Dynamics of Complex Fluids

The project deals mainly with the dynamics of complex fluids. This includes magnetic liquids, ferrofluids, mixtures of magnetic liquids and pure fluids as well as superfluid He4, liquids and mixtures. We also study the statics as it is necessary for the understanding of such systems. The goal of the project is to understand the dynamic modes of the systems. Several different regions where different theoretical tools have to be used are considered: the region near a phase transition (magnetic, gas liquid, liquid liquid, superfluid) or further away from this singular points. There we are interested in hydrodynamic modes (small wave vector modulus compared to the inverse interaction length) and the modes at larger wave vector modulus. The theoretic tools are either the generalize collective mode approach, the renormalization group method, and computer simulation. This is one of the attractive features of the project that there is overlap between all these methods. The results of our analytic calculations are quantities like transport coefficients or correlation functions (measurable in scattering experiments) and these will be compared with experiments or computer simulations. Comparison with other theoretical approaches like mode coupling theory or density functional theory will be included where appropriate. Besides the study of physical quantities another goal of the project is to improve the theoretical methods used. This concernes improvements in the dynamical field theoretic renormalization group formalism as well as the improvments of the algorithm used in the computer simulation (molecular dynamic and Monte Carlo simulations).

The project Dynamics of complex fluids` investigates properties of fluids showing not only the usual interaction between their molecules but also additional `inner` degrees of freedom. These are for example orientational degrees of freedom like magnetic spins but also degrees of freedom leading to superfluidity (in He). A general question is how the macroscopically observable quantities of such systems are connected to their microscopic properties. In other words: How does one get from the interactions between the smallest parts of the system to properties that are in most cases even visible to the naked eye? For instance, under which circumstances (pressure, temperature, concentration) does a magnetic fluid (inner degree of freedom a magnetic spin) become magnetic or gaseous? When does demixing occur in a mixture? How does the onset of superfluidity influence the thermal conductivity of liquid He? The first question is that concerning the phase diagram of a substance. Such a phase diagram can be calculated from the molecule interactions using a computer (Molecular Dynamics or Monte Carlo simulations), or analytically via approximate equations describing the substance. There one has the mean-field theory, but also different complicated integral equation theories. Both methods were studied and compared, since the numerical techniques have to replace experiments. Thus one learns to understand which approximation is good, perhaps also in which way new aspects must be incorporated into an approximation, but also what is not so promising. In this respect, the knowledge of magnetic fluids and their mixtures was enhanced. Phase diagrams of magnetic fluids with different interactions were simulated and compared with integral equation methods. This was also done for mixtures of a magnetic fluid and a nonmagnetic fluid. The resulting phase diagrams show a variety of interesting phase transitions with complicated topological structure. The specific behavior at second order phase transitions and multicritical points can be calculated with the renormalization group theory. This theory utilizes what causes problems in the simulations and integral equation theories, namely the invariance of the system under length- and time-scale transformations at the critical point. This invariance is a result of the increasing fluctuations in the vicinity of the phase transition. In this project, these methods were applied in order to calculate the transport properties at the superfluid phase transition in mixtures of 3 He and 4 He. Furthermore, the critical properties of a dynamical system were investigated, where the order parameter (describing the phase) couples to a conserved quantity, and thus a long-standing problem was solved. This model was then generalized, and the base for further investigations was built. These continuative projects allow describing the tricritical behavior of transport properties, which was also an open problem up to now. This tricritical phase transition is a multicritical phase transition where the mixture of 3 He and 4 He passes into the superfluid phase and a demixing occurs as well.