Multilayer shearing flows of viscous liquids arise in a multitude of applications, including the generation of ocean waves by wind, the lubricated pipeline transport of viscous oils, and the manufacture of bicomponent fibers and films. The evolution of the shape of the interface is of great interest, since it affects practically important quantities such as the flux/pressure drop relation in lubricated transport and the properties of the final product in bicomponent manufacturing. In principle, many interface shapes are possible, and issues of stability and dynamics take on a crucial significance.
The paper in the Annual Reviews gives a brief overview of the issues posed by the science and technology for 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.
Experiments on core-annular flows of oil and water in a downward, gravity-driven flow have shown the emergence of cork-screw shaped waves traveling on the interface. In the final papers, the flow is examined at the onset of a non-axisymmetric instability. This poses a pattern selection problem; the bifurcating solutions are traveling 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. The corkscrews are found to be preferred when the annulus is narrow and snakes are preferred when the annulus is wide.