What is it about?
Water displacing oil is an inherently unstable process. Attempting to sweep an oil-filled reservoir (here, the region between two closely spaced rigid plates) leads to an unpredictable pattern of water and oil displacements. However, if the flow is in a deformable channel (for example, one plate is replaced by an elastic sheet), a "clean sweep" is possible. This paper addresses the mathematical theory of the stabilization process in a deformable geometry.
Why is it important?
The fluid flow between two closely spaced plates is a well known lab model of a porous medium. Water displacing oil (or, more generally, a less viscous displacing a more viscous fluid) is a process common to every type of secondary oil recovery. The inherent instability of this process leads to inefficiencies in recovering fossil fuels. Understanding the physics and mathematics of when the process can lead to a "clean sweep" of a reservoir is critical as we enter "the energy century".
The following have contributed to this page: Prof. Ivan C Christov