Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.     

Allgemeine Mikrochemie

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EPR study of radical anions of C60 and C70

Utilizing highly polar solvents for the stabilization of Fullerene anions, electrochemical and chemical reduction resulted in narrow single line EPR spectra for the monoanions of C₆₀ and C₇₀ being characterized byg=2.0001(1), ΔB=0.075 mT,g=2.0019(1), ΔB=0.016 mT, respectively. Apparently, the orbital degeneracy of the C₆₀ monoanion is lifted under these conditions to such an extent, that the abnormal large spin lattice relaxation rate believed to be responsible for the approximately 5 mT line width of the monoanion is sufficiently reduced.¹³C enrichment resulted in noticeable line broadening, allowing an estimate of the average¹³C hyperfine coupling constanta _ave=0.1 mT.     

The solvent extraction of some thallium(I) chelates

Fourteen different chelating reagents have been investigated, as possible extradants for radioiabelled 10^-6M thallium(I) from aqueous solutions into chloroform. The data have beun analyzed theoretically to identify the predominant species involved and to estimate association and distribution constanta.     

Studies of the solvent extraction of cadmium and silver dithizonates

An extensive study was made of the solvent extraction of cadmium and silver dithizonates into chloroform A few extractions of silver dithizonate were made into carbon tetrachloride. In most cases extraction curves of PH versus % metal extracted were obtained and reported in terms of the PH of 50% extraction. The shift of the extraction curves to higher PH values due to the effect of ions in the aqueous phase which complex with the cadmium or silver ions was investigated An equation was developed which would predict the PH of 50% extraction for the extraction from the solutions containing these complexing ions The effects of chloride, bromide and iodide ions on the extraction of cadmium and the effects of chloride, bromide, iodide, thiocyanate and thiosulfate ions on the extraction of silver. Extraction constants for the various extractions were determined.     

Wavelength-dependent triplet state populating mechanisms of naphthalene in heavy-atom hosts

We have made zero-field optically-detected magnetic resonance measurements on the triplet state of naphthalene-d₈ incorporated in the heavy-atom host crystals p-dichlorobenzene, p-dibromobenzene, and s-tetrachlorobenzene. The dependence of the relative triplet sublevel populating rates on the exciting wavelength is interpreted in terms of the electronic excitation transfer mechanisms. We find that upon excitation of the host S₁ ← S₀ transition in p-dichlorobenzene, energy transfer to the guest T₁ takes place via the guest S₁, whereas in the other host crystals the intermediate is mainly the host T₁ band. Upon host T₁ ← S₀ excitaton, trapping takes place from a spin-aligned excitor band in s-tetrachlorobenzene, whereas the initial alignment is lost prior to trapping in the dihalobenzene hosts.     

Modelling collective opinion formation by means of active Brownian particles

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical “social” temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems. Received 26 November 1999     

Eine neue Muffel zur Veraschung von Zucker

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