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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 3217-3226 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Previously reported isothermal linear stability analyses of viscoelastic Taylor–Couette flow have predicted transitions to nonaxisymmetric and time-dependent secondary flows for elasticity numbers E≡De/Re〉0.01. In contrast, recent experiments by Baumert and Muller using constant viscosity Boger fluids have shown that the primary flow transition leads to axisymmetric and stationary Taylor-type toroidal vortices. Moreover, experimentally observed onset Deborah number is an order of magnitude lower than that predicted by isothermal linear stability analyses. In this work, we explore the influence of energetics on the stability characteristics of the viscoelastic Taylor–Couette flow. Our analysis is based on a thermodynamically consistent reformulation of the Oldroyd-B constitutive model that takes into account the influence of thermal history on polymeric stress, and an energy equation that takes into account viscous dissipation effects. Our calculations reveal that for experimentally realizable values of Peclet and Brinkman numbers, the most dangerous eigenvalue is real, corresponding to a stationary and axisymmetric mode of instability. Moreover, the critical Deborah number associated with this eigenvalue is an order of magnitude lower than those associated with the nonisothermal extensions of the most dangerous eigenvalues of the isothermal flow. Eigenfunction analysis shows stratification of perturbation hoop stress across the gap width drives a radial secondary flow. The convection of base state temperature gradients by this radial velocity perturbation leads to this new mode of instability. The influence of geometric and kinematic parameters on this instability is also investigated. © 1999 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 1056-1064 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recently, based on a linear stability analysis we demonstrated the existence of a new thermoelastic mode of instability in the viscoelastic Taylor–Couette flow [Al-Mubaiyedh et al., Phys. Fluids 11, 3217 (1999); J. Rheol. 44, 1121 (2000)]. In this work, we use direct time-dependent simulations to examine the nonlinear evolution of finite amplitude disturbances arising as a result of this new mode of instability in the postcritical regime of purely elastic (i.e., Re=0), nonisothermal Taylor–Couette flow. Based on these simulations, it is shown that over a wide range of parameter space that includes the experimental conditions of White and Muller [Phys. Rev. Lett. 84, 5130 (2000)], the primary bifurcation is supercritical and leads to a stationary and axisymmetric toroidal flow pattern. Moreover, the onset time associated with the evolution of finite amplitude disturbances to the final state is comparable to the thermal diffusion time. These simulations are consistent with the experimental findings. © 2002 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 100 (1992), S. 297-305 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 31 (1992), S. 413-420 
    ISSN: 1435-1528
    Keywords: Interfacial stability ; viscoelastic fluids ; plane Poiseuille flow ; multiphase flow ; elastic instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 36 (1997), S. 345-366 
    ISSN: 1435-1528
    Keywords: Key words Interfacial stability ; encapsulation phenomenon ; multilayer flow ; viscoelastic flow ; flow visualization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 36 (1997), S. 367-383 
    ISSN: 1435-1528
    Keywords: Key words Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (We c ), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above We c which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above We c a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplified spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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  • 7
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 32 (1992), S. 221-230 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A critical part of any master model used to simulate or control a composite material manufacturing process is the description of resin flow through the fiber bed. We present here a review of both theoretical and experimental studies of fluid flow through porous media, including fiber beds. For the practical porosity range of interest in continuous fiber composites processing (0.3〈 ∊ 〈 0.6), the permeability cannot be accurately described using the Blake-Kozeny-Carman equation, even though the flow is Newtonian at very low Reynold's number. For aligned fiber situations, the Kozeny constant, k, deviates radically from theory, depends on bed nonuniformities, and is only constant over very narrow porosity ranges. Thus, one cannot experimentally determine k at high porosities and use this value to describe low porosity situations. Theoretical attempts, based on perfectly spaced and aligned arrays of cylinders, adequately describe the transverse permeability of ideal fiber beds in the high porosity range, but do not succeed at porosities below 0.6. For axial flow through aligned fiber beds, the theory yields permeabilities much lower than are experimentally observed throughout the entire porosity range. For randomly arranged fibers, random cylinder theory also predicts permeabilities that are significantly lower than are measured.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 36 (1988), S. 877-889 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The effects of flow history, processing temperature, and exit draw ratio have been studied for a poly(vinylidene fluoride) resin. Quantification of the stress fields and flow kinematics were described in Part I while, in this publication, attention has been addressed to the evaluation of film properties. Hot-stage and differential scanning colorimetry (DSC) analyses were used to characterize the thermal behavior; polarized light optical microscopy and electron microscopy were used to characterize the morphology; Fourier transform infrared (FTIR) and wide-angle x-ray scattering (WAXS) were used to evaluate crystal structure; and mechanical testing was used to evaluate tensile properties. Extensional melt stresses on the order of 1.4 × 106 dyne/cm2 were necessary to induce row-nucleated crystallization in undrawn samples, and in all cases, preorientation of the melt by extensional flow enhanced the efficiency of the α → β transformation with drawing. The various transformations on drawing were as follows: unoriented α to oriented superheatable α phase for draw ratio (DR) 〈 5; transformation from α to β phase for 5 〈 DR ≤ 25; transformation to more highly oriented α and β phases, DR 〉 25.
    Additional Material: 9 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 36 (1988), S. 859-876 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A numerical and experimental analysis of the melt flow history of poly(vinylidene fluoride), PVF2, in an extensional flow, film-processing geometry is presented. Numerical computations were carried out for both Newtonian and power law flow in an impinging channels die using a finite-element technique. Computations demonstrate that a strong extensional flow exists in the region from the stream impingement point to a distance about 0.75 D downstream where D is the channel height at the impingement point. Measurements of the stress fields using the technique of flow birefringence showed that in consequence of the changing flow kinematics from the stream impingement region to the downstream converging channels region, both the isochromatic and isoclinic patterns exhibit a pronounced axial positional dependence. Excellent qualitative and quantitative agreement was found between measured and calculated shear stress fields. However, large differences were exhibited between calculated and measured normal stress differences along the symmetry axis of flow. Results to be presented in a companion paper (Part II) demonstrate that the strong extensional flow which occurs in this geometry is sufficient to produce oriented, row-nucleated structures in the extruded PVF2 films.
    Additional Material: 18 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 32 (1992), S. 231-239 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Proper description of the resin flow through fibrous media is an important input to the modeling of composite manufacturing processes. Based on our conclusions in a recent review of pertinent literature (see Part I, this issue), Newtonian flow through ideal cylinder arrangements has been analyzed and measured. The analytical and numerical solutions agreed well with both our own experimental observation and those of others. Experiments with actual carbon fiber beds revealed significant deviations from ideal bed behavior. These deviations include dependence of the permeability on the nature of the permeant and the applied pressure difference, both of which make questionable the use of the Blake-Kozeny-Carman (BKC) equation to describe flow in real carbon fiber beds. Experiments that simulate the autoclave process by featuring combined permeation and consolidation of fiber beds have yielded additional dependencies of the permeability on process characteristics, such as the consolidation load and the original resin-rich areas within the fiber beds.
    Additional Material: 8 Ill.
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