Stability boundaries of roll and square convection in binary fluid mixtures with positive separation ratio

Rayleigh-B\'{e}nard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multi-mode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.Comment: 19 pages + 15 figures, accepted by Journal of Fluid Mechanic

Faraday instability in a two-component Bose Einstein condensate

Motivated by recent experiments on Faraday waves in Bose Einstein condensates (BEC) we investigate the dynamics of two component cigar shaped BEC subject to periodic modulation of the strength of the transverse confinement. It is shown that two coupled Mathieu equations govern the dynamics of the system. We found that the two component BEC in a phase mixed state is relatively more unstable towards pattern formation than the phase segregated state.Comment: 6 pages, 4 figure

Roll convection of binary fluid mixtures in porous media

We investigate theoretically the nonlinear state of ideal straight rolls in the Rayleigh-B\'enard system of a fluid layer heated from below with a porous medium using a Galerkin method. Applying the Oberbeck-Boussinesq approximation, binary mixtures with positive separation ratio are studied and compared to one-component fluids. Our results for the structural properties of roll convection resemble qualitatively the situation in the Rayleigh--B\'enard system without porous medium except for the fact that the streamlines of binary mixtures are deformed in the so-called Soret regime. The deformation of the streamlines is explained by means of the Darcy equation which is used to describe the transport of momentum. In addition to the properties of the rolls, their stability against arbitrary infinitesimal perturbations is investigated. We compute stability balloons for the pure fluid case as well as for a wide parameter range of Lewis numbers and separation ratios which are typical for binary gas and fluid mixtures. The stability regions of rolls are found to be restricted by a crossroll, a zigzag and a new type of oscillatory instability mechanism, which can be related to the crossroll mechanism

Magnetization and susceptibility of ferrofluids

A second-order Taylor series expansion of the free energy functional provides analytical expressions for the magnetic field dependence of the free energy and of the magnetization of ferrofluids, here modelled by dipolar Yukawa interaction potentials. The corresponding hard core dipolar Yukawa reference fluid is studied within the framework of the mean spherical approximation. Our findings for the magnetic and phase equilibrium properties are in quantitative agreement with previously published and new Monte Carlo simulation data.Comment: 8 pages including 4 figure

Novel trends in optical non-destructive testing methods

Non-destructive testing (NDT) describes a wide range of methods for measuring and comparing physical quantities against a nominal condition. In this paper we describe and compare different optical NdT (ONDT)-methods with respect to their characteristics and capability for different measurement tasks. ONDT may be specified in two categories, passive and active. The NDT principles of the first category just use a measurement method like view inspection, elipsometry or reflectometry to detect defects which are easily accessible. The principles of the second category use an excitation force, such as heat or mechanical vibration introduced by transducers to detect hidden defects. This category can be specified into two subcategories. The first subcategory "time-/depth-resolved" includes measurement methods delivering detailed information of the geometric features of a hidden defect. Therefore the excitation of the material and the detection of the reaction have to provide a time step which enables depth-solved measurements. Phase-resolved thermography and laser ultrasound are examples for this category. The second subcategory "Integrating" includes measurement technique coupled with an excitation that enables detection of defects but not evaluation of their geometric features. Examples for these measurement techniques are shearography, reflectometry, vibrometry and thermography coupled with excitation method like simple heating or loading with a constant force. We demonstrate experimental results obtained using methods developed in our institute and highlight directions of further development

Wear recording at micro deep drawing tools with comparative digital holography

We present a method to record the wear on samples of micro deep drawing tools. The method is based on the basic idea of comparative holography and captures three dimensionally the surface of the tool in the initial state and compares it with used state after processing several parts. The comparison reveals scratches and other effects caused by wear. In an industrial environment the comparative method must compensate for linear and rotational displacement of the present tool with respect to the initial state. As a consequence to the single-step-measurement with sufficiently high illumination intensity the developed set-up can be made insusceptible against stray light and the method is capable of inline quality control during a production process in a micro deep drawing machine

Magnetic properties of colloidal suspensions of interacting magnetic particles

We review equilibrium thermodynamic properties of systems of magnetic particles like ferrofluids in which dipolar interactions play an important role. The review is focussed on two subjects: ({\em i}) the magnetization with the initial magnetic susceptibility as a special case and ({\em ii}) the phase transition behavior. Here the condensation ("gas/liquid") transition in the subsystem of the suspended particles is treated as well as the isotropic/ferromagnetic transition to a state with spontaneously generated long--range magnetic order.Comment: Review. 62 pages, 4 figure