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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 309-355 
    ISSN: 1572-9222
    Keywords: chemically reacting flow ; continuous flow stirred tank reactor ; shadow system ; large diffusivity ; Arrhenius kinetics ; incompressible Navier–Stokes equations ; reaction–diffusion equations ; Boussinesq models ; mixed Neumann and Robin boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider the relationship between chemically reacting flows and continuous flow stirred tank reactors (CSTR). In particular, we show that in the limit as the chemical and thermal diffusivities go to infinity, the solutions of the reacting flow PDE approach the solutions to the CSTR ODE. We further show that the global attractors for the reacting flow come arbitrarily close top the CSTR global attractor as the diffusivities go to infinity. An important feature of the reacting flow model we use is Robin–Neumann boundary conditions for the chemistry and temperature, which we use to mimic the CSTR inflow and outflow terms. The key in our analysis is an examination of how the Laplacian with Robin–Neumann boundary conditions converges to the Laplacian with Neumann boundary conditions as the diffusivity goes to infinity.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 273-307 
    ISSN: 1572-9222
    Keywords: chemically reacting flow ; combustion ; Arrhenius kinetics ; incompressible Navier–Stokes equations ; reaction diffusion equations ; Boussinesq models ; strong solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we consider the existence and properties of strong solutions for a model of incompressible chemically reacting flows where reactants enter the domain, react, and then leave the domain. We show results which exactly parallel those of the Navier–Stokes equations, i.e., in two dimensions strong solutions exist for all time, and in three dimensions we show existence only for small times. In two dimensions, we also show the existence of global attractors which are compact in L 2. Rather than considering a specific set of boundary conditions, we instead state our results based on a series of assumptions, which would be proved using the boundary conditions. This allows our results to be applied directly to the two sets of boundary conditions which appear in the literature.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2617-2628 
    ISSN: 0887-6266
    Keywords: dibenzylidene sorbitol ; polymer crystal nucleation ; polypropylene ; clarifying agent ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Recent studies have demonstrated that addition of a small quantity of dibenzylidene sorbitol (DBS) to a molten polymer may result in a physical gel if conditions permit the DBS molecules to self-organize into a three-dimensional network composed of highly connected nanofibrils. If the polymer crystallizes, DBS may also serve as a nucleating agent, promoting the formation of spherulites, especially in commercially important polyolefins such as polypropylene. We examine the thermal and mechanical properties, as well as the morphological characteristics, of an isotactic polypropylene copolymer with 3 wt % ethylene upon addition of less than 1 wt % of 1,3:2,4-di-p-methylbenzylidene sorbitol (MDBS). From dynamic rheological measurements, pronounced complex viscosity increases, attributed to MDBS nanofibril network formation, are observed at concentration-dependent temperatures above the melting point of the nucleated copolymer. Transmission electron micrographs of RuO4-stained sections confirm the existence of MDBS nanofibrils measuring on the order of 10 nm in diameter and, at higher concentrations, fibrillar bundles measuring up to about 200 nm across and several microns in length. The addition of MDBS at different concentrations is also found to promote increases in optical clarity, yield strength, tensile strength, and ultimate elongation of modified copolymer formulations. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2617-2628, 1997
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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