Ingo Rehberg

A theoretical and experimental study of double-layer convection

The onset of thermal convection in a double layer of two superimposed immiscible fluids heated from below is investigated. The linearized equations of the problem are analysed in a much wider region of the parameter space than has been studied before. It is shown that the onset of steady convection in the two layers may occur in the form of either viscously or thermally coupled motions. In addition to the oscillatory interfacial instability, which depends on a non-vanishing distortion of the interface, there exists another oscillatory instability which corresponds to a cyclic variation between viscous and thermal coupling. Conditions for the onset of this instability are outlined and its connections with the other modes of the system are demonstrated in bifurcation diagrams. In the experiments the shadowgraph method is used for the visualization of the onset of convection and for the measurement of its wavelength. Changeovers between viscous and thermal coupling can be identified, but the experimental realization of an oscillatory onset has been elusive so far.

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.

The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation

The normal field instability in magnetic liquids is investigated experimentally by means of a radioscopic technique which allows a precise measurement of the surface topography. The dependence of the topography on the magnetic field is compared to results obtained by numerical simulations via the finite-element method. Quantitative agreement has been found for the critical field of the instability, the scaling of the pattern amplitude and the detailed shape of the magnetic spikes. The fundamental Fourier mode approximates the shape to within 10% accuracy for a range of up to 40 % of the bifurcation parameter of this subcritical bifurcation. The measured control parameter dependence of the wavenumber differs qualitatively from analytical predictions obtained by minimization of the free energy.

Pattern selection and transition to turbulence in propagating waves

Abstract We present a study of oscillatory convection in two experimental systems: ethanol-water mixtures in a rectangular container heated from below and a thin layer of nematic liquid crystals under low frequency ac voltage. In both systems the first bifurcation is the transition to travelling waves (TW) with finite wave vector and frequency. We report experimental observations of a sequence of spatial structures and dynamical behaviour of nonlinear TW in a regime of a weak nonlinearity. Most of the rich variety of spatial and dynamical behaviour which we observe in one-dimensional finite geometries has been reproduced by numerical simulations based on a simple model of coupled Ginzburg-Landau equations which considers only the combination of translation and finite geometry. More complicated spatio-temporal behaviour of TW in cells with two-dimensional geometry which initiated by defect nucleation is attributed to the mechanism of modulational instability of TW.

Coefficient of restitution for wet particles

The influence of a liquid film on the coefficient of restitution (COR) is investigated experimentally by tracing freely falling particles bouncing on a wet surface. The dependence of the COR on the impact velocity and various properties of the particle and liquid is presented and discussed in terms of dimensionless numbers that characterize the interplay between inertial, viscous, and surface forces. In the Reynolds number regime where lubrication theory does not apply, the ratio of the film thickness to the particle size is found to be a crucial parameter determining the COR.

Formation of a drop: viscosity dependence of three flow regimes

We observe the drop pinch-off at a nozzle for different viscosities and investigate three consecutive flow types. In its first stage the neck of the drop shrinks in an accelerated manner similar to the instability of a liquid cylinder. In the vicinity of the pinch point the motion becomes self-similar at a certain time. The self-similar domain consists of two flow regimes separated by a second transition point. The viscosity dependence of the transition points can be described by linear functions. Moreover, it is uncovered that both transitions occur when two different critical neck radii are reached. These radii are found to be independent of viscosity.

Measuring the deformation of a ferrogel sphere in a homogeneous magnetic field

A sphere of a ferrogel is exposed to a homogeneous magnetic field. In accordance to theoretical predictions, it gets elongated along the field lines. The time dependence of the elastic shear modulus causes the elongation to increase with time, similar to mechanic creep experiments, and the rapid excitation causes the sphere to vibrate. Both phenomena can be well described by a damped harmonic oscillator model. By comparing the elongation along the field to the contraction perpendicular to it, we can calculate Poissons ratio of the gel. The magnitude of the elongation is compared to the theoretical predictions for elastic spheres in homogeneous fields.

Thixotropy in macroscopic suspensions of spheres

An experimental study of the viscosity of a macroscopic suspension, i.e. a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density-matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown for the first time that a macroscopic suspension shows thixotropic viscosity, i.e. shear-thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10000 times larger than the viscous time scale and about 1000 times smaller than the thermodynamic time scale. The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern.

Fluid pumped by magnetic stress

A magnetic field rotating on the free surface of a ferrofluid layer is shown to induce considerable fluid motion toward the direction the field is rolling. The measured flow velocity (i) increases with the square of the magnetic field amplitude, (ii) is proportional to the thickness of the fluid layer, and (iii) has a maximum at a driving frequency of about 3kHz. The pumping speed can be estimated with a two-dimensional flow model.

Critical exponents of directed percolation measured in spatiotemporal intermittency

An experimental system showing a transition to spatiotemporal intermittency is presented. It consists of a ring of hundred oscillating ferrofluidic spikes. Four of five of the measured critical exponents of the system agree with those obtained from a theoretical model of directed percolation.