* officialy retired since June 1, 2013
At the moment the following topics are actively pursued:
Hydrodynamics of simple fluids is a classical textbook subject that still bears a lot of interesting and unsolved problems (e.g. turbulence) due to its inherent nonlinear nature. On the other hand it has become possible to apply hydrodynamics also to more complex systems. This was facilitated by a deeper understanding of hydrodynamics based on symmetries and thermodynamics. It can now be used as a general method to describe macroscopically the dynamics of many condensed systems including liquid crystals, superfluid liquids, polymers, magnetic systems etc. The hydrodynamic method is based on the observation that in most condensed systems there is only a small number of slow, long living processes compared to the huge number of fast, microscopic degrees of freedom, which can be discarded in a description of the macroscopic behavior. The hydrodynamic variables describe cooperative phenomena that do not relax in finite time in the homogeneous limit. The point is that these hydrodynamic variables can uniquely be identified using conservation laws (related to global symmetries) and broken symmetries (in the case of complex systems). For time and lengths scales, on which all the fast, local microscopic degrees of freedom have relaxed to their equilibrium value, this hydrodynamic description is exact.
In some cases a few of the non-hydrodynamic, relaxing processes become so slow that their relaxation time is comparable to hydrodynamic time scales. Examples are elastic strain relaxation in polymers and order parameter relaxation near second order (or weakly first order) phase transitions (giving rise to soft modes). In that situation it is reasonable to extend hydrodynamics to ``macroscopic dynamics" incorporating the slowly relaxing variables. There are no general rules or arguments, when or what kind of slowly relaxing variables exist in a given system. However, there are some classes of systems, where one can expect such variables. One is that of 'almost hydrodynamic' systems: If two variables are coupled by a rather small interaction energy, their relative dynamics can become very slow. Examples are relative rotations of nematic side chains with respect to the backbone segments in side-chain polymers, relative rotations of director and bond-orientational order in tilted hexatic liquid crystals, spin - orbit rotations in 3He-A, or relative translations in incommensurate solid systems with small excitation gaps. Second, in chemical reaction systems the non-hydrodynamic concentration fields sometimes couple to the hydrodynamic ones on rather long time and length scales. Another class are spatial superstructures (like cholesteric liquid crystals, blue phases or twist-grain-boundary phases), where the strict hydrodynamic description is restricted to length scales larger than those of the superstructure, while a description inside the superstructure requires additional relaxing variables. Heterogeneous systems, like emulsions (polymer dispersed liquid crystals) microemulsions (surfactant systems), suspensions (colloids) and microsuspensions (ferrofluids), are often described by two-fluid theories, where distinct non-hydrodynamic momentum densities for the different constituents are used. Finally, all systems, whose elements change shape or structure already under weak external disturbances, have to be mentioned here. Examples are worm-like micelles and vesicles (shape and topological changes), electro- and magnetorheological fluids (chaining) and sponge phases (phase transitions) leading to shear-thinning and -thickening, field-dependent effective viscosities and shear birefringence, respectively.
The main advantage of the hydrodynamic method rests in its high generality, which allows its application to very different systems. There are no model dependent assumptions and only very fundamental symmetry and thermodynamic arguments are used. The occurrence of phenomenological parameters in the static and dynamic expansions, however, are the prize one has to pay for this generality. The only restriction on the applicability of a hydrodynamic theory arises from the validity of the static and dynamic expansions used. Going beyond hydrodynamics it is not possible to predict, if and which non-hydrodynamic variables can become slow, although the generalized theory, which includes such variables, is still a powerful theory albeit less fundamental than a purely hydrodynamic theory. Its practical use is confined to situations with a clear-cut separation of the macroscopic time scale (relevant for only a few variables) from the microscopic one (relevant for all the others).
A detailed exposition of the method and its application to complex fluids can be found in
H. Pleiner and H.R. Brand, "Hydrodynamics and Electrohydrodynamics of Liquid Crystals", in Pattern
Formation in Liquid Crystals, Chap.2, eds. A. Buka and L. Kramer, Springer N.Y. (1996) [200 kB ps.gz-file], [751 kB pdf-file]
H. Pleiner, "Hydrodynamik komplexer Fluide" in Komplexe Systeme zwischen Atom und Festörper
25. IFF Ferienkurs, Forschungszentrum Jülich, p.\ 20.1-32 (1994) [178 kB pdf-file] (ohne Figuren) and
"Komplexe Fluide -- ein Überblick", in Dynamik und Strukturbildung in kondensierter Materie,
28. IFF Ferienkurs, Forschungszentrum Jülich, p. E1-19 (1997) [150 kB ps.gz-file], [804 kB pdf-file], see also
"Macroscopic variables in commensurate and incommensurate condensed phases", in Incommensurate Crystals, Liquid Crystals, and Quasicrystals p.241, eds. J.F. Scott and N.A. Clark, Plenum New York (1987).
31. Arbeitstagung Flüssigkristalle 2003, in Mainz
1st Workshop on Liquid Crystalline Elastomers 2001, at the Ebernburg
2nd Workshop on Liquid Crystalline Elastomers 2003, in Bleibach near Freiburg
4. Dresdner Herbstseminar Nichtlineare Physik 2003
5. Dresdner Herbstseminar Nichtlineare Physik 2004
Nonequilibrium Phenomena in Complex Elastomers and Gels 2007, International Discussion Meeting, in Mainz
8th German Ferrofluid Workshop 2008, in Mainz
38th German Workshop on Liquid Crystals 2010, in Mainz
24th International Liquid Crystal Conference 2012, in Mainz
Nonlinear Response and Non-Equilibrium Dynamics of Anisotropic Systems 2012, in Mainz (Japanese - German Satellite Meeting of ILCC2012 within the JSPS core-to-core program)
Complex Fluids and Soft Matter Physics 2013, Symposium on the occasion of my official retirement, in Mainz