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  • 2000-2004  (7)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    A low-dimensional approach to nonlinear plane-Couette flow of viscoelastic fluids (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 345-365 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear stability of the one-dimensional plane Couette flow is examined for a Johnson–Segalman fluid. The velocity and stress are represented by symmetric and antisymmetric Chandrasekhar functions in space. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. For given Reynolds number and viscosity ratio, two critical Weissenberg numbers are found at which an exchange of stability occurs between the Couette and other steady flows. The critical points coincide with the two extrema of the stress/rate-of-strain curve. At low (high) Reynolds number, the flow decays monotonically (oscillatorily) toward the steady-state solution. The number and stability of the nontrivial branches around the critical points are examined using the method of multiple scales. Comparison between the approximate and the numerical branches leads to excellent agreement in the vicinity of the critical points. The influence of the higher-order modes is assessed, showing low-order convergence and good accuracy when the flow profiles are compared against existing finite-element results. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870313
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  • 2
    Electronic Resource
    Electronic Resource
    Influence of inertia, gravity, and substrate topography on the two-dimensional transient coating flow of a thin Newtonian fluid film (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 355-367 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The interplay between inertia, gravity, and substrate topography is examined in this study for the transient two-dimensional flow of a thin Newtonian film. Surface tension effect is assumed to be negligible. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The lubrication equations are solved by expanding the flow field in terms of orthonormal modes in the vertical direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. The leading-order mode is found to be clearly dominant. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on the level of fluid inertia. The wave and flow structures are examined for high- and low-inertia fluids. It is found that low-inertia fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating high-viscosity fluids. The topography of the substrate has a drastic effect on the flow. A secondary wave emerges in the presence of a bump or a depression in the substrate. The wave structure is again highly dependent on the level of inertia. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1336154
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Influence of inertia on the transient axisymmetric free-surface flow inside thin cavities of arbitrary shape (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 13 (2001), S. 3636-3651 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The influence of inertia is examined for transient axisymmetric free surface flow inside a thin cavity of arbitrary shape. The flow field is obtained by solving the lubrication equations, which are averaged over the cavity gap by expanding the velocity in terms of Chandrasekhar functions and using the Galerkin projection method. The formulation accounts for the transverse flow, as well as nonlinearities stemming from inertia and front location. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and cavity geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow. Comparison with existing results shows full qualitative agreement for cavities of various geometries and flow conditions. Inertia is found to have a significant influence on early transient behavior, leading to the development of a flow of the "boundary-layer" type upon inception. The effect of inertia is further explored by developing a multiple-scale analysis to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple-scale approach, even in the moderately small Re range. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1414312
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  • 4
    Electronic Resource
    Electronic Resource
    Influence of inertia and topography in thin-cavity flow (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 1703-1719 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The influence of inertia and cavity topography is examined for the steady-state flow inside thin cavities of arbitrary shape. The problem is closely related to the die casting process. The flow is determined by solving the thin-film equations, using a coupled spectral/finite-difference method. The flows inside flat, contracting, and modulated cavities of rectangular cross section are examined. The interplay between inertia and cavity modulation is particularly emphasized. Regions of shear and elongation are identified; their size and location are strongly dependent on inertia and cavity thickness. The flow inside a grooved cavity (of nonrectangular cross section) is also investigated. In this case, the problem reduces to Poisson's equation for the streamwise velocity component, and an exact solution is obtained, which is compared against the thin-film solution. The range of validity of the thin-film approximation is thus identified, and is influenced by the cross-section aspect ratio, the modulation (groove) amplitude and wavelength. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1465422
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  • 5
    Electronic Resource
    Electronic Resource
    Transient coating flow of a thin non-Newtonian fluid film (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 2202-2215 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The interplay between non-Newtonian effects, gravity, and substrate topography is examined in this theoretical study for the transient two-dimensional flow of a thin non-Newtonian film. The study is a continuation of the previous work by Khayat and Welke [Phys. Fluids 13, 355 (2001)], which focused on the influence of inertia on a Newtonian film. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The flow is dictated by the thin-film equations of the "boundary layer" type, which are solved by expanding the flow field in terms of orthonormal modes in the transverse direction and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on whether the fluid is Newtonian, shear thinning or shear thickening. Wave formation and propagation, as well as steady film flow are examined. It is found that shear-thickening fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating shear-thickening fluids at any level of inertia. The influence of the substrate topography has been explored in the case of undulated substrate. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1483306
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  • 6
    Electronic Resource
    Electronic Resource
    A low-dimensional approach to nonlinear plane–Poiseuille flow of viscoelastic fluids (2002)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 14 (2002), S. 1757-1767 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear stability and bifurcation of the one-dimensional plane–Poiseuille flow is examined for a Johnson–Segalman fluid. The methodology used is closely related to that of Ashrafi and Khayat [Phys. Fluids 12, 345 (2000)] for plane–Couette flow. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio, cursive-epsilon. The range of shear rate or Weissenberg number for which the base flow is unstable increases (from zero) as the fluid deviates from the Newtonian limit (as cursive-epsilon decreases). Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily when the Reynolds number is small, and monotonically at large Reynolds number (when elastic effects are dominated by inertia). © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1465425
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  • 7
    Electronic Resource
    Electronic Resource
    Influence of non-isothermal fluid properties on the growth of spherical fluid shells (2002)
    Bradford : Emerald
    International journal of numerical methods for heat & fluid flow 12 (2002), S. 142-162 
    Details
    ISSN: 0961-5539
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This numerical study explores the influence of the time dependence of material fluid parameters on the transient temperature evolution during the growth of fluid shells. The shell is spherical, the fluid is Newtonian, and the flow is induced by a constant driving pressure. The coupled heat and flow equations are solved numerically using the cobody (Lagrangian) transformation and a central difference discretization in space. The range of material values is adjusted from existing experiments. It is generally found that the variation in viscosity, surface tension and specific heat can have a significant influence on both the growth rate and temperature evolution. Thermal conductivity is found to be of little influence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/09615530210418302
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