# 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.

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
- duenwegZ..@ZZIs-mpip-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
- eggerRUI@VPUBOEemathematik.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
- lukacovahbYaAsCj.@fjtmathematik.uni-mainz.de
- http://www.mathematik.uni-mainz.de/Members/lukacova