Showing papers by "Yuriko Renardy published in 1997"

Core-annular flows

Abstract: This paper gives an overview of the issues posed by the science and technology of transporting heavy oils in a sheath of lubricating water. It touches on measures of energy efficiency, industrial experience, fouling, stability, models of levitation, and future directions.

Snakes and corkscrews in core annular down-flow of two fluids

Abstract: Core–annular flow of two fluids is examined at the onset of a non-axisymmetric instability. This is a pattern selection problem: the bifurcating solutions are travelling waves and standing waves. The former travel in the azimuthal direction as well as the axial direction and would be observed as corkscrew waves. The standing waves travel in the axial direction but not in the azimuthal direction and appear as snakes. Weakly nonlinear interactions are studied to see whether one of these waves will be stable to small-amplitude perturbations. Sample situations for down-flow are discussed. The corkscrews tend to be preferred when the annulus is narrow, while snakes are more likely when the annulus is wide.

Small-amplitude oscillatory forcing on two-layer plane channel flow

Abstract: The eect of oscillatory forcing as a dynamic stabilization or destabilization mechanism for two-layer plane Couette‐Poiseuille flow at low Reynolds number is studied using numerical and asymptotic methods. The flow is driven by the relative planar motion of the upper boundary and a pressure gradient in the streamwise direction. Both driving forces are composed of a steady part and small-amplitude time-periodic fluctuations. An asymptotic expansion for the growth rates for small amplitudes is developed and the correction terms are quadratic in the amplitudes. The modulations to the steady flow can have either a stabilizing or destabilizing influence depending upon the conditions of flow. Complete stabilization is possible for certain flows which are otherwise unstable owing to the viscosity stratification across the interface. The combined pressure and velocity fluctuations can have an opposite eect on the flow stability to that induced by the separate time-periodic forcing mechanisms.

Thin film core-annular flow of upper-convected maxwell liquids

Abstract: Pressure-driven pipe flow of two upper-convected Maxwell liquids in a vertical core-annular arrangement is studied. The annulus and core liquids have different relaxation times and viscosities. Weakly nonlinear evolution equations which describe the interface shape are derived. Lubrication theory is used in the annulus but not in the core. Motions periodic in the streamwise direction are addressed, with the aim of describing short-time behavior driven by capillary forces. Numerical and analytical results for the spatio-temporal dynamics are given for two subcases. In the first case, the liquids have the same viscosity. White noise non-axisymmetric initial data are found to evolve into axisymmetric motion. When axisymmetry is assumed, the evolution equation is a Kuramoto-Sivashinsky equation; the bifurcation parameter depends on the fluid elasticities, interfacial tension, Reynolds number and Weissenberg number. The second case concerns axisymmetric motions with wavelengths in the axial direction that are long compared with the annulus thickness. This asymptotic analysis places a restriction on the size of the Weissenberg number. A jump in the viscosities introduces dispersion, which may be enhanced by fluid elasticity; this can lead to a transition from an unstable regime or a chaotic regime to one in which organized traveling wave pulses move in the axial direction.