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  • 1
    Electronic Resource
    Electronic Resource
    The curvature of material lines in a three-dimensional chaotic flow (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1942-1952 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.869710
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  • 2
    Electronic Resource
    Electronic Resource
    The statistics of stretching and stirring in chaotic flows (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 822-834 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The statistics of stretching and stirring in time-periodic chaotic flows is studied numerically by following the evolution of stretching of O(105) points. The ratio between stretchings accumulated by each point at successive periods is referred to as a multiplier, and the total stretching is the product of multipliers. As expected, the mean stretching of the population increases exponentially whereas the probability density function of multipliers converges—in just two periods or so—to a time-invariant distribution. There is, however, a considerable degree of order in the spatial distribution of stretching in spite of conditions of global chaos. The self-correlation of multipliers shows as well considerable structure and often there are segregated populations of points: the largest population consists of points that experience extensive stretching, efficient stirring, and have a distribution of stretching values that evolves asymptotically—in about ten periods—into a limiting time-invariant scaling distribution. The remaining points experience slow stretching and, although they also exhibit scaling behavior, are effectively segregated from the rest of the system in the time scale of our simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858013
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  • 3
    Electronic Resource
    Electronic Resource
    The curvature of material lines in chaotic cavity flows (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 75-83 
    Details
    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
    URL: http://dx.doi.org/10.1063/1.868815
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  • 4
    Electronic Resource
    Electronic Resource
    Scaling and multifractal properties of mixing in chaotic flows (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1439-1456 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Mixing (stretching and folding of fluid elements) in chaotic flows is an iterative process generating presumably self-similar distributions of stretching and striation thickness. This hypothesis is investigated using scaling and multifractal techniques for two prototypical time-periodic chaotic flows: one containing no detectable islands (egg-beater flow), the other involving sizable islands as well as no-slip boundaries (flow between eccentric cylinders). The simplest picture arises in the egg-beater flow. Stretching is well described by multifractal scaling if the very high tail of the distribution of stretchings is neglected. Different methods for obtaining the spectrum of fractal dimensions f(α) agree reasonably well, producing a time-independent self-similar distribution. On the other hand, in the flow between eccentric cylinders, the negative moments do not scale, and the spectrum f(α) is time-dependent (and therefore, it is not self-similar). Due to the extremely wide range of values of stretching, a very large number of points needs to be considered in order to characterize mixing in chaotic systems using a multifractal formalism; this suggests that more work is needed in order to understand finite-size effects and how asymptotic states are reached. However, for cases where multifractal scaling applies, it is possible to relate coarse-grained variables (e.g., intermaterial area density) to microscopic features of the flow (e.g., finite-time Lyapunov exponents).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858419
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  • 5
    Electronic Resource
    Electronic Resource
    Harmonic patterns in fine granular vibrated beds (2000)
    Springer
    Granular matter 2 (2000), S. 65-69 
    Details
    ISSN: 1434-7636
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract We examine the spontaneous formation of numerous previously unreported patterns in deep beds of fine grains vibrated at frequencies ranging from 10 to 100 Hz and accelerations ranging from 1 to 14 times gravity. Similarly to shallow beds, we find stripes, closed cells and labyrinthine patterns. In addition, we observe traveling waves, cannibalizing cells and other behaviors that are unexpected and remain unexplained. All of these patterns vary spatiotemporally, and unlike shallow bed patterns, are harmonic rather than subharmonic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100350050036
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  • 6
    Electronic Resource
    Electronic Resource
    Structure of the stretching field in chaotic cavity flows (1994)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 40 (1994), S. 1273-1286 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Stretching of material elements in time-periodic cavity flows is investigated numerically. The spatial structure of the stretching field is determined not only by nonchaotic islands and by unstable manifolds of hyperbolic periodic points, but also by singularities of the flow field at the cavity corners. For the short time scales interesting to most mixing applications, regions of very high stretching (good local mixing) are determined by unstable manifolds that pass close to the corners of the cavity. Low stretching (poor local mixing) regions are usually found both inside and near islands. In some cases, however, the unstable manifolds wrap themselves around the islands, preventing the formation of segregated low stretching subregions within the chaotic region.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690400802
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  • 7
    Electronic Resource
    Electronic Resource
    Effects of injection location, flow ratio and geometry on kenics mixer performance (1997)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 43 (1997), S. 3121-3132 
    Details
    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
    URL: http://dx.doi.org/10.1002/aic.690431202
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