M. Lücke

Roll and square convection in binary liquids: A few-mode Galerkin model

We present a few-mode Galerkin model for convection in binary fluid layers subject to an approximation to realistic horizontal boundary conditions at positive separation ratios. The model exhibits convection patterns in form of rolls and squares. The stable squares at onset develop into stable rolls at higher thermal driving. In between, a regime of a so-called cross roll structure is found. The results of our few-mode model are in good agreement with both experiments and numerical multimode simulations.

Magnetization of Rotating Ferrofluids: Predictions of Different Theoretical Models

We consider a ferrofluid cylinder, that is rotating with constant rotation frequency Omega e_z as a rigid body. A homogeneous magnetic field H_0 e_x is applied perpendicular to the cylinder axis e_z. This causes a nonequilibrium situation. Therein the magnetization M and the internal magnetic field H are constant in time and homogeneous within the ferrofluid. According to the Maxwell equations they are related to each other via H = H_0 - M/2. However, H and M are not parallel to each other and their directions differ from that of the applied field H_0. We have analyzed several different theoretical models that provide equations for the magnetization in such a situation. The magnetization M is determined for each model as a function of Omega and H_0 in a wide range of frequencies and fields. Comparisons are made of the different model results and the differences in particular of the predictions for the perpendicular components H_y =-M_y/2 of the fields are analyzed.Summary We consider a ferrofluid cylinder, that is rotating with constant rotation frequency Ω = Ωez as a rigid body. A homogeneous magnetic field H0 = H0ex is applied perpendicular to the cylinder axis ez. This causes a nonequilibrium situation. Therein the magnetization M and the internal magnetic field H are constant in time and homogeneous within the ferrofluid. According to the Maxwell equations they are related to each other via H = H0 − M/2. However, H and M are not parallel to each other and their directions differ from that of the applied field H0. We have analyzed several different theoretical models that provide equations for the magnetization in such a situation. The magnetization M is determined for each model as a function of Ω and H0 in a wide range of frequencies and fields. Comparisons are made of the different model results and the differences in particular of the predictions for the perpendicular components Hy = −My/2 of the fields are analyzed.

Spiral vortices and Taylor vortices in the annulus between counter-rotating cylinders

Vortices in the Taylor-Couette system with counter-rotating cylinders are investigated numerically in a set up with radius ratio η = 0.5. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Structure, dynamics, and bifurcation behavior of Taylor vortices and of spiral vortex solutions are elucidated. Some of their properties obtained for axially periodic boundary conditions are compared with recent experimental results.

Equilibrium and Nonequilibrium Behaviour of Ferrofluids - Experiments and Theory

Selected results on the spatiotemporal behaviour of equilibrium and nonequilibrium properties of ferrofluids in different magnetic fields are reviewed. They have been obtained in the project B13 Transport, response and instability behaviour of ferrofluids of the SFB 277 by experiments and by various theoretical methods ranging from purely analytical calculations to full numerical approaches.

Magnetization of rotating ferrofluids: the effect of polydispersity

The influence of polydispersity on the magnetization is analysed in a nonequilibrium situation where a cylindrical ferrofluid column is forced to rotate with constant frequency, like a rigid body in a homogeneous magnetic field that is applied perpendicular to the cylinder axis. Then, the magnetization and the internal magnetic field are no longer parallel to each other and their directions differ from that of the applied magnetic field. Experimental results on the transverse magnetization component perpendicular to the applied field are compared and analysed as functions of rotation frequency and field strength with different polydisperse Debye models that take into account the polydispersity in different ways and to a varying degree.

Convective Patterns in Binary Fluid Mixtures with Positive Separation Ratios

We summarize our findings about laterally periodic convection structures in binary mixtures in the Rayleigh-Benard system for positive Soret effect. Stationary roll, square, and crossroll solutions and their stability are determined with a multimode Galerkin expansion. The oscillatory competition of squares and rolls in the form of crossroll oscillations is reviewed. They undergo a subharmonic bifurcation cascade where the oscillation period grows in integer steps as a consequence of an entrainment process.

Periodically Forced Ferrofluid Pendulum: Effect of Polydispersity

Summary We investigate a torsional pendulum containing a ferrofluid that is forced periodically to undergo small-amplitude oscillations. A homogeneous magnetic field is applied perpendicular to the pendulum axis. We give an analytical formula for the ferrofluid-induced “selfenergy” in the pendulum’s dynamic response function for monodisperse as well as for polydisperse ferrofluids.

Modulated Taylor Vortex Flow

We have studied the rotating Couette system, i.e., the flow between two concentric cylinders of radii R1 and R2), with the outer cylinder at rest. The rotation rate of the inner cylinder is modulated periodically Ω(t)=Ω(1+Δcosωt). We use a finite difference numerical simulation and a four-mode Galerkin model to investigate both the threshold shift of the onset of Taylor vortex flow (TVF) and the fully nonlinear behaviour of TVF (Kuhlmann et al., 1989). Our calculations were done for a radius ratio η=R1/R2=0.65 but we found that the results presented here are practically independent of η.