The weakly nonlinear interfacial stability of a core-annular flow in a corrugated tube

Hsien-Hung Wei, David S. Rumschitzki

研究成果: Article同行評審

19 引文 斯高帕斯(Scopus)

摘要

A core-annular flow, the concurrent axial flow of two immiscible fluids in a circular tube or pore with one fluid in the core and the other in the wetting annular region, is frequently used to model technologically important flows, e.g. in liquid-liquid displacements in secondary oil recovery. Most of the existing literature assumes that the pores in which such flows occur are uniform circular cylinders, and examine the interfacial stability of such systems as a function of fluid and interfacial properties. Since real rock pores posses a more complex geometry, the companion paper examined the linear stability of core-annular flows in axisymmetric, corrugated pores in the limit of asymptotically weak corrugation. It found that short-wave disturbances that were stable in straight tubes could couple to the wall's periodicity to excite unstable long waves. In this paper, we follow the evolution of the axisymmetric, linearly unstable waves for fluids of equal densities in a corrugated tube into the weakly nonlinear regime. Here, we ask whether this continual generation of new disturbances by the coupling to the wall's periodicity can overcome the nonlinear saturation mechanism that relies on the nonlinear (kinematic-condition-derived) wave steepening of the Kuramoto-Sivashinsky (KS) equation. If it cannot, and the unstable waves still saturate, then do these additional excited waves make the KS solutions more likely to be chaotic, or does the dispersion introduced into the growth rate correction by capillarity serve to regularize otherwise chaotic motions? We find that in the usual strong surface tension limit, the saturation mechanism of the KS mechanism remains able to saturate all disturbances. Moreover, an additional capillary-derived nonlinear term seems to favour regular travelling waves over chaos, and corrugation adds a temporal periodicity to the waves associated with their periodical traversing of the wall's crests and troughs. For even larger surface tensions, capillarity dominates over convection and a weakly nonlinear version of Hammond's no-flow equation results; this equation, with or without corrugation, suggests further growth. Finally, for a weaker surface tension, the leading-order base flow interface follows the wall's shape. The corrugation-derived excited waves appear able to push an otherwise regular travelling wave solution to KS to become chaotic, whereas its dispersive properties in this limit seem insufficiently strong to regularize chaotic motions.

原文English
頁(從 - 到)149-177
頁數29
期刊Journal of Fluid Mechanics
466
DOIs
出版狀態Published - 2002 九月 10

All Science Journal Classification (ASJC) codes

  • 凝聚態物理學
  • 材料力學
  • 機械工業

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