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  • 1
    Monograph available for loan
    Monograph available for loan
    New York [u.a.] : Springer
    Associated volumes
    Call number: 19/M 93.0569
    In: Applied mathematical sciences
    Type of Medium: Monograph available for loan
    Pages: xvii, 755 S.
    ISBN: 0387971556
    Series Statement: Applied mathematical sciences vol. 84
    Classification:
    C.3.7.
    Language: English
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 567-580 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Experiments in which vortex rings of one immiscible liquid are created in another from drops falling from rest under gravity are presented and interpreted. These rings are associated with circulations generated by viscosity and, unlike classical vortex rings which occur in miscible liquids at high Reynolds numbers, they can exist even at very low Reynolds numbers. Since the rings do not diffuse, they are well-defined. Nonetheless, there are many similarities in the dynamics of formation and flow of miscible and immiscible rings. Parameters are identified which appear to correlate the authors' observations and photographs of some of the more interesting events are shown.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 2672-2679 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Different nonlinear amplitude equations for long waves in core-annular flow are compared. Each equation has its own limits of validity that can be critically assessed by comparing the linearization of approximate and exact theories. Long wave theory gets the dispersion relation for the longest waves correctly but cannot accommodate cases like capillary instability, in which the most dangerous wave is not surpassingly long. Small gap lubrication based theories accommodate shorter waves of the size of the core when various extra conditions are satisfied, but various stabilizing mechanisms associated with inertia may not be well represented. One theory in which lubrication theory is used in the water film but not in the core captures the shear stabilization of inertia when the gap is small enough. The criterion for small enough is not uniform in the viscosity ratio and surpassingly small films are required for validity when the oil viscosity is large. The results of lubrication theory are not robust with respect to changes to larger gaps outside the regime of asymptotic validity; for example, the stabilizing effects of the inertia of the core and annulus may reverse for larger, but still small thicknesses.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 2 (1990), S. 1945-1954 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It is known that the stability problem for core-annular flow of very viscous crude oil and water is singular, the water annulus appears to be inviscid with boundary layers at the pipe wall and at the interface. In the present paper, this singular problem is treated by the method of matched asymptotic expansions using ε=m/Rα as a small parameter. There are two cases of instability corresponding to different positions of the critical point in the annulus. One case is when the critical point is far away from the interface, the other is when the critical point is close to the interface within a distance of order ε1/3. In both cases, we derive the equations for the eigenvalues, and give the explicit forms for the neutral curves. The stability problem is also treated by the modified finite element code used by Hu and Joseph [J. Fluid Mech. 205, 359 (1989); Phys. Fluids A 1, 1659 (1989)], taking into account the boundary layers at the pipe wall and at the interface. The results of the two methods agree where they overlap, but the finite element technique goes further.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 626-644 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We formulated a theory of simple mixtures of incompressible miscible liquids in terms of the mass averaged velocityu and the solenoidal volume averaged velocityW, We derived simplified equations for miscible displacement in a Hele-Shaw cell. We obtained a steady solution of these equations corresponding to displacement under gravity with prescribed values of concentration and mean normal stress at the inlet and exit of the cell. We studied the stability of this steady flow. This differs from previous works which treat the stability of unsteady miscible displacement using a quasi-static assumption and classical equations based on divu=0. In our problem, replacingu withW gives rise to a difference in the mean normal stress, which alters the pressure drop across the cell and changes the velocity of free fall. We found that the stability equations are the same in the two formulations, but the boundary conditions are slightly different; however the difference will be small if diffusion is slow or the thickness of the cell is small. The results show that steady miscible displacement in a Hele-Shaw cell is stable to long and short waves. Within certain ranges of parameters, the displacement of glycerin into water can be unstable. This instability is basically of a Rayleigh-Taylor type, regularized by diffusion. As the diffusion parameterS becomes smaller, the waves of disturbances become finer and are confined to an increasingly thin diffusion layer. Water displacing glycerin is always stable. This is due to the fact that the steady equilibrium profile is not steep enough to create a fingering instability.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 66 (1977), S. 311-344 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 58 (1975), S. 369-380 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 62 (1976), S. 323-352 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 64 (1977), S. 245-267 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Archive for rational mechanics and analysis 59 (1975), S. 359-387 
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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