City College of New York, CUNY

Abstract

A two-fluid core-annular flow consists of two immiscible fluids flowing concurrently in a tube or pore, where one (the annular) wets the tube wall and surrounds the other (core). The interfacial stability of these flows has attracted attention for practically important problems such as secondary oil recovery and two-fluid flows in packed beds. The theory for such systems is well developed for straight tubes of uniform cross section, where capillarity, and viscosity and density stratification are the dominant contributions to the flow’s stability. Unfortunately, the pores in rocks and the interstices in packed beds are not uniform in cross section, and it is conceivable that this geometric non-uniformity might be as important to the flow geometry’s stability as the effects already considered. We develop a systematic approach to examine the effect of pore corrugation on the linear stability of a viscous core annular film flow in the presence of interfacial tension and viscosity stratification. By means of perturbation techniques via two small parameters, the ratio of the film thickness to the core radius, and the corrugation amplitude with respect to the film thickness, we asymptotically develop a non-trivial base flow and its corresponding linear stability.

With the solution of corrugated base flow, the system’s linear stability is determined by the core-annulus interface’s evolution equation, which contains contributions from the corrugated base flow. We employ Floquet-Bloch analysis to obtain the eigenvalue spectra and compare them with the interfacial dynamics given by direct numerical solution of the interfacial evolution equation for a variety of initial conditions and parameters. Results reveal that the wavelength of the initial disturbance to the interface are modified due to interaction with the wall’s corrugation. In contrast to the case of straight tube, an initial disturbance whose wavelength is shorter than the circumference of the undisturbed fluid-fluid interface can also leads to instability due to the unstable higher wall corrugation harmonics excited by the initial disturbance.