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   Accueil > Annuaire > C. Ruyer-Quil > resume-Dietze-241014

Georg Dietze (FAST)

We consider the axisymmetric arrangement of an annular liquid film, coating the inner surface of a narrow cylindrical tube, in interaction with an active core-fluid. This configuration encompasses several flows subject to long-wave interfacial instability: (a) gravity-free films, where the Plateau-Rayleigh instability produces deformations of the fluid/fluid interface; (b) falling liquid films, developing travelling surface waves due to the Kapitza instability; and (c) pressure-driven core-annular flows, where the same occurs due to the Yih instability. Here, we introduce a low-dimensional model which is capable of capturing these mechanisms and is based on the two-phase Weighted Residual Integral Boundary Layer formalism previously applied to planar flows (J. Fluid Mech., vol. 722, 2013, pp. 348-393). Our model improves upon existing works by fully representing interfacial coupling and accounting for inertia as well as streamwise viscous diffusion in both phases. We apply this model to gravity-free liquid-film/core-fluid arrangements in narrow capillaries with specific attention to the dynamics leading to flooding, i.e. when the liquid film drains into large-amplitude collars that occlude the tube cross-section. We do this against the background of numerical calculations based on the full Navier-Stokes equations, i.e. Orr-Sommerfeld linear stability calculations and direct numerical simulations of the nonlinear two-phase flow dynamics. Thanks to the improvements of our model, we have found a number of novel/salient physical features of these flows. Firstly, accounting for inertia and full inter-phase coupling is essential to capture the temporal evolution of flooding for fluid combinations that are not dominated by viscosity, e.g. water/air and water/silicone-oil. Secondly, we elucidate a viscous-blocking mechanism that drastically delays flooding in thin films which are too thick to form unduloids. This mechanism involves buckling of the residual film between two liquid collars, generating two very pronounced film troughs where viscous dissipation is drastically increased and growth effectively arrested. Only at very long times, breaking of symmetry in this region initiates a sliding motion of the liquid film similar to observations by Lister et al. (J. Fluid Mech., vol. 552, 2006, pp. 311-343) in thin non-flooding films. This kick-starts the growth of liquid collars anew and ultimately leads to flooding. We show that streamwise viscous diffusion is essential to this mechanism. During the delayed flooding sequence, the two-phase flow generates an increasing number of vortices by subdivisions in the film-trough-region. Finally, we show that low-frequency core flow oscillations, such as occur in human pulmonary capillaries, set off the sliding-induced flooding mechanism much earlier. Here, the flow pattern displays alternating vorticity-carrying structures in-phase with the oscillating core flow.

Dernière modification : October 31 2014, 11:33:13.