Physics – Fluid Dynamics
Scientific paper
2009-12-04
Physics
Fluid Dynamics
there is companion experimental paper
Scientific paper
The steady, coaxial flow in which two immiscible, incompressible fluids move past each other in a cylindrical tube has a continuum of possibilities due to the arbitrariness of the interface between the fluids. By invoking the presence of surface tension to at least restrict the shape of any interface to that of a circular arc or full circle, we consider the following question: which flow will maximise the exchange when there is only one dividing interface Gamma? Surprisingly, the answer differs fundamentally from the better-known co-directional two-phase flow situation where an axisymmetric (concentric) core-annular solution always optimises the flux. Instead, the maximal flux state is invariably asymmetric either being a `side-by-side' configuration where Gamma starts and finishes at the tube wall or an eccentric core-annular flow where Gamma is an off-centre full circle in which the more viscous fluid is surrounded by the less viscous fluid. The side-by-side solution is the most efficient exchanger for a small viscosity ratio beta less than or equal to 4.60 with an eccentric core-annular solution optimal otherwise. At large beta, this eccentric solution provides 51% more flux than the axisymmetric core-annular flow which is always a local minimiser of the flux.
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