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  • 1
    Electronic Resource
    Electronic Resource
    FLUID MECHANICS OF SPIN CASTING OF METALS (1997)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 29 (1997), S. 373-397 
    Details
    ISSN: 0066-4189
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Casting of molten metals against a spinning wheel substrate is considered. Issues of fluid mechanics divide between steady and unsteady behavior (stability). The previous work on steady casting is hung on a framework provided by the long-puddle model of planar flow casting. Heat and fluid flow interact only through the shape of the solidification front in this case. In contrast, there is little previous work concerning stability issues. Stability is discussed in a broad-brush manner using the planar flow process for illustration. Issues range from meniscus motion and resulting ribbon texture to morphological-type instabilities of the solidification front. Fundamental and applied questions arise for both steady and unsteady behavior.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fluid.29.1.373
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  • 2
    Electronic Resource
    Electronic Resource
    Contacting and forming singularities: Distinguishing examples (1999)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 9 (1999), S. 164-172 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A thin film bridge breaks in a way that starts at one equilibrium state and ends at another equilibrium state. The dynamical trajectory that carries it from connected to disconnected provides rare evidence regarding the singularity of passage through topological change. This nonequilibrium trajectory, called a "forming" flow, is discussed in an attempt to frame it within the larger class of singularities for which bounding surfaces do not remain material surfaces. As a contrast, the weaker "contacting" singularity is illustrated by a stagnation flow where material points reach the stagnation point in finite time. A classification scheme based on pathology of the nonunique Lagrangian motions is suggested. New results for the disconnection example include healing of surgery in post-disconnection simulations, different dynamical scalings of the just-disconnected components and a comparison of post-disconnection simulation to experiment. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166387
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  • 3
    Electronic Resource
    Electronic Resource
    Time-periodic thermal convection in Hele–Shaw slots: The diagonal oscillation (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2382-2393 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical simulations show that the diagonal oscillation, previously observed in Bénard convection experiments in Hele–Shaw slots, arises from an internal layer instability; an internal stagnation point is essential to the oscillation mechanism. This is contrasted with the more classical oscillation arising from a convected boundary-layer instability. From a dynamical systems viewpoint, the diagonal oscillation occurs in its purest form as a simultaneous temporal and spatial symmetry breaking (a Takens–Bogdanov bifurcation). Continuation methods yield the relevant bifurcation diagrams and show that the existence of the diagonal oscillation is robust with respect to modifications of the boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858479
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  • 4
    Electronic Resource
    Electronic Resource
    Shear stabilization of the capillary breakup of a cylindrical interface (1989)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 1926-1937 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A cylindrical interface containing a viscous liquid set into axial motion is subject to a capillary and to a surface-wave instability. Clues from previous studies suggest that, even though both mechanisms separately are destabilizing, under certain circumstances their mutual interaction can lead to a stable interface; shear can stabilize capillary breakup. These clues lead the authors to consider an axial flow through an annular cross section bounded on the inside by a rigid rod and on the outside by a deformable interface. The competition between the two mechanisms is studied through the temporal growth of infinitesimal axisymmetric and nonaxisymmetric disturbances. This examination of temporal stability shows that, indeed, for geometries corresponding to thin annular layers both instabilities can be completely suppressed—disturbances of all wavelengths decay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857518
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  • 5
    Electronic Resource
    Electronic Resource
    Transition to chaotic natural convection in tall Hele–Shaw slots (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 1929-1937 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical simulations show that natural convection in tall Hele–Shaw slots has a dynamics similar to that of the convection loop. A Hopf bifurcation followed by homoclinic explosion is the route of transition to chaotic flow. The Hopf bifurcation leads to one-sided periodic motion while the homoclinic bifurcation point is the origin of the two-sided diagonal oscillation. Periodic regimes are separated by a Lorenz-type strange attractor. The instability of an internal boundary layer is the physics underlying the diagonal oscillation. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868972
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  • 6
    Electronic Resource
    Electronic Resource
    Container geometry and the transition to unsteady Bénard convection in porous media (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 925-933 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: For convection in three-dimensional boxes of fluid-saturated porous media, an analog of the Rayleigh–Bénard problem at high Prandtl number, it is shown that cascades to time-dependent motion cannot occur within the weakly nonlinear regime for boxes up to moderate size. The convective nonlinearity forces the phase space that describes the interaction of finite-amplitude convection patterns to be globally attracting to large disturbances. In addition, the fastest growing patterns inhibit others in a way that precludes transitions to time-periodic motions. The analysis exploits a closed-form dependence on geometry for the infinite set of coefficients describing the nonlinear interactions in a representation of the governing equations by eigenfunction expansion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865687
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  • 7
    Electronic Resource
    Electronic Resource
    Suppression of the capillary instability in the Rayleigh–Taylor slot problem (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 97-102 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The classical Rayleigh–Taylor instability for an interface of finite extent is modified by two independently controlled perturbation effects. A component of gravitational acceleration tangent to the interface is imposed and the interface is subjected to a flow-induced pressure field. The stability of the flat horizontal interface when surface tension holds heavier liquid above ambient gas is considered in a 2D model problem. The two perturbations are realized by tilting the interface to the horizontal and by inducing a flow with shear. It is found that the effect of tilt angle or shear on its own is destabilizing, while together, in the right combination, they can stabilize. It is thereby shown how to extend the stability limit over the classical Rayleigh–Taylor result. The framework for the analysis is the classical unperturbed pitchfork bifurcation (codimension 2). The coefficients in the unfolding are calculated by applying the Lyapunov–Schmidt technique to a pinned deformable interface that holds a shear-induced lubrication flow. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868818
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  • 8
    Electronic Resource
    Electronic Resource
    Fluid mechanics of the planar-flow melt-spinning process (1988)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 34 (1988), S. 1673-1682 
    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 planar-flow melt-spinning process which is used to rapidly solidify metals from the molten state is shown to be dominated by the fluid mechanics of the “puddle” region even though heat-transfer limits the overall thickness of the metal ribbon product. The process is modeled to account for the hydrodynamical forces in the molten region with the influence of heat-transfer entering through a parameter measuring solidification rate relative to wheel speed. It is shown that this parameter H controls the deviation of the flow behavior from classical coating flow solutions; these solutions are recovered in a limiting case of low solidification rate. A perturbation solution in H distinguishes the melt spinning from the coating process and yields the ribbon thickness as a function of wheel-speed and the other process parameters for a class of contact-line conditions. Most interesting of these predictions is the result that under certain conditions there is a window of wheel-speeds for which there is no steady solution. The relationship of predictions with the limited available data from experiment is briefly discussed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690341011
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  • 9
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    Droplet motions fill a periodic table (2019)
    National Academy of Sciences
    Details
    Publication Date: 2019-02-21
    Description: Drawing parallels to the symmetry breaking of atomic orbitals used to explain the periodic table of chemical elements; here we introduce a periodic table of droplet motions, also based on symmetry breaking but guided by a recent droplet spectral theory. By this theory, higher droplet mode shapes are discovered and a wettability spectrometer is invented. Motions of a partially wetting liquid on a support have natural mode shapes, motions ordered by kinetic energy into the periodic table, each table characteristic of the spherical-cap drop volume and material parameters. For water on a support having a contact angle of about 60°, the first 35 predicted elements of the periodic table are discovered. Periodic tables are related one to another through symmetry breaking into a two-parameter family tree.
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Published by National Academy of Sciences
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  • 10
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    Capillarity-based switchable adhesion (2010)
    National Academy of Sciences
    Details
    Publication Date: 2010-02-03
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Published by National Academy of Sciences
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