Alignment and aggregation effects in suspensions of spheres in non-Newtonian media

Summary Photographs are presented which demonstrate the alignment and aggregation effects in suspensions of spheres in viscoelastic media. Pictures were taken from plane shear flows between two glass plates. The spheres line up in flow direction and come into contact. If the spheres touch, the rotation ceases. This alignment and association was also observed and photographed in elongational and in pipe flow.The alignment process could be related to normal stresses. A further observation is that the ratio of the first normal stress difference to the shear stress is the determining parameter.Practical aspects are mentioned.

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Zusammenfassung Ausrichtungs- und Aggregationseffekte in Kugelsuspensionen mit viskoelastischer Suspensionsflüssigkeit werden aufgezeigt. Bei einem Teil der Bilder handelt es sich um Mikroaufnahmen von ebenen Schichtenströmungen zwischen zwei Glasplatten. Die Kugeln richten sich in Strömungsrichtung aus und kommen einander näher. Bei Berührung verschwindet die Rotationsgeschwindigkeit der Kugeln. Diese Ausrichtung und Anlagerung wird auch in der Dehn- und Rohrströmung beobachtet.Der Orientierungsvorgang ist ein Normalspannungseffekt. Nicht die absolute Höhe der ersten Normalspannungsdifferenz, sondern das Verhältnis der ersten Normalspannungsdifferenz zur Schubspannung ist der wesentliche Parameter.Auf praktische Folgerungen wird kurz hingewiesen.

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With 7 figures in 11 details     

PHOTOFRAGMENTATION OF PHOTOTOXIC DIBENZOCYCLOHEPTADIENE ANTIDEPRESSANTS

Abstract— Abstract-The products of photochemical reaction of a family of phototoxic tricyclic antidepressants have been determined, both in the presence and absence of oxygen. Under all conditions photofrag-mentation of the phototoxic compounds is an important reaction-in some cases it is virtually the only photoreaction observed. The mechanism of photoreaction appears to involve excited state electron transfer from the side chain to give a reactive exciplex, which fragments via both radical and ionic pathways. These reactive intermediates are likely to contribute to the in vivo phototoxicity of these compounds.     

Submodular set functions,matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem

For the problem maxlcub;Z(S): S is an independent set in the matroid Xrcub;, it is well-known that the greedy algorithm finds an optimal solution when Z is an additive set function (Rado-Edmonds theorem). Fisher, Nemhauser and Wolsey have shown that, when Z is a nondecreasing submodular set function satisfying Z(?)=0, the greedy algorithm finds a solution with value at least half the optimum value. In this paper we show that it finds a solution with value at least 1/(1 + α) times the optimum value, where α is a parameter which represents the ‘total curvature’ of Z. This parameter satisfies 0≤α≤1 and α=0 if and only if the set function Z is additive. Thus the theorems of Rado-Edmonds and Fisher-Nemhauser-Wolsey are both contained in the bound 1/(1 + α). We show that this bound is best possible in terms of α. Another bound which generalizes the Rado-Edmonds theorem is given in terms of a ‘greedy curvature’ of the set function. Unlike the first bound, this bound can prove the optimality of the greedy algorithm even in instances where Z is not additive. A third bound, in terms of the rank and the girth of X, unifies and generalizes the bounds (e?1)/e known for uniform matroids and $\text{1}\text{2}$ for general matroids. We also analyze the performance of the greedy algorithm when X is an independence system instead of a matroid. Then we derive two bounds, both tight: The first one is [1?(1?α/K)^k]/α where K and k are the sizes of the largest and smallest maximal independent sets in X respectively; the second one is 1/(p+α) where p is the minimum number of matroids that must be intersected to obtain X.     

Vibrational spectroscopy at very high pressures. Part 35.1 A Raman study of K2M(CN)4, (M = Zn,Cd, Hg)

Each of the complex cyanides K₂M(CN)₄, (M = Zn, Cd, Hg), shows two high pressure first-order phase transitions which have been characterized using Raman spectroscopy. The phase changes are at 1.5 and 8.5 kbar for M = Hg, 3 and 8 kbar for M = Cd, and 4 and 14 kbar for M = Zn. It is concluded that, for each material, phase II has the trigonally-distorted spinel structure of room temperature Rb₂Hg(CN)₄, whilst phase III is probably of the hausmanite type (a tetragonally-distorted spinel).     

Heterocyclic rearrangements. Phenylhydrazones and N-methyl-N-phenylhydrazones of 3-acylisoxazoles

The reaction of 3-benzoyl-5-phenylisoxazole ( 4 ) and 3-acetyl-5-methylisoxazole ( 5 ) with phenylhydrazine and N-methyl-N-phenylhydrazine has been investigated and the reactivity of (E)- and (Z)-phenylhydrazones and N-methyl-N-phenylhydrazones has been studied.     

Reference value standards for pH measurements in 5, 15 and 30% (w/w) acetonitrile/water solvent mixtures at temperatures from 288.15 to 308.15 K

Reference value standards, pH (RVS), for 0.05 mol kg^?1 potassium hydrogenphthalate (KHPh) reference buffer solutions in 5, 15 and 30% (w/w) acetonitrile/water mixed solvents at temperatures from 288.15 to 308.15 K are determined from reversible e.m.f. measurements of the cell Pt¦H₂¦KHPh + KCl¦AgCl|Ag|Pt. Values of the first ionisation constant of o-phthalic acid (H₂Ph; benzene-1,2-dicarboxylic acid) in these mixed solvents are also determined from analogous measurements. The consistency of the results is analysed by multilinear regression of the quantity p(a_HγCl) as a function of both solution composition and temperature. The standard pH (RVS) values determined are given by the equation pH (RVS) = 4.0080 + 6.330x + 16.177x² ? 115.3x³ + 0.3089u ? 201.0ux² + 909ux³ + 13.04v, where x is the mole fraction of acetonitrile in the mixed solvent, u = z/(1 + z), v = [ln(1 + z) ? u], z = (T ? θ)/θ, and θ = 298.15 K.     

Primarite DeL p(L r), 1<p,r<∞

In this article we show thatL ^p(L ^r) is primary forp andr in ]1,+∞[. If (h _k) _k≧1 denote the Haar basis, we begin with a study of the sequence (h _k ⊗h _i) and, in particular, the space generated by a subsequence of this sequence. In the first part we study the base ofL ^p(L ^r) and in the second part we show that this space is primary.