# C3: Spinodal decomposition of polymer-solvent systems

The goal of the project is to obtain stable and consistent descriptions of flow dynamics on multiple scales in a class of systems exhibiting highly complex non-equilibrium dynamics, namely phase-separating polymer solutions. This is done by combining (i) the derivation, analysis, and simulation of macroscopic two-fluid models describing the dynamics of viscoelastic phase separation, (ii) the mesoscopic simulation of viscoelastic phase separation by extension of a coupled Lattice-Boltzmann / Molecular Dynamics method, and (iii) the calibration of the macroscopic models to results from mesoscopic simulations by means of parameter estimation and inverse problems methodology.

Existence, regularity and weak-strong uniqueness for the three-dimensional Peterlin viscoelastic model

Commun. Math. Sci. ,
(2021 );

https://www.intlpress.com/site/pub/pages/journals/items/cms/_home/acceptedpapers/index.php

Systematic derivation of hydrodynamic equations for viscoelastic phase separation

Journal of Physics: Condensed Matter 33 (36),
364001
(2021);

URL: https://iopscience.iop.org/article/10.1088/1361-648X/ac0d17

doi:https://doi.org/10.1088/1361-648X/ac0d17

Analysis of a viscoelastic phase separation model

Journal of Physics: Condensed Matter 33 (23),
234002
(2021);

doi:10.1088/1361-648x/abeb13

A Second-Order Finite Element Method with Mass Lumping for Maxwell's Equations on Tetrahedra

SIAM Journal on Numerical Analysis 59 (2),
864-885
(2021);

doi:10.1137/20m1318912

On the Energy Stable Approximation of Hamiltonian and Gradient Systems

Computational Methods in Applied Mathematics 21 (2),
335-349
(2020);

doi:10.1515/cmam-2020-0025

On a Second-Order Multipoint Flux Mixed Finite Element Methods on Hybrid Meshes

SIAM Journal on Numerical Analysis 58 (3),
1822-1844
(2020);

doi:10.1137/19m1236862

Chemotaxis on networks: Analysis and numerical approximation

ESAIM: Mathematical Modelling and Numerical Analysis 54 (4),
1339-1372
(2020);

doi:10.1051/m2an/2019069

Structure Preserving Discretization of Allen–Cahn Type Problems Modeling the Motion of Phase Boundaries

Vietnam Journal of Mathematics 48 (4),
847-863
(2020);

doi:10.1007/s10013-020-00428-w

A mass-lumped mixed finite element method for acoustic wave propagation

Numerische Mathematik 145 (2),
239-269
(2020);

doi:10.1007/s00211-020-01118-y

On the transport limit of singularly perturbed convection–diffusion problems on networks

Mathematical Methods in the Applied Sciences 44 (6),
5005-5020
(2020);

doi:10.1002/mma.7084

Semiautomatic construction of lattice Boltzmann models

Physical Review E 101 (4),
(2020);

doi:10.1103/physreve.101.043310

Structure preserving approximation of dissipative evolution problems

Numerische Mathematik 143 (1),
85-106
(2019);

doi:10.1007/s00211-019-01050-w

A hybrid mass transport finite element method for Keller–Segel type systems

J. Sci. Comp 80,
1777-1804
(2019);

doi:10.1007/s10915-019-00997-0

Energy-stable linear schemes for polymer-solvent phase field models

Comp. Math. Appl. 77 (1),
125-143
(2019);

URL: https://www.sciencedirect.com/science/article/pii/S0898122118305303?via%3Dihub

doi:https://doi.org/10.1016/j.camwa.2018.09.018

Existence of global weak solutions to the kinetic Peterlin model

Nonlinear Analysis: Real World App. 44,
465-478
(2018);

URL: https://www.sciencedirect.com/science/article/pii/S1468121818305480?via%3Dihub

doi:https://doi.org/10.1016/j.nonrwa.2018.05.016

Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method. Part I: a nonlinear scheme

ESAIM Math. Model. Numer. Anal. 51 (5),
1637–1661.
(2017);

URL: https://www.esaim-m2an.org/

An improved dissipative coupling scheme for a system of Molecular Dynamics particles interacting with a Lattice Boltzmann fluid

Computer Physics Communications 216,
102-108
(2017);

doi:10.1016/j.cpc.2017.03.009

Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme

Mathematical Modelling and Numerical Analysis ,
(2017);

doi:10.1051/m2an/2017032

Global existence result for the generalized Peterlin viscoelastic model

SIAM J. Math. Anal.,
1-14
(2017);

URL: https://www.siam.org/journals/sima.php

Energy-stable numerical schemes for multiscale simulations of polymer-solvent mixtures

in Mathematical Analysis of Contimuum Mechanics and Industrial Applications II , Editor: Patrick van Meurs, Masato Kimura, Hirofumi Notsu, Chapter Chap5: Interface Dynamics , Pages 1-12, Springer International Publishing AG/ Eds. Patrick van Meurs, Masato Kimura, Hirofumi Notsu (2017);

URL: https://link.springer.com/chapter/10.1007/978-981-10-6283-4_13

The Cassie-Wenzel transition of fluids on nanostructured substrates: Macroscopic force balance versus microscopic density-functional theory

The Journal of Chemical Physics 145 (13),
134703
(2016);

doi:10.1063/1.4963792

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 81,
523-557
(2016);

URL: wileyonlinelibrary.com

doi:10.1002/ﬂd.4195

## Contact

- Prof. Dr. Burkhard Dünweg
- Max Planck-Institut für Polymerforschung
- Ackermannweg 10
- D-55128 Mainz
- Tel: +49 6131 379198
- duenwegsLjhZPyVcS@hvRmpip-mainz.mpg.de
- http://www2.mpip-mainz.mpg.de/~duenweg/

- Prof. Dr. Herbert Egger
- Department of Mathematics
- Technische Universität Darmstadt
- Dolivostraße 15
- D-64293 Darmstadt
- Tel: +49 6151 16-23170
- eggerjjwA@xdmathematik.tu-darmstadt.de
- https://www.mathematik.tu-darmstadt.de/numerik-und-wissenschaftliches-rechnen/personen_numerik/details_num/herbert_egger.de.jsp

- Prof. Dr. Maria Lukáčová
- Institut für Mathematik
- Universität Mainz
- Staudingerweg 9
- D-55128 Mainz
- Tel: +49 6131 39 22831
- Fax: +49 6131 39 23331
- Sekr: +49 6131 39 22270
- lukacovaLiivzLKD@Rvm.QhLmathematik.uni-mainz.de
- http://www.mathematik.uni-mainz.de/Members/lukacova