Pseudoähnlichkeitslösung des Rayleighschen Problems für reinviskose nicht-newtonsche Flüssigkeiten

Zusammenfassung Die exakte Ähnlichkeitslösung des Problems der nichtstationären Strömung einer hypothetischen Potenzflüssigkeit in der Umgebung einer ruckartig beschleunigten Platte (Rayleighsches Problem) wird zur Konstruktion einer Näherungslösung des analogen rheodynamischen Problems für reinviskose nicht-newtonsche Flüssigkeiten benutzt. Die Überprüfung der Genauigkeit der genäherten Pseudoähnlichkeitslösung basiert auf Berechnungen der Residuen der integralen Bilanzen des Impulses und der mechanischen Energie. Numerische Ergebnisse dieses Problems werden für das Powell-Eyringsche Modell der Viskositätsfunktion angegeben.

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Summary The exact similarity solution of the problem of the unsteady flow of a hypothetic power-law liquid near a suddenly started plate (Rayleigh's problem) is employed for the construction of an approximative solution of the same problem for arbitrary purely viscous non-Newtonian liquids. The testing of accuracy of this approximative pseudosimilarity solution is based on calculation of residua in the macroscopic balances of momentum and mechanical energy. Numerical results are reported for the Powell-Eyring model of the viscosity function.

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Symbole a Parameter der Ähnlichkeitslösung, definiert durch die Gln. [21] und [22],a =C ₀/B ₀ - B ₀ Parameter der Ähnlichkeitslösung, definiert durch Gl. [22] - B ₁ Parameter der Ähnlichkeitslösung, definiert durch Gl. [37] - C ₀ Parameter der Ähnlichkeitslösung, definiert durch Gl. [21] - D Differentialoperator, Gl. [10a, b] - Ey Kennzahl der rheologischen Ähnlichkeit für das Powell-Eyringsche Modell der Viskositätsfunktion, Gl. [43]G = / _I G _w = _w/ _I - K Konsistenzkoeffizient, Parameter des Potenzmodells der Viskositätsfunktion [7] - K scheinbarer Konsistenzkoeffizient, Gl. [23b] - n Fließindex des Potenzmodells der Viskositätsfunktion [7] - n scheinbarer Fließindex - n Index der logarithmischen Konvexität der Viskositätsfunktion - r unabhängige Veränderliche in der Ähnlichkeitslösung des Rayleighschen Problems, Gl. [17] - r unabhängige Veränderliche der Pseudoähnlichkeitslösung, Gl. [26]S = / _I S _w = _w/_I - t Zeit - T normierte Zeitvariable, Gl. [9c] - u ₀ Geschwindigkeit der Platte - U (Y, T) Pseudoähnlichkeitsnäherung des FeldesV (Y, T) - V (Y, T) normiertes Geschwindigkeitsfeld, Gl. [9a — c] - Y normierte Entfernung von der Platte, Gl. [9b] - W(r; n) Ähnlichkeitsdarstellung des Geschwindigkeitsfeldes, Gl. [20a, b] - Schergeschwindigkeit, Gl. [4] - _I Schergeschwindigkeits-Parameter der Viskositätsfunktion (Stoffkonstante) - _w momentane Schergeschwindigkeit an der Wand - _M normiertes Residuum der Impulsbilanz - _E normiertes Residuum der Bilanz der mechanischen Energie - dimensionsloser Parameter, definiert durch die Gln. [13] und [14] - dimensionsloser Parameter, definiert durch Gl. [23c] - Dichte - ₁₂, Schubspannung bei einer viskometrischen Strömung - [] Viskositätsfunktion - _I Schubspannungs-Parameter der Viskositätsfunktion (Stoffkonstante) - _w momentane Schubspannung an der Wand Mit 2 Abbildungen     

Three-segment electrodiffusion probes for measuring velocity fields close to a wall

Three-segment electrodiffusion probes embedded in a wall allow to determine simultaneously the three kinematic parameters of flow close to the probe surface: the flow direction, the wall shear rateq, and the normal velocity coefficientA,v _z = –A z ². A well-controlled three-dimensional flow, generated by a rotating disk, was used to demonstrate the capabilities of this new kind of electrodiffusion probes by comparing experimental results with the prediction based on the well-known hydrodynamical theory.List of symbols A normal flow coefficient, Eq. (1) - A axis of the adjustment rod, Fig. 2 - c ₀ concentration of depolarizer (mol/m³) - D diffusivity of depolarizer (m²/s) - E correction of total current on normal flow effect - e _x reference direction of the probe, Figs. 1 and 3 - F Faraday constant (F = 96,464 C/mol) - F _s normalized directional characteristic fors-th segment - f _sm ,g _sm Fourier coefficients of directional characteristics, Eq. (4) and Table 3 - h _m corrections of Fourier coefficients on normal flow effect, Eqs. (4) and (7) - i _s limiting diffusion current throughs-th segment (A) - i _tot (r) total current through the probe in dependence on its eccentricity (A) - K transport coefficient, Eqs. (3) and (5) - n number of electrons involved in redox reaction - O axis of the rotating disk, Fig. 2 - P centre of the probe, Fig. 2 - q magnitude of vectorial wall shear rate (s^-1) - q _x ,q _y components of vectorial wall shear rate - Q ratio of the currents in an eccentric and the central position of the probe, Eq. (15) - r radial coordinate, eccentricity of the probe - r _A eccentricity of the adjustment rod (r _A = , Fig. 2) - r, , z polar coordinates on the rotating disk - R effective radius of the probe (R = 0.337 mm) - S macroscopic area of the probe (S = 0.357 mm²) - x, y, z Cartesian coordinates moving with the probe - adjustment angle, Figs. 2 and 3 - angle included between local radius-vector ¯P of the probe and local direction of flow, Fig. 3 - angle included between reference directione _x of the probe and local direction of flow, Fig. 3 - ₀ theoretical prediction of, Eq. (11) - x ₀ theoretical prediction ofx, Eq. (14) - x _exp x calculated from experimental data using Eq. (4) - v kinematic viscosity (m²/s) - angle implied between gradient ofq and direction of flow, Eq. (8) - angular speed of the rotating disk (rad/s)     

End effects in rotational viscometry I. No-slip shear-thinning samples in the Z40 DIN sensor

Neglect of end effects in Couette rotational viscometry introduces a 10–30% error in the estimate of shear stress at the spindle surface. Actual deviations depend on the shear-thinning level of a given sample. We tackle the end effect for the standard sensor Z40 DIN according to the ISO 3219 by solving the related 2D boundary-value problem for a class of shear-thinning viscosity functions. The pseudosimilarity method of treating the primary data leaves an error of about 0.5% in shear stresses. Further reduction in the errors needs a full numerical simulation for each point of the primary data based on a suitable wide-range representation of the viscosity function. To support a high accuracy of torque calibrations, the effect of inertia on torque for Newtonian liquids in standard sensor Z40 DIN at Re < 500 is calculated using the FLUENT 6.2 commercial software. Paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Minimizing average completion time in the presence of release dates

A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of schedulingn jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constant-factor approximation algorithms for several variants of the single and parallel machine models. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of averageweighted completion time as well. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This work was performed under US Department of Energy contract number DE-AC04-76AL85000.Research partly supported by NSF Award CCR-9308701, a Walter Burke Research Initiation Award and a Dartmouth College Research Initiation Award.Research partially supported by NSF Research Initiation Award CCR-9211494 and a grant from the New York State Science and Technology Foundation, through its Center for Advanced Technology in Telecommunications.     

Synthesis and characterization of Cu(II) paddlewheel complexes possessing fluorinated carboxylate ligands

The goal of this study was to establish the relationship between the ¹⁹F NMR line broadening and the varying distance between the ¹⁹F nucleus and copper(II) ion, with the aim of gathering data that can be used to interpret ¹⁹F NMR spectra of subsequent fluorine-labeled, copper-binding proteins. Fluorinated alkyl and aryl copper(II) carboxylates were synthesized from fluorinated carboxylic acids and Cu(OH)₂. The copper(II) carboxylates were characterized using ¹⁹F NMR, IR, and single crystal X-ray diffraction. In the alkyl carboxylate compounds, the line broadening and chemical shift lessened with increased distance between the fluorine atom and the copper ions; however, in the aryl carboxylate derivatives, increased distance was not a factor in the amount of line broadening or change in chemical shift between the acid and metal salt. The compound, bis(3-(trifluoromethyl)butyrate) copper(II) (5) was found to possess the optimum combination of decreased line broadening and increased chemical shift sensitivity in ¹⁹F NMR. The crystal structures obtained for compounds 1, 2, 4, and 6 were analogous to previous copper(II) carboxylate complexes, though it is noted that compound 6, bis(5,5,5-trifluoropentanoate) copper(II) assumes a tetrameric structure lacking apical ligands, and thus enables the formation of an extended network of near-neighbor copper(II) ions.     

硝基胍H迁移异构化反应动力学的从头计算研究

采用MP2/6-31G(d,p)从头计算方法优化获得硝基胍两种异构体及过渡态的几何结构,在相同水平上计算了各驻点频率,并进行了IRC分析.利用过渡态理论,计算了在200~1773K的H迁移异构化反应的速率常数.结果表明,β型硝基胍中形成大范围的离域大∏键,存在显著的共轭效应使其比α型稳定,能量比α型低28.16kJ/mol;硝基胍由α型向β型H迁移异构化反应的活化能为132.95kJ/mol.298K时速率常数为1.99×10-11s-1,平衡常数为1.00×105;硝基胍的异构化是一个典型的同面H迁移放热反应,随温度升高,平衡常数逐渐减小,不利于α型通过H迁移向β型转化.     

Couette-Str?mung thixotroper Substanzen bei Schwingung

Ohne Zusammenfassung     

New Cyclolignan Esters and Their Antidiabetic Activitity from the Root of Rhus semialata

Rhus semialata is one of five Rhus species (Anacardiaceae), distributed in the island of Taiwan. In the early days,the pericarp of R. semialata was commonly used as a substitute of salt by indigenous mountain people. The root of it is also a folk herb for treating diarrhea, spermatorrhea and malaria.[1,2] This paper describes the isolation and structural elucidation of new cyclolignan esters 3 and 4, and two known compounds: cyclolariciresinol (1) and lynoiresinol (2) isolated from the n-butanol extract of R. semialata.     

Chiral extrapolation of nucleon wave function normalization constants

Within the framework of two-flavor covariant baryon chiral perturbation theory we have expressed the Chernyak-Zhitnitsky, Ioffe and Dosch currents in terms of chiral fields to provide leading one-loop extrapolation formulae for the leading and next-to-leading twist normalization constants f _N , λ₁ and λ₂. Finite-volume effects due to pion loops have been taken into account. The occurring low-energy constants are fitted to data obtained from recent lattice QCD simulations in order to extract the values at the physical point.