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  • 1995-1999  (3)
Material
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Year
  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1942-1952 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Folding of material filaments was examined computationally in the three-dimensional flow in a cylindrical duct with helical deflectors by tracking the curvature of line elements in the flow. Two geometries were analyzed: a configuration in which the flow is globally chaotic, and an alternative geometry which has a mixture of chaotic and regular motion. The behavior of the curvature field in this complex flow geometry was in agreement with that previously observed for much simpler two-dimensional model flows [Phys. Fluids 8, 75 (1996)]. Curvature profiles along individual element trajectories indicate that an inverse relationship exists between the rates of stretching and curvature. Material elements are compressed when they are folded. After an initial transient, the mean curvature oscillates within a finite range with a periodicity matching that of the flow geometry. The spatial structure of the curvature field becomes period-independent, and the probability density functions of curvature computed for different numbers of periods collapse to an invariant, self-similar distribution without the need for scaling. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 75-83 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Material line folding is studied in two-dimensional chaotic cavity flows. Line folding is measured by the local curvature k=l×l′/||l||3, where l(q) is an infinitesimal vector in the tangential direction of the line, q is a coordinate along the line, and l′ is the derivative of l with respect to q. It is shown both analytically and numerically that folding is always accompanied by compression. The vector l′ plays a crucial role as a driving force for the stretching and folding processes. A material line is stretched when l′ is tangential to the line and it is folded when l′ is normal to the line. The spatial structure of the curvature field is computed numerically. The short-time structure of the curvature field is similar to the structure of unstable manifolds of periodic hyperbolic points, and closely resembles patterns observed in tracer mixing experiments and in stretching field computations. The long time structure of the field asymptotically approaches an entirely different time-independent structure. Probability density functions of curvature are independent of both time and initial conditions. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 43 (1997), S. 3121-3132 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The performance of the Kenics static mixer for mixing small streams of passive tracer into the bulk flow is investigated as a function of injection location and flow ratio. Flow ratios of 1/99 and 10/90 are simulated at nine different injection locations, and two alternative geometries are considered in addition to the standard Kenics mixer. Mixing is evaluated qualitatively by examining the spread of the tracer on cross-sectional slices from the mixer and quantitatively by computing the variation coefficient as a function of axial position. For the standard Kenics geometry, injection location strongly affects the extent of mixing only for the first few elements, after which the mixing rate is independent of injection location. In a sufficiently long mixer, material injected at any location spreads to the entire flow, but the least effective injection locations require up to four elements more than the most effective locations to achieve the same variation coefficient. A faster rate of decrease in variation coefficient is observed for a flow ratio of 1/99 us. 10/90. An alternative geometry in which the elements have 120° of twist instead of the standard 180° of twist shows a similar dependence on injection location and flow ratio, but is more energy-efficient than the standard Kenics geometry. In another alternative geometry in which all elements have the same direction of twist, segregated islands exist in the flow. For injection locations inside the segregated islands, virtually no mixing takes place; for injection locations outside of the segregated islands, the tracer spreads to the remaining flow but does not penetrate the islands.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
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