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  • 1
    Electronic Resource
    Electronic Resource
    Sedimentation of Noncolloidal Particles at Low Reynolds Numbers (1985)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Fluid Mechanics 17 (1985), S. 91-118 
    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
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.fl.17.010185.000515
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  • 2
    Electronic Resource
    Electronic Resource
    Enhanced sedimentation in vessels with inclined walls: Experimental observations (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1905-1914 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Observations made in various batch and continuously operated inclined settlers are reported. The systems considered are the so-called "low aspect ratio'' devices in which the width of the vessel is large enough such that the presence of the enclosing walls does not affect the dynamic phenomena. The principal aim of these experiments was to test the predictions of the recent theoretical papers of Shaqfeh and Acrivos [Phys. Fluids 29, 3935 (1986); 30, 960 (1987)] concerning the laminar base state convective flow and accompanying instability wave growth under conditions in which inertial effects play an important role. The observations confirm that the theory predicts various characteristics of the laminar flow both quantitatively and qualitatively and that, within the range of experimental conditions, the more recent linear stability theory qualitatively describes the salient features of the instability wave growth in these systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866205
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  • 3
    Electronic Resource
    Electronic Resource
    On the nature of the instability in buoyancy-driven flows in inclined settlers (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1156-1164 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The instability in a buoyancy-driven convective flow, which develops when solid particles in a solid–liquid suspension settle under gravity in vessels having inclined walls, is investigated on the basis of a small disturbance linear theory [A. Bers, in Handbook of Plasma Physics, edited by M. N. Rosenbluth and R. Z. Sagdeev (North-Holland, New York, 1983), p. 451], which properly takes into account the distinction between a convective and an absolute instability, as well as the physical significance of the growing spatial modes. It is shown for the case of dilute monodisperse suspensions that, in general, the flow is convectively unstable, in that it develops spatially growing waves at the interface between the suspension and the clarified fluid above it. On the other hand, due to the action of a newly discovered instability mode, the flow becomes absolutely unstable if the viscosity of the suspending fluid is reduced to a value close to that of water. Moreover, within the convectively unstable range, the growth rate of the most highly amplified two-dimensional spatial disturbances is found to increase monotonically with a decrease in the suspending-fluid viscosity, while the corresponding wavelengths are found to monotonically decrease. These results provide an excellent qualitative description of the experimentally observed interfacial instabilities in such flows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858234
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  • 4
    Electronic Resource
    Electronic Resource
    The effects of inertia on the buoyancy-driven convection flow in settling vessels having inclined walls (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 3935-3948 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The bulk-averaged equations of motion, which describe the buoyancy driven flow in particle settlers having inclined walls, are solved over a wide range of the relevant parameter space. The solution assumes that the flow is laminar, that the particle Reynolds number is small, that the suspension is monodisperse, and that the settling occurs in a parallel plate vessel whose length to width ratio is not too large. It is shown that, in the asymptotic limit, Λ→∞, where Λ is the ratio of a sedimentation Grashof number to a sedimentation Reynolds number, R, inertial effects in the flow are O(ξ1/6), where ξ is given explicitly in terms of R, Λ, the inclination angle, θ, and the dimensionless distance from the vessel bottom. Using regular and singular perturbation techniques, the asymptotic form of the equations for Λ(very-much-greater-than)1 are then solved over the entire range of ξ and the solutions are shown to reduce to those given by Acrivos and Herbolzheimer [J. Fluid Mech. 92, 435 (1979)] and by Schneider [J. Fluid Mech. 120, 323 (1982)] in the limits ξ→0 and ξ→∞, respectively. Since typically in practice Λ∼O(106–109), the present solutions give expressions for the velocity profiles and the thickness of the clear-fluid slit that forms underneath the downward facing vessel wall, which are valid for a wide class of systems of practical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865733
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  • 5
    Electronic Resource
    Electronic Resource
    Bounds on the effective properties of polydispersed suspensions of spheres: An evaluation of two relevant morphological parameters (1990)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 67 (1990), S. 6088-6098 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Expressions for the two microstructural parameters that appear in the variational third-order bounds [G. W. Milton, Phys. Rev. Lett. 46, 542 (1981)] for the effective conductivity and elastic moduli of composite media are derived analytically to first order in the sphere concentration c for random well-mixed dispersions of impenetrable spheres with an arbitrary size distribution. These relations lead to rigorous bounds on the effective properties which are exactly valid to order c2 for such models. The apparent linear behavior of the microstructural parameters up to moderately high c enables one to apply the bounds beyond second-order in c, however. Employing these results, the effect of polydispersivity on the effective properties is examined. It is worth noting that, under some conditions, polydispersivity can actually lead to a slight decrease of the shear modulus, whereas, for highly conducting particles, polydispersivity always increases the effective conductivity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.345169
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  • 6
    Electronic Resource
    Electronic Resource
    The sedimentation of nondilute suspensions in inclined settlers (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 3488-3501 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The base-state convective flows, which are set up when a nondilute sedimenting suspension is placed beneath an inclined wall, are analyzed theoretically using a two-fluid model. Their hydrodynamic stability and the corresponding spatial growth of small two-dimensional disturbances at the clear fluid–suspension interface are then determined over the entire range of the governing parameters through numerical solutions of the relevant Orr–Sommerfeld equations. Two mechanisms for the growth of instability waves at the interface are identified. The results demonstrate that the base-state flow becomes more unstable as inertial effects in the base state become more pronounced and thus, contrary to what has been suggested by earlier investigators, there is no restabilization as the base state approaches the inviscid limit. Increasing the concentration of the suspension is found to have a stabilizing effect on the two-phase interface, particularly when inertial effects dominate in the base state. Similarly, increasing the angle of inclination enhances the stability of the interface when viscous forces are dominant in the base flow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866917
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  • 7
    Electronic Resource
    Electronic Resource
    The effects of inertia on the stability of the convective flow in inclined particle settlers (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 960-973 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A linear stability analysis of the base-state convective flows, which occur in inclined particle settlers and which were studied in a companion paper by Shaqfeh and Acrivos [Phys. Fluids 29, 3935 (1986)], is described. The analysis considers the spatial growth of small two-dimensional disturbances over the entire range of the parameters θ (the angle of inclination of the vessel), ωˆ (the wave frequency), Rˆ (a stability Reynolds number), and ξ1/6 (the parameter governing inertial effects in the base flow). Numerical solutions to the relevant Orr–Sommerfeld equations for the wave growth rates and other important quantities are presented over this entire range. It is shown that, for very large values of Rˆ, these solutions approach asymptotically those of a certain set of Rayleigh equations which are also derived and solved. The results demonstrate that the base flows become most unstable when ξ1/6≈O(1), primarily owing to the development of an inviscid instability. This instability is shown to have a number of interesting characteristics including the fact that (a) it is insensitive to the inclination of the vessel, and (b) it tends to destabilize higher frequencies. In addition, it is demonstrated that, although it is very unstable for ξ1/6≈O(1), the flow restabilizes as ξ1/6→∞, as predicted by Prasad [J. Fluid. Mech. 150, 417 (1985)]. The analysis, therefore, bridges the gap between previous asymptotic results and, at the same time, resolves the existing paradox between the experimental observations of Schaflinger [Int. J. Multiphase Flow 11, 189 (1985)] and theoretical predictions. Moreover, it provides a theoretical basis for predicting the vigorous instabilities which are witnessed in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866283
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  • 8
    Electronic Resource
    Electronic Resource
    On computer generated analytic solutions to the equations of fluid mechanics. The case of creeping flows
    Amsterdam : Elsevier
    Journal of Computational Physics 12 (1973), S. 403-411 
    Details
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0021-9991(73)90161-7
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  • 9
    Electronic Resource
    Electronic Resource
    Experiments on buoyancy driven convection in non-Newtonian fluid (1970)
    Springer
    Rheologica acta 9 (1970), S. 447-455 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Experimentell wurde die auf dem Auftrieb beruhende Konvektion in horizontalen Schichten verdünnter Wasserlösungen von ionischen und nichtionischen Polyacrylamiden zwischen festen, parallelen, leitfähigen Oberflächen untersucht. Durch Bestimmung der Temperaturdifferenz an dem Punkt, an dem die Konvektion einsetzt, wurden die Viskositätswerte für die Schergeschwindigkeit Null in guter Übereinstimmung mit den Ergebnissen aus Rheogoniometermessungen ermittelt. Die Wärmeübergangseigenschaften der Lösungen und die konvektiven Stromlinienbilder erweisen sich nach diesem Punkt als sehr ähnlich einer viskosen newtonschen Flüssigkeit fürRayleigh-Zahlen bis 5 · 104. Die hier durchgeführten Experimente beziehen sich auf diesen Bereich. DieNusselt-Zahlen sind für jede gegebeneRayleigh-Zahl immer etwas größer als die für eine newtonsche Flüssigkeit mit vergleichbarer Viskosität. Außerdem war die Gleichmäßigkeit der Stromlinienbilder ausgeprägter.
    Notes: Summary Buoyancy-driven convection in horizontal layers of dilute water solutions of ionic and nonionic polyacrylamides confined between rigid, parallel, conducting surfaces was studied experimentally. By determining the temperature difference at the point where convection first sets in, values of the zero shear rate viscosity were calculated in good agreement with those obtained from rheogoniometer data. Beyond this point, the heat transfer characteristics of the solutions and the associated convective flow patterns were found to be rather similar to those of a viscous Newtonian fluid forRayleigh numbers up to 5 × 104, the range covered by the present experiments. However, theNusselt numbers at any givenRayleigh number were slightly but consistently higher than those of a Newtonian fluid of comparable viscosity. Also, the regularity of the flow patterns was more pronounced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01975415
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  • 10
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    The effects of inertia on the buoyancy-driven convection flow in settling vessels having inclined walls (1986)
    American Institute of Physics
    Details
    Publication Date: 1986-01-01
    Print ISSN: 0031-9171
    Topics: Physics
    Published by American Institute of Physics
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