both results rely on a contraction principle valid for systems of mixed type that behave like the compressible Navier- Stokes equations. The linearised parabolic part of the operator possesses the self map property with respect to some closed ball in the state space, while being contractive in a lower order norm only. In this paper, we implement these ideas by means of precise a priori estimates in spaces of exact regularity.

      • A. Münch, B. Wagner, Self-consistent field theory for a polymer brush. Part II: The effective chemical potential, Preprint no. 2649, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2649 .
        Abstract, PDF (318 kByte)
        The most successful mean-field model to describe the collective behaviour of the large class of macromolecular polymers is the self-consistent field theory (SCFT). Still, even for the simple system of a grafted dry polymer brush, the mean-field equations have to be solved numerically. As one of very few alternatives that offer some analytical tractability the strong-stretching theory (SST) has led to explicit expressions for the effective chemical potential and consequently the free energy to promote an understanding of the underlying physics. Yet, a direct derivation of these analytical results from the SCFT model is still outstanding. In this study we present a systematic asymptotic theory based on matched asymtptotic expansions to obtain the effective chemical potential from the SCFT model for a dry polymer brush for large but finite stretching.

      • A. Münch, B. Wagner, Self-consistent field theory for a polymer brush. Part I: Asymptotic analysis in the strong-stretching limit, Preprint no. 2648, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2648 .
        Abstract, PDF (854 kByte)
        In this study we consider the self-consistent field theory for a dry, in- compressible polymer brush, densely grafted on a substrate, describing the average segment density of a polymer in terms of an effective chemical potential for the interaction between the segments of the polymer chain. We present a systematic singular perturbation analysis of the self-consistent field theory in the strong-stretching limit, when the length scale of the ratio of the radius of gyration of the polymer chain to the extension of the brush from the substrate vanishes. Our analysis yields, for the first time, an approximation for the average segment density that is correct to leading order in the outer scaling and resolves the boundary layer singularity at the end of the polymer brush in the strong-stretching limit. We also show that in this limit our analytical results agree increasingly well with our numerical solutions to the full model equations comprising the self-consistent field theory.

      • P.-É. Druet, Global-in-time existence for liquid mixtures subject to a generalised incompressibility constraint, Preprint no. 2622, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2622 .
        Abstract, PDF (510 kByte)
        We consider a system of partial differential equations describing diffusive and convective mass transport in a fluid mixture of N > 1 chemical species. A weighted sum of the partial mass densities of the chemical species is assumed to be constant, which expresses the incompressibility of the fluid, while accounting for different reference sizes of the involved molecules. This condition is different from the usual assumption of a constant total mass density, and it leads in particular to a non-solenoidal velocity field in the Navier-Stokes equations. In turn, the pressure gradient occurs in the diffusion fluxes, so that the PDE-system of mass transport equations and momentum balance is fully coupled. Another striking feature of such incompressible mixtures is the algebraic formula connecting the pressure and the densities, which can be exploited to prove a pressure bound in L1. In this paper, we consider incompressible initial states with bounded energy and show the global existence of weak solutions with defect measure.

      Talks, Poster

      • B. Wagner, Phase-field models of the lithiation/delithiation cycle of thin-film electrodes, Oxford Battery Modelling Symposium, 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.

      • P.-É. Druet, Analysis of mass transfer, Navier-Stokes equations for multicomponent fluids subject to a volume constraint, 5th Applied Mathematics Münster Symposium: Transport, Mixing and Fluids, February 11 - 13, 2019, Westfälische Wilhelms-Universität Münster, February 12, 2019.

      • P.-É. Druet, Multicomponent diffusion in fluids: Some mathematical aspects, Technische Universität Wien, Institut für Analysis und Scientific Computing, Austria, April 3, 2019.

      • P.-É. Druet, The low Mach number limit for complex fluids: Recent results on strong and weak solvability, PDE 2019: Partial Differential Equations in Fluids and Solids, September 9 - 13, 2019, WIAS, Berlin, September 9, 2019.

      • M. Landstorfer, Mathematical modeling of intercalation batteries with non-equilibrium thermodynamics and homogenization theory, ModVal 2019 -- 16th Symposium on Modeling and Experimental Validation of Electrochemical Energy Technologies, Braunschweig, March 12 - 13, 2019.

      • M. Landstorfer, Modelling porous intercalation electrodes with continuum thermodynamics and multi-scale asymptotics, Oxford Battery Modelling Symposium, March 18 - 19, 2019, University of Oxford, Pembroke College, UK, March 18, 2019.

      • M. Landstorfer, Theory and validation of the electrochemical double layer, PC Seminar, AG Prof. Baltruschat, Universität Bonn, Abt. Elektrochemie, March 8, 2019.

      • R. Müller, Transport of solvated ions in nanopores: Modeling, asymptotics and simulation, Conference to celebrate the 80th jubilee of Miroslav Grmela, May 18 - 19, 2019, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Prag, Czech Republic, May 18, 2019.

      • R. Müller, Transport phenomena in electrolyte within a battery cell, Battery Colloquium, Technische Universität Berlin, April 18, 2019.

      • A. Münch, B. Wagner, Nonlinear visco-elastic effects of polymer and hydrogel layers sliding on liquid substrates, 694. WE-Heraeus-Seminar, Bad Honnef, April 11 - 13, 2019.

      • S. Cap, M. Landstorfer, D. Klein, R. Schlägl, N. Nickel, Silicon thin films deposited by low pressure chemical vapor deposition on planer current collectors as model system for lithium ion batteries, Advanced Lithium Batteries for Automobile Applications (ABAA 12), Ulm, October 6 - 9, 2019.

      • B. Wagner, S. Reber, J. Iglesias, A. Fritsch, E. Meca, Hierarchical spindle assembly: Sequence-dependent energy landscapes for a cytoplasmic condensate, Kick-Off Meeting DFG SPP 2191 ``Molecular Mechanisms of Functional Phase Separation'', Heidelberg, June 6 - 7, 2019.

      • B. Wagner, Free boundary problems of active and driven hydrogels, PIMS-Germany Workshop on Modelling, Analysis and Numerical Analysis of PDEs for Applications, June 24 - 26, 2019, Universität Heidelberg, Interdisciplinary Center for Scientific Computing and BIOQUANT Center, June 24, 2019.

      • B. Wagner, Free boundary problems of active and driven hydrogels, EUROMECH 604, Fluid and Solid Mechanics for Issue Engineering, September 23 - 25, 2019, University of Oxford, Mathematical Institute, UK, September 24, 2019.

      • B. Wagner, Ill-posedness of two-phase flow models of concentrated suspensions, 9th International Congress on Industrial and Applied Mathematics ICIAM2019, Minisymposium MS ME-0-7 6 ``Recent Advances in Understanding Suspensions and Granular Media Flow -- Part 2'', July 15 - 19, 2019, Valencia, Spain, July 17, 2019.

      • B. Wagner, Mathematical modeling of real world processes, CERN Academic Training Programme 2018--2019, March 14 - 15, 2019, CERN, Geneva, Switzerland.

      • J. Fuhrmann, A. Linke, Ch. Merdon, R. Müller, Induced charge electroosmotic flow including finite ion size effects, 13th International Symposium on Electrokinetics (ELKIN), Cambridge, USA, June 12 - 14, 2019.

      • O. Klein, On uncertainty quantification for models involving hysteresis effects, Seminar Nichtlineare Optimierung und Inverse Probleme, WIAS, Berlin, May 21, 2019.

      External Preprints

      • J. Fuhrmann, C. Guhlke, Ch. Merdon, A. Linke, R. Müller, Induced charge electroosmotic flow with finite ion size and solvation effects, Preprint no. arXiv:1901.06941, Cornell University Library, 2019, DOI 10.1016/j.electacta.2019.05.051 .

Research Groups