Adrian Lange

Kelvin force in a layer of magnetic fluid

The Kelvin force in a layer of magnetic fluid subjected to a homogeneous magnetic field and local heating is studied. The study is motivated by the question about the corresponding Kelvin force density (Phys. Rev. Lett. 84 (2000) 2762). It is shown that the usual and the newly proposed formulation of the Kelvin force are entirely equivalent. It is only when approximations are introduced that differences arise.

Thermomagnetic convection of magnetic fluids in a cylindrical geometry

The thermomagnetic convection of magnetic fluids in a cylindrical geometry subjected to a homogeneous magnetic field is studied. The study is motivated by a novel thermal instability [W. Luo et al., Phys. Rev. Lett. 82, 4134 (1999)]. As model system a composite cylinder with inner heating is considered which reflects the symmetry of the experimentally setup. The general condition for the existence of a potentially unstable stratification in the magnetic fluid is derived. Within a linear stability analysis the critical external induction for the onset of thermomagnetic convection is determined for dilute and nondilute magnetic fluids. The difference between both thresholds allows to test experimentally whether a test sample is a dilute fluid or not.

Magnetic Soret effect: application of the ferrofluid dynamics theory.

The ferrofluid dynamics theory is applied to thermodiffusive problems in magnetic fluids in the presence of magnetic fields. The analytical form for the magnetic part of the chemical potential and the most general expression of the mass flux are given. By applying these results to experiments, global Soret coefficients in agreement with measurements are determined. An estimate for a hitherto unknown transport coefficient is also made.

Surface Instabilities of Ferrofluids

We report on recent progress in understanding the formation of surface protuberances on a planar layer of ferrofluid in a magnetic field oriented normally to the surface. This normal field or Rosensweig instability can be tackled by a linear and a nonlinear description. In the linear regime of small amplitudes we focus on the wave number of maximal growth, its corresponding growth rate and the oscillatory decay of metastable pattern, accessible via a pulse technique. A quantitative comparison of measurements with predictions of the linear stability analysis is performed, whereby the viscosity and the finite depth of the liquid layer are taken into account.

Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

Abstract To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.

Multifractality in forgetful memories

Learning rules of a forgetful memory generate their synaptic efficacies through iterative procedures that operate on the input data, random patterns. We analyse invariant distributions of the synaptic couplings as they arise asymptotically and show that they exhibit fractal or multifractal properties. We also discuss their dependence upon the learning rule and the parameters specifying it, and indicate how the nature of the invariant distribution is related to the network performance.

Thermodiffusion in concentrated ferrofluids: Experimental and numerical results on magnetic thermodiffusion

Ferrofluids consist of magnetic nanoparticles dispersed in a carrier liquid. Their strong thermodiffusive behaviour, characterised by the Soret coefficient, coupled with the dependency of the fluids parameters on magnetic fields is dealt with in this work. It is known from former experimental investigations on the one hand that the Soret coefficient itself is magnetic field dependent and on the other hand that the accuracy of the coefficients experimental determination highly depends on the volume concentration of the fluid. The thermally driven separation of particles and carrier liquid is carried out with a concentrated ferrofluid (φ = 0.087) in a horizontal thermodiffusion cell and is compared to equally detected former measurement data. The temperature gradient (1 K/mm) is applied perpendicular to the separation layer. The magnetic field is either applied parallel or perpendicular to the temperature difference. For three different magnetic field strengths (40 kA/m, 100 kA/m, 320 kA/m) the diffusive ...

Thermodiffusion in concentrated ferrofluids: A review and current experimental and numerical results on non-magnetic thermodiffusion

Ferrofluids are colloidal suspensions consisting of magnetic nanoparticles dispersed in a carrier liquid. Their thermodiffusive behaviour is rather strong compared to molecular binary mixtures, leading to a Soret coefficient (ST) of 0.16 K−1. Former experiments with dilute magnetic fluids have been done with thermogravitational columns or horizontal thermodiffusion cells by different research groups. Considering the horizontal thermodiffusion cell, a former analytical approach has been used to solve the phenomenological diffusion equation in one dimension assuming a constant concentration gradient over the cells height. The current experimental work is based on the horizontal separation cell and emphasises the comparison of the concentration development in different concentrated magnetic fluids and at different temperature gradients. The ferrofluid investigated is the kerosene-based EMG905 (Ferrotec) to be compared with the APG513A (Ferrotec), both containing magnetite nanoparticles. The experiments prov...

Thermal convection of magnetic fluids in a cylindrical geometry

Abstract The thermal convection in a layer of magnetic fluid confined in a two-dimensional cylindrical geometry is studied. The critical external induction for the onset of thermal convection is determined for dilute and non-dilute magnetic fluids. The detected difference between both thresholds allows to test experimentally whether a test fluid is a dilute one or not.

Finger-like patterns in sedimenting water}sand suspensions

Abstract The temporal evolution of a water–sand interface driven by gravity is experimentally investigated. By means of a Fourier analysis of the evolving interface the growth rates are determined for the different modes appearing in the developing front. To model the observed behavior we apply the idea of the Rayleigh–Taylor instability for two stratified fluids. Carrying out a linear stability analysis we calculate the growth rates from the corresponding dispersion relations for finite and infinite cell sizes and compose those results with the experimental data. Alternatively, the situation of the sedimenting sand can be modeled by a two-dimensional cellular automaton. A qualitative similarity between that model and the experimental situation is obtained.