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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2554-2555 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Many authors, both in quantum mechanics and signal theory, are concerned with a condition of positivity for the generalized Wigner functions. They give (and use) as necessary and sufficient the condition that the kernel be the characteristic function of another Wigner function. It is shown that the condition is not necessary, but only sufficient.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2016-05-03
    Description: We review and discuss the characteristics of dip-coating of yield stress fluids on the basis of theoretical considerations, numerical simulations of the flow in the bath, and experimental data with different materials. We show that in general, due to the yield stress, viscous dissipations are sufficiently large for capillary effects to be negligible in the process. Dip-coating with yield stress fluids is thus essentially governed by an equilibrium between viscous and gravity effects. In contrast with simple liquids, the coated thickness is uniform and remains fixed to the plate. At low velocities, it appears to tend to a value significantly smaller than the Derjaguin and Levi prediction [B. V. Derjaguin and S. M. Levi, Film Coating Theory (The Focal Press, London, 1964)], i.e., critical thickness of stoppage of a free surface flow along a vertical plate. We show that this comes from the fact that in the bath only a relatively small layer of fluid is in its liquid regime along the moving plate, while the rest of the material is in a solid regime. From numerical simulations, we describe the general trends of this liquid layer, and in particular, its thickness as a function of the rheological characteristics and plate velocity. We finally propose a model for the dip-coating of yield stress fluid, assuming that the solid volume of fluid finally fixed to the plate results from the mass flux of the liquid layer in the bath minus a mass flux due to some downward flow under gravity in the transition zone. A good agreement between this model and experimental data is found for a fluid with a yield stress larger than 20 Pa.
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
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