# C3: Spinodal decomposition of polymer-solvent systems

The project plans to study the same physical non-equilibrium soft-matter system by two different levels of coarse-graining. A semidilute polymer solution whose polymer component precipitates shall be simulated by both a hybrid Molecular Dynamics / Lattice Boltzmann method on the one hand, and a finite-volume discretization of a macroscopic two-fluid model on the other. The parameters of the latter are to be adjusted to match the behavior of the former. The mathematical structure of the two-fluid model, of its discretization, and of the adjustment procedure shall be subjected to detailed analysis.

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
- duenwegueI.uXXLo_p@HDCprYAmYrJmpip-mainz.mpg.de
- http://www2.mpip-mainz.mpg.de/~duenweg/

- 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
- lukacova-MCKuL@iIzR.ZOimathematik.uni-mainz.de
- http://www.mathematik.uni-mainz.de/Members/lukacova