Stability of Core-Annular Flow with Very Small Viscosity Ratio

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 ∈ = 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 ∈1/3. In both cases, the equations for the eigenvalues are derived, and the explicit forms for the neutral curves are given. 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. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Hu, Howard H., Thomas S. Lundgren and Daniel D. Joseph. (1990). Stability of core-annular flow with very small viscosity ratio. Physics of Fluids. Vol. 2(11). Copyright 1990 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids and may be found at http://link.aip.org/link/PFADEB/ v2/i11/p1945/s1 NOTE: At the time of publication, author Howard H. Hu was affiliated with the University of Minnesota. Currently, he is a faculty member in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/216