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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 1749-1756 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We show that for shear flow of an upper convected Maxwell fluid with small but nonzero slip velocity, an increasing dependence of the slip velocity on the elastic normal stress in the flow direction leads to short wavelength flow instability at sufficiently high Weissenberg number ((approximately-greater-than)10). Pressure-dependent slip can also lead to instability, but only at unrealistically large Weissenberg number. If the slip velocity depends only on shear stress, then the flow is always stable. These analytical results are valid in a specific asymptotic limit, but are independent of the specific form of the model for slip. Numerical results for specific, phenomenological slip models and the Phan-Thien–Tanner bulk constitutive model show that the results are robust in the presence of nonlinear viscoelasticity. The scaling of the critical shear stress for instability with modulus and molecular weight and of the distortion period with polymer relaxation time are qualitatively consistent with experimental observations of the sharkskin instability in linear polyethylenes. The results may also have some relationship to the recent experimental observation of short wavelength instability in plane Couette flow of an entangled solution with wall slip. © 1999 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 2823-2836 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: When a chemical reaction is carried out on a catalytic ribbon, the spatial average temperature of which is kept constant by electrical heating, spatiotemporal temperature patterns form when the uniform steady state is unstable at the set temperature. Numerical simulations reveal periodic and aperiodic patterns of moving pulses, "breathing'' pulses, or stationary and oscillatory fronts. The transitions between some of these patterns are intricate and proceed via global bifurcations. Bifurcation maps of parameter regions leading to specific patterns are used to gain insight into pattern formation and organization of these parameter regions. The relations among the dynamics of the uncontrolled system, the ribbon length, and the selected pattern are discussed. Similar patterns are expected to evolve in other reaction–diffusion systems subject to control of space-averaged properties.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 3045-3055 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We investigate the centrifugal instability of a pair of radially stratified immiscible liquids in the annular gap between concentric, corotating cylinders: two-fluid Taylor–Couette flow. Experiments show that a two-layer flow with a well-defined interface and Taylor vortices in each phase can be obtained. The experimental results are in good agreement with predictions of inviscid arguments based on a two-phase extension of Rayleigh's criterion, as well as with detailed linear stability calculations. For a given geometry, the most stable configuration occurs for fluids of roughly (exactly in the inviscid limit) equal dynamic viscosities. For fluids with sufficiently low viscosity, we also experimentally observe another instability that is evidently the two-fluid analog of the instability of a thin film of liquid coating the inside of a rotating drum. © 1998 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 9 (1999), S. 154-163 
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. © 1999 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2382-2393 
    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.
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 97 (1993), S. 889-894 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 97 (1993), S. 7564-7571 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 9996-10010 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have investigated the ability of a simple phenomenological theory to describe the behavior of symmetric diblock copolymer thin films confined between two hard surfaces. Prior knowledge of the morphology in the confined films is crucial for applying this theory to predict the phase diagram of such systems. Taking advantage of our observations in Monte Carlo simulations, we use the theory to construct phase diagrams for thin films confined between patterned-homogeneous surfaces, and obtain good agreement with our results of simulations. Two conditions are essential for obtaining long-range ordered perpendicular lamellae: a lower stripe-patterned surface with the surface pattern period Ls comparable to the bulk lamellar period L0, and an upper neutral or weakly preferential surface. We have also examined the undulation of perpendicular lamellae between two hard surfaces. For the cases of two homogeneous (preferential) surfaces and patterned-preferential surfaces, our calculations using the phenomenological theory indicate that the amplitudes of the undulation are on the same order of magnitude as observed in our Monte Carlo simulations, and are one order of magnitude larger than previously reported. The theory, however, is unable to capture the shape of the undulation. For the case of patterned-neutral surfaces, we find that an earlier analysis is unable to yield the undulations that would stabilize the perpendicular lamellar morphology. We have addressed this issue and obtained undulations that are consistent with our observations from Monte Carlo simulations. © 2000 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 294-303 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We computationally investigate the stability of a pair of radially stratified immiscible liquids undergoing countercurrent axial flow in the annular gap between rapidly corotating coaxial cylinders: two-fluid Taylor-Couette flow with counterflow. A simple analysis determines conditions under which a nearly cylindrical interface is maintained in the presence of counterflow (i.e., axial pressure gradients). Stability analysis reveals that for small axial Reynolds numbers, the flow is slightly stabilized against Taylor-Couette instability, consistent with results for a single phase. At axial Reynolds numbers greater than about ten, however, the flow is susceptible to a (generally nonaxisymmetric) Kelvin-Helmholtz instability, which precedes the Taylor-Couette mode. Furthermore, new results are presented for the case without axial flow. A bifurcation to vortices that corotate with their counterparts in the other phase is found. Finally, limitations of the generalized Rayleigh criterion developed in our earlier work are elucidated. In particular, we show how it fails if one of the fluid layers is very thin. © 2000 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 2894-2900 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have simulated Brownian bead-spring chains of up to 125 units with fluctuating hydrodynamic and excluded volume interactions using the Chebyshev polynomial approximation proposed by Fixman [Macromolecules 19, 1204 (1986)] for the square root of the diffusion tensor. We have developed a fast method to continuously determine the validity of the eigenvalue range used in the polynomial approximation, and demonstrated how this range may be quickly updated when necessary. We have also developed a weak first order semiimplicit time integration scheme which offers increased stability in the presence of steep excluded volume potentials. The full algorithm scales roughly as O(N2.25) and offers substantial computational savings over the standard Cholesky decomposition. The above algorithm was used to obtain scaling exponents for various static and zero shear rate dynamical properties, which are found to be consistent with theoretical and/or experimental predictions. © 2000 American Institute of Physics.
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