On trifactorized soluble minimax groups

This research was done while the last two authors were visitors at the University of Mainz. They are grateful to the Department of Mathematics for its excellent hospitality.     

Superpositioned dielectrophoresis for enhanced trapping efficiency

One of the major applications for dielectrophoresis is selective trapping and fractionation of particles. If the surrounding medium is of low conductivity, the trapping force is high, but if the conductivity increases, the attraction decreases and may even become negative. However, high-conductivity media are essential when working with biological material such as living cells. In this paper, some basic calculations have been performed, and a model has been developed which employs both positive and negative dielectrophoresis in a channel with interdigitated electrodes. The finite element method was utilized to predict the trajectories of Escherichia coli bacteria in the superpositioned electrical fields. It is shown that a drastic improvement of trapping efficiency can be obtained in this way, when a high conductivity medium is employed.     

Radial segregation due to weak convection in a floating zone

The influence of weak convection, caused by surface tension forces, on radial dopant segregation occurring in crystals grown under microgravity conditions is studied numerically. The geometry considered corresponds to a floating-zone configuration with partially coated melt surfaces consisting of small evenly distributed spots of free surfaces. In order to distinguish dopant distribution due to weak convection clearly from distribution due to diffusion the spots only cover one quarter of the periphery. Thus, surface tension-driven convection is allowed only over one quarter of the floating-zone configuration resulting in an asymmetric dopant distribution. The percentage of free surfaces present is varied in order to alter the Marangoni flow rates. The maximum dopant concentration due to radial segregation is plotted as a function of a certain convection level. The results of the present numerical study are supposed to be used to design corresponding space experiments launched at the end of the year 2000.     

Formation of 3-acyloxy-γ-butyrolactones from 4-pentenols in vanadium-catalyzed oxidations

O-Acyl derivatives of 3-hydroxy-γ-butyrolactone are formed in up to 20% yield as by-products from 1-alkyl- and 1-phenyl-substituted 4-pentenols and tert-butyl hydroperoxide (TBHP) in vanadium-catalyzed synthesis of (tetrahydrofuran-2-yl)-methanols. The lactones are secondary products formed from (tetrahydrofuran-2-yl)-methanols via hydrogen atom abstraction in positions 4 and 5, as derived from experiments starting from deuterium-labeled alkenols. Stereocenters at tetrahydrofuran carbon 2 and the proximate hydroxyl carbon of the alkanol side chain retain configuration in the course of oxidative tetrahydrofuran conversion. In an atmosphere of nitrogen or argon, no γ-butyrolactone formation occurs, pointing to dioxygen as terminal oxidant for the secondary oxidation. Adding cyclohexa-1,4-diene or γ-terpinene to a solution of a 4-pentenol, TBHP, and a vanadium catalyst exposed to air inhibits formation of γ-butyrolactones. A third approach to prevent γ-butyrolactones from being formed in oxidative 4-pentenol cyclization uses cis-2,6-bis-(methanol)-piperidine instead of N-salicylidene-ortho-aminophenol as tridentate auxiliary for the vanadium catalyst.     

Some problems in metallurgical fluid mechanics

Application of computational fluid mechanics in two areas of metallurgy is considered: solidification of liquid alloys and MHD turbulence. In the first class of problems, where the technical issue is to obtain a reasonably homogeneous composition of the cast, one has to consider not only the completely molten and solidified regions but also the “mushy zone” that is made up of small-scale dendrites, which appear between the first two regions. In the completely molten region, the composition is practically constant and the fluid is set into motion due to the inhomogeneous temperature field. In the mushy zone, on the other hand, solutal convection often dominates strongly over thermal convection. It is shown that laminar convection is of prime importance for the composition of the solidified alloy. In the second class of problems, two cases of turbulent MHD flows in cylindrical containers are considered: an electromagnetic furnace and an electromagnetic stirrer. In the electromagnetic furnace, the mean flow consists of two toroidal vortices. The mean motion in the electromagnetic stirrer is a swirling motion that is accompanied by a weak meridional circulation, which is reminiscent of that occuring in spin down phenomena. The MHD flows are computed by using large eddy simulation methodology with a new subgrid model of the Smagorinsky type that accounts for a variable mesh. Predictions from the all model computations are compared with experimental observations. In general, the agreement between theory and experiments is satisfactory.     

Experimental and numerical investigation of nonlinear thermocapillary oscillations in an annular geometry

The present work investigates thermocapillary flow in a cylindrical configuration using large Prandtl number liquids. The flow is studied using coordinated simulations and experimental optical methods such as PIV and flow visualization. In this way, properties of the oscillatory state can be obtained in great detail. Considerable attention is given to the search for the parameters influencing the onset of the instability. It is found that the onset of oscillations can be correlated using a thermocapillary Reynolds number. The oscillations take the form of a standing wave close to the onset, which is replaced by a travelling wave for stronger forcing. The selection of azimuthal wave number of the oscillatory mode is determined from geometrical parameters, and resembles the wave number selection in vortex ring instabilities. Throughout we obtain good agreement between experiments and simulations using a mathematical model with an undeformed adiabatic free surface.     

Visualization of boundary layers in a sectioned centrifuge

We are interested in the flow of a suspension in a rotating, conical cavity with a dividing barrier that blocks any azimuthal motion around the axis. In order to simplify the experiment, the flow of a homogeneous fluid, slightly denser than the bulk fluid filling the container, has been used. The theoretical predictions of a previous paper have been tested, in particular those relating to the intense current on the dividing barrier that was found. This current has been visualized. A quantitative comparison between theory and experiment is made. The qualitative findings of the theory that apply to this experiment are completely verified. The quantitative agreement is fair.