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  • 1990-1994  (10)
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  • 1
    Electronic Resource
    Electronic Resource
    The extensional viscosity and effective thermal conductivity of a dispersion of aligned disks (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 1955-1962 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: This paper discusses the properties of a semidilute suspension of disks, for which nl3(very-much-greater-than)1 and φ(very-much-less-than)1, where n is the number of disks per unit volume, l is their large dimension, and φ is their volume fraction. The effective conductivity of a dispersion of aligned, highly conducting disks is shown to be O[k(nl3)2], where k is the conductivity of the matrix. The extensional viscosity is shown to be O[μ(nl3)2], where μ is the viscosity of the fluid. In addition, similar scaling results are shown to hold for the case of a semidilute suspension of aligned, two-dimensional slabs which are of infinite extent in the direction perpendicular to their plane of cross section. Specifically, for nl2(very-much-greater-than)1, the effective conductivity and the extensional viscosity are shown to be O[k(nl2)2] and O[μ(nl2)2] respectively, where n is now the number of slabs per unit area and l is the width of the slab. Planar extensional flow simulations of a periodic array of aligned slabs confirm the quadratic scaling for stress in the semidilute regime. The simulations also show the crossover from a linear dependence of the stress on particle concentration in the dilute regime to the quadratic, semidilute scaling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868202
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Averaged-equation and diagrammatic approximations to the average concentration of a tracer dispersed by a Gaussian random velocity field (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 887-894 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Approximate methods for predicting the spread of a passive tracer due to a Gaussian random velocity field are examined. Previous methods such as the direct-interaction approximation [J. Fluid Mech. 11, 257 (1961)] and Phythian's short-time expansion [J. Fluid Mech. 67, 145 (1975)] make predictions for the second moment of the concentration that are qualitatively consistent with numerical simulations [Phys. Fluids 13, 22 (1970)]. However, it is shown that the higher moments obtained from these approximations are incorrect. The derivations of the direct-interaction approximation using a diagrammatic expansion and the method of averaged equations are reviewed [Phys. Fluids A 1, 47 (1989)]. A higher-order (two-body) approximation is developed which makes predictions for the fourth moment that are qualitatively correct in both the short- and long-time limits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858268
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The effects of inertia on the viscoelastic Dean and Taylor–Couette flow instabilities with application to coating flows (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2415-2431 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The effects of inertia on the elastic instabilities in Dean and Taylor–Couette flows are investigated through a linear stability analysis. The critical conditions and the structure of the vortex flow at the onset of these instabilities are presented. The results reveal that the purely elastic Dean flow is destabilized by inertial effects. It is also found that inertia destabilizes elastic Taylor–Couette flow if the rotation of the inner cylinder is the flow driving force, while it stabilizes the flow driven by rotation of the outer cylinder. The mechanism of destabilization or stabilization of these viscoelastic instabilities is investigated through an examination of the disturbance-energy equation. It is shown that Dean flow is destabilized by two separate mechanisms: a purely elastic mechanism discussed previously (i.e., energy production due to the coupling of a perturbation velocity to the polymeric stress gradient in the base state) [see Phys. Fluids A 3, 1691 (1991)] and a purely inertial mechanism discussed by Dean [Proc. R. Soc. London Ser. A 121, 402 (1928)] (i.e., energy production from Reynolds stresses). It is also shown that, when rotation of the inner cylinder drives Taylor–Couette flow, the Reynolds stresses produce energy, and thus are destablizing, while for the flow driven by the rotation of the outer cylinder alone, the Reynolds stresses dissipate energy, thus stabilizing the flow. The elastic forces remain destabilizing in both modes of operation. In a second study, a pressure-driven viscoelastic coating flow over a curved surface is examined. The results demonstrate the existence of a purely elastic stationary instability in the coating flow on a concave wall which is very similar to that which occurs in viscoelastic Dean flow. It is demonstrated that the mechanisms of instability in Dean flow and the coating flow are the same, again through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858483
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2043-2046 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor–Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbance-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857886
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  • 5
    Electronic Resource
    Electronic Resource
    Viscoelastic Poiseuille flow through a curved channel: A new elastic instability (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1691-1694 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor-Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech. 218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbande-energy equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858223
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  • 6
    Electronic Resource
    Electronic Resource
    Observations of axisymmetric tracer particle orientation during flow through a dilute fixed bed of fibers (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2516-2528 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Direct microstructural evidence for net tracer particle orientation induced solely by hydrodynamic interactions in a dilute, disordered, fibrous media is reported. A dilute fixed bed of randomly placed fibers was constructed and glycerol/water suspensions of either synthetic akaganeite (βFeOOH, average aspect ratio 6.3) or hematite (αFe2O3, average aspect ratio 1.6) tracer particles were made to flow axially through the bed at prescribed flow rates. Conservative linear dichroism, a noninvasive light scattering technique, was employed to provide a direct measure of the orientational order parameter for the tracer particle population at the end of the bed. The effect of Brownian motion on the hydrodynamically induced order in the suspensions was studied over three orders of magnitude in scaled rotary Peclet number, 5〈P〈2000. The steady degree of particle alignment exhibited by each suspension as it exited the fiber bed was found to be in good quantitative agreement with theory [Phys. Fluids 31, 728 (1988); ibid. 31, 2769 (1988)]. Time scales characterizing the development of net order induced in the tracer populations were investigated and compared qualitatively to theoretically derived bounds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858193
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  • 7
    Electronic Resource
    Electronic Resource
    The average rotation rate of a fiber in the linear flow of a semidilute suspension (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 2093-2102 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Shaqfeh and Fredrickson [Phys. Fluids A 2, 7 (1990)] renormalized the multiple reflection expansion for hydrodynamic fiber interactions in a semidilute suspension, nl3(very-much-greater-than)1 and φ(very-much-less-than)1, where φ is the fiber volume fraction, n is the number of fibers per unit volume, and l is the fiber half-length. We use the results of Shaqfeh and Fredrickson to obtain the average rotation rate of a fiber in linear shear flows of a semidilute suspension. Specific results are obtained for the case where most of the fibers are oriented in a preferred direction, as occurs in simple shear and extensional flows. The correction to the O(γ(ring)) Jeffrey rotation rate [Proc. R. Soc. London Ser. A 102, 161 (1922); J. Fluid Mech. 14, 284 (1962)] due to hydrodynamic interactions is shown to be O[γ(ring)/ln(1/φ)], where γ(ring) is the shear rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857795
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  • 8
    Electronic Resource
    Electronic Resource
    The hydrodynamic stress in a suspension of rods (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 7-24 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green's function as developed in the authors' previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A 1, 3 (1989)]. The "best one-body approximation'' is used to calculate the wavenumber-dependent, ensemble-averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit unit of the previously obtained wavenumber-dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech. 46, 813 (1971)] is recovered for both orientation distributions and its relation to short range "screening'' is discussed. Corrections to this result in a "semidilute expansion'' for small volume fraction are calculated and the dependence of these corrections on orientation distribution and particle shape is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857683
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  • 9
    Electronic Resource
    Electronic Resource
    Orientational dispersion of fibers in extensional flows (1990)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1077-1093 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A kinetic theory is presented that predicts the dispersion of particle orientation, solely as a result of hydrodynamic interactions, about the principal axis of extension in uniaxial and planar extensional flows. The mean-squared displacement of the orientation vector is calculated in both the asymptotic dilute and semidilute concentration regimes. In the dilute regime (where nL3(very-much-less-than)1, with n the fiber number density and L the fiber length) it is found that the mean-squared displacement is O[nL3/ln2(r)], where r is the fiber aspect ratio. For semidilute suspensions (where nL3(very-much-greater-than)1) it is predicted that the dispersion is O[ln(nL3)/nL3]. Thus the dispersion increases as the concentration is increased from infinite dilution and then ultimately decreases in the semidilute regime. The physical reasons for this behavior are discussed and, in particular, the semidilute scaling is demonstrated to be a consequence of the short-range particle screening that develops in semidilute suspensions [Phys. Fluids A 1, 3 (1989); 2, 7 (1990)]. The effect of this orientational dispersion on the material properties of fiber composites is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.857608
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  • 10
    Electronic Resource
    Electronic Resource
    A purely elastic instability in Dean and Taylor–Dean flow (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 524-543 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear stability of the viscoelastic flow of an Oldroyd-B fluid between rotating cylinders with an applied, azimuthal pressure gradient is considered. It is found that this Taylor–Dean flow is unstable in certain flow parameter regimes even in the limit of vanishingly small Reynolds number. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These are determined in the limit as the channel width to radius of curvature becomes small. The present results reveal that the instability is a stationary mode when the pressure gradient becomes the dominant flow driving force, while it is an oscillatory instability when the shearing by the cylinder rotation is dominant. In addition, it is found that the direction of the pressure gradient controls the characteristics of the instability: A pressure gradient applied along the cylinder rotation destabilizes the flow, while if applied against the rotation, the flow is substantially stabilized. The mechanism of these instabilities is also investigated through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic, stationary instability is associated with the coupling of the perturbation velocity field to the polymeric stress gradients in the base flow. To the authors' knowledge this mechanism has not been reported elsewhere. In contrast, the mechanism for the elastic, oscillatory instability in Taylor–Dean flow involves the coupling between the disturbance polymeric stresses and the base state velocity gradients, as reported by Larson et al. [J. Fluid Mech. 218, 573 (1990)] for the elastic, oscillatory instability in Taylor–Couette flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858325
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