On the spiral form of instability of couette flow of a viscous fluid

Summary The instability of Couette flow caused by vortices with spiral symmetry is studied; the equations of motion in a suitable spiral metric turn out to be analogous with those describing vortices with axial symmetry. The approximate solution is obtained by discretization of the differential equations. Special numerical techniques reduce drastically the dimensions of the matrices involved in the calculations. The Taylor number for transition is computed; comparisons with known results are established. The results are shown in a number of graphs.

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Sommario Si studia la forma di instabilità del moto alla Couette per vortici con simmetria a spirale. In una opportuna metrica a spirale le equazioni risultano analoghe a quelle che descrivono i vortici a simmetria assiale. La soluzione approssimata delle equazioni è ottenuta per discretizzazione mediante differenze finite, usando opportuni accorgimenti per ridurre notevolmente le dimensioni delle matrici su cui si eseguono i calcoli. Viene fatto il calcolo del numero critico di Taylor per le equazioni linearizzate in funzione dei parametri significativi e si stabiliscono confronti con risultati noti. Alcuni grafici mostrano i risultati ottenuti.

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Interaction between pentaethylene glycol n-octyl ether and poly(acrylic acid): effect of the polymer molecular weight

The effect of the polymer molecular weight on the interaction between pentaethylene glycol n-octyl ether (C(8)E(5)) and poly(acrylic acid) (PAA) has been investigated by a combined experimental strategy including tensiometry, potentiometry, calorimetry, fluorescence quenching and intradiffusion (pulsed gradient spin echo-NMR) measurements. PAA samples with an average molecular weight varying in a wide range (M (w)=2000, 100,000, 250,000, and 450,000) have been considered. The measurements have been performed at constant polymer concentration (0.1% w/w) with varying surfactant molality. In all the considered systems, at low surfactant concentration, adsorption of surfactant monomers onto the polymer chain has been detected. At a C(8)E(5) molality (T(1)) independent of the PAA M (w), surfactant molecules start to aggregate, forming clusters to which the polymer co-participates. Above this concentration, the behavior of the system depends on M (w). In fact, if polymer samples with high molecular weight (M (w)100,000) are employed, all the added surfactant aggregates onto the polymer leading to the polymer saturation and, subsequently, to free micelles formation. Both saturation and free micellization occur at surfactant concentrations which are independent of the polymer molecular weight. C(8)E(5) aqueous mixtures containing PAA with low molecular weight (M (w)=2000) behaves differently, in that, above T(1), only a fraction ( approximately 20%) of the added surfactant molecules interact with the polymer, forming aggregates to which more than one PAA chain participate. In this case, C(8)E(5) free micellization occurs before polymer saturation. The experimental evidences have been interpreted in terms of the subtle balance between the various molecular interactions driving the surfactant-polymer aggregation.     

Preparation,characterization, and properties of nanofibers based on poly(vinylidene fluoride) and polyhedral oligomeric silsesquioxane

Nanostructered nanofibers based on poly(vinylidene fluoride) (PVDF) and polyhedral oligomeric silsesquioxane (POSS) have been prepared by electrospinning process. The starting solutions were prepared by dissolving both the system components in the mixture N,N‐dimethylacetamide/acetone. The characteristics of the fiber prepared, studied by scanning electron microscopy, atomic force microscopy, and wide angle X‐ray diffraction, have been compared with those of PVDF fibers. Morphological characterization has demonstrated the possibility to obtain defect‐free PVDF/POSS nanofibers by properly choosing the electrospinning conditions, such as voltage, polymer concentration, humidity, etc. Conversely, in the case of fibers based on the neat polymer, it was not possible to attain the complete elimination of beads in the electrospun nanofibers. The different behavior of the two types of solutions has been ascribed to silsesquioxane molecules, which, without influencing the solution viscosity or conductivity, favor the formation of uniform structures by decreasing the system surface tension. Concerning POSS distribution in the fibers, the morphological characterization of the electrospun films has shown a submicrometric dispersion of the silsesquioxane. It is relevant to underline that cast films, prepared by the same solutions, have been found to be characterized by POSS aggregation, thus demonstrating a scarce affinity between the two‐system components. Indeed, the peculiar solvent evaporation of the electrospun solution, which is much faster than that occurring during the cast process, prevents POSS aggregation, thus leading to the formation of nanofibers characterized by a silsesquioxane dispersion similar to that present in solution. Finally, the presence of POSS improves the electrospun film mechanical properties. Copyright © 2011 John Wiley & Sons, Ltd.     

Interaction between cationic, anionic, and non-ionic surfactants with ABA block copolymer Pluronic PE6200 and with BAB reverse block copolymer Pluronic 25R4

The interaction in aqueous solution between either the normal block copolymer poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide): Pluronic PE6200 [(EO)(11)-(PO)(28)-(EO)(11)], or the reverse block copolymer poly(propylene oxide)-poly(ethylene oxide)-poly(propylene oxide): Pluronic 25R4 [(PO)(19)-(EO)(33)-(PO)(19)] and the surfactants sodium decylsulfate, C(10)OS, decyltrimethyl ammonium bromide, C(10)TAB, and pentaethylene glycol monodecyl ether, C(10)E(5), was investigated and the aggregation behavior of these surfactants with Pluronics was compared. Surface tension measurements show that Pluronics in their non-aggregated state better interact with the anionic surfactant C(10)OS than with cationic and non-ionic ones. The presence of the two Pluronics induces the same lowering of the aggregation number of C(10)OS as shown by fluorescence quenching measurements. The number of polymer chains necessary to bind each C(10)OS aggregate has been estimated to be approximately 6 for PE6200 and approximately 2 for 25R4. Furthermore, this surfactant also induces the same increment in the gyration radius of the polymers as revealed by viscosimetry. Calorimetric results have been reasonably reproduced by applying a simple equilibrium model to the aggregation processes.     

Thermal behaviour of poly(dimethylsiloxane) hybrid silicas prepared by radiation grafting

This paper reports our investigation regarding the thermal properties of new polymer-silica hybrid materials obtained by radiation grafting. The polymer poly(dimethylsiloxane),bis(3-aminopropyl)terminated is γ-grafted on a silica gel surface. The thermal behaviour of γ-grafted hybrid materials reveals remarkable differences compared to the thermal behaviour of physically adsorbed polymers. These differences allow us to assess the ability of γ-rays to produce a polymer chemically bonded on a silica surface. The chemical bonds formed by irradiation give to the polymer a high conformational stability confirmed by DTA analysis.     

Measuring in dynamic geometry environments as a tool for conjecturing and proving

This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of measuring, based on our previous work on dragging. The modalities are illustrated through the analysis of 15–16 year-old students’ proving processes, which focuses on how these modalities relate to the moves between the spatio-graphical field and the theoretical field and may either support or hinder the proving process. The classification of the modalities of measuring enables researchers to access students’ cognitive processes and teachers to be aware of the different possible uses and interpretation of measuring, giving them tools to support students when difficulties arise.

Isotope exchange in disulfur monoxide-water charged complexes: A mass spectrometric and computational study

A hitherto unknown, isotope-exchange reaction is studied in ionized gaseous mixtures containing disulfur monoxide and water. The kinetics, mechanism, and intermediate of the reaction are investigated by experimental and theoretical methods. The reactivity of the S(2)O(*+) cation with water is investigated under a wide range of pressures ranging from 10(-7) to 10(-4) Torr, by FT-ICR, TQ, and high-resolution CAD mass spectrometry. In the high-pressure limit the reaction proves to be a route to strongly bound sulfur-containing species.