Study of the non-isothermal glass fibre drawing process

The glass fibre drawing process is simulated using a finite-element method. The two-dimensional energy and momentum equations are solved in their fully non-linear forms. These are coupled via the temperature-sensitive viscosity function. Both convective and radiative cooling mechanisms are taken into account on the filament surface. An effective emissivity of about 0.2 is found to be applicable to the drawing conditions in this paper. Even at this fairly low effective emissivity, radiation is found to be the dominant mode of cooling. The material thermal conductivity is found to have a small but definite influence on the filament profiles. Two-dimensionsl effects of the kinematic field are only significant up to a distance of about two orifice radii from the nozzle exit.The symbols in the square brackets show the dimensions of the parameters;M Mass,L Length,T Temperature,t Time. a Constant radius of a uniform cylinder [L] - A Local cross-sectional area of the filament [L ² ] - b _i Total tension applied on the filament boundary surface in thei ^th direction [ML/t ² ] - c Specific heat [L ² /t ² T] - D Local filament diameter [L] - f _i i ^th component of the body-force vector [L/t ² ] - h Surface convective heat transfer coefficient of the filament [M/t ³ T] - H Total equivalent heat transfer coefficient due to both convection and radiation [M/t ³ T] - k Thermal conductivity [ML/t ³ T] - M Mass-flow rate [M/t] - n Coordinate normal to the local filament surface [L] - Nu Local Nusselt number [–] - Average Nusselt number [–] - Q Rate of heat transfer [ML ² /t ³ ] - Volume-flow rate [ ³ /t] - r Radial coordinate [L] - R Local radius of the filament [L] - Re _x Reynolds number based on characteristic length scalex [–] - s Coordinate along the filament surface [L] - T Temperature [T] - u Radial component of the velocity [T/t] - U Free-stream velocity of a uniform flow [L/t] - v Local speed of a fluid particle defined by v = ;[L/t] - V Volume [L ³ ] - v _f Constant velocity of a filament with a uniform radius [L/t] - w Axial component of the velocity [L/t] - Average axial velocity of the fluid inside the tube [L/t] - z Axial coordinate, i.e. axial distance from the orifice exit [L] - Exponential coefficient of the viscosity function [T ^–1 ] - _ij Kronecker delta [–] - Emissivity or total hemispherical emissivity [–] - µ Viscosity [M/Lt] - µ ₀ Reference viscosity defined byµ = µ ₀ e ^–T [M/Lt] - Fluid density [M/L ³ ] - Stefan-Boltzmann constant [M/t ³ T ⁴ ] - Viscous dissipation function [M/Lt ³ ] - a Of air - a Based on the (constant) filament radius - C.L. Referred to the centre line of the filament - conv Referred to convection - D Dased on the diameter - f Referred to the filament local condition - g Referred to glass - i,j Species in multi-component systems - o Quantity evaluated at the orifice exit - R Based on the radius - rad Referred to radiation - s Evaluated at the filament surface - tot Referred to the total heat transfer from the filament surface - w Evaluated at the tube wall - Ambient condition - * Refers to non-dimensional quantities - — Indicating quantities averaged over the filament cross-section     

A Laplace transform certified reduced basis method; application to the heat equation and wave equation

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach.     

Formation of an in situ nanosilica nanomatrix via graft copolymerization of vinyltriethoxysilane onto natural rubber

Natural rubber (NR) with an in situ nanosilica nanomatrix was characterized in present work. The in situ nanosilica nanomatrix was prepared via graft copolymerization of a silane monomer, vinyltriethoxysilane (VTES), onto deproteinized NR (DPNR) in latex stage using tetrapentamine (TEPA)/tert‐butylhydroperoxide (TBHPO) as initiators. VTES conversion of more than 80% was obtained, and it depended on VTES concentration. The graft copolymer structure was characterized by Fourier transform infrared (FT‐IR), solution‐state proton nuclear magnetic resonance (¹H‐NMR), and solid‐state ²⁹Si‐NMR spectroscopy. FT‐IR analysis of the graft copolymer confirmed the formation of in situ silica particles, while solution‐state ¹H‐NMR and solid‐state ²⁹Si‐NMR revealed the partial hydrolysis of the ethoxy groups and polycondensation of the silanol groups. The formation of nanosilica particles enhanced thermal and mechanical properties of the graft copolymer. Morphology observations of the in situ nanosilica nanomatrix through scanning electron microscopy (SEM) and transmission electron microscopy (TEM) indicated that the spherical nanosilica particles form a nanomatrix surrounding NR particle. The formation of the nanomatrix was proved to enhance mechanical properties for NR materials.     

Accelerating Biphasic Biocatalysis through New Process Windows

Process intensification through continuous flow reactions has increased the production rates of fine chemicals and pharmaceuticals. Catalytic reactions are accelerated through an unconventional and unprecedented use of a high‐performance liquid/liquid counter current chromatography system. Product generation is significantly faster than in traditional batch reactors or in segmented flow systems, which is exemplified through stereoselective phase‐transfer catalyzed reactions. This methodology also enables the intensification of biocatalysis as demonstrated in high yield esterifications and in the sesquiterpene cyclase‐catalyzed synthesis of sesquiterpenes from farnesyl diphosphate as high‐value natural products with applications in medicine, agriculture and the fragrance industry. Product release in sesquiterpene synthases is rate limiting due to the hydrophobic nature of sesquiterpenes, but a biphasic system exposed to centrifugal forces allows for highly efficient reactions.     

Synthesis,structure and in vitro cytotoxicity testing of some 2‐aroylbenzofuran‐3‐ols

Five 2‐aroyl‐5‐bromobenzo[b]furan‐3‐ol compounds (two of which are new) and four new 2‐aroyl‐5‐iodobenzo[b]furan‐3‐ol compounds were synthesized starting from salicylic acid. The compounds were characterized by mass spectrometry and ¹H NMR and ¹³C NMR spectroscopy. Single‐crystal X‐ray diffraction studies of four compounds, namely, (5‐bromo‐3‐hydroxybenzofuran‐2‐yl)(4‐fluorophenyl)methanone, C₁₅H₈BrFO₃, (5‐bromo‐3‐hydroxybenzofuran‐2‐yl)(4‐chlorophenyl)methanone, C₁₅H₈BrClO₃, (5‐bromo‐3‐hydroxybenzofuran‐2‐yl)(4‐bromophenyl)methanone, C₁₅H₈Br₂O₃, and (4‐bromophenyl)(3‐hydroxy‐5‐iodobenzofuran‐2‐yl)methanone, C₁₅H₈BrIO₃, were also carried out. The compounds were tested for their in vitro cytotoxicity on the four human cancer cell lines KB, Hep‐G2, Lu‐1 and MCF7. Six compounds show good inhibiting abilities on Hep‐G2 cells, with IC₅₀ values of 1.39–8.03 µM.     

Metabolic pathway elucidation towards time- and dose-dependent electrophoretic screening of stable oxidative phenolic compounds

This study demonstrates an untested link between model phenolic compounds and the formation/electrophoretic separation of stable urinary metabolites. Sterically encumbered carbonyl groups were examined, and mass determination was used to confirm the presence and stability of two oxidative metabolites of pentachlorophenol: tetrachloro-1,2-benzoquinone and tetrachloro-1,4-dihydroquinone. Subsequently, baseline resolved separation of pentachlorophenol and the two oxidative metabolites was demonstrated under the following conditions: 75 mM sodium tetraborate buffer (pH?=?8.5) with 5 % methanol and 50 mM SDS, +10.0 kV running voltage, injection time?=?5.0 s, effective capillary length?=?55 cm, and run temperature?=?20 °C. Results not only provide key metabolic inferences for pentachlorophenol, they also exhibit improvements in the ability to separate and detect changes in urinary metabolites in response to phenolic-related exposure.

Forward and Pullback Dynamics of Nonautonomous Integrodifference Equations: Basic Constructions

In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an aperiodic influence on the models leading to nonautonomous integrodifference equations. In order to capture their long-term behaviour comprehensively, both pullback and forward attractors, as well as forward limit sets are constructed for general infinite-dimensional nonautonomous dynamical systems in discrete time. While the theory of pullback attractors, but not their application to integrodifference equations, is meanwhile well-established, the present novel approach is needed in order to understand their future behaviour.

     

Quasi-injective modules withacc ordec on essential submodules

Research supported by the Alexander von Humboldt-Stiftung.     

Characterization of iron counter-ion environment in bulk and supported phosphomolybdic acid based catalysts

Extended X-ray absorption fine structure (EXAFS) was used to characterize the environment of iron counter-cations in Keggin type phosphomolybdic compounds used as catalysts for oxidation reactions. Iron doped compounds corresponding to bulk acid and to acid supported on the cesium salt were prepared and studied. Iron formed hexa-hydrated complex of both Fe³⁺ and Fe²⁺ in the bulk acid, whereas it was present as Fe(OH)₂⁺ hydroxy-cations in the acid supported on the cesium salt. Upon heating the hexa-hydrated complex lost one molecule of water to bind to the Keggin anion through a terminal oxygen. (Fe-O-Mo bond). The environment of the iron hydroxy-cation changed upon heating while its closer coordination append to remained unchanged.