Exchange flow of two immiscible fluids and the principle of maximum flux

TL;DR

This paper investigates the maximum exchange flow of two immiscible fluids in a cylindrical tube, revealing that asymmetric configurations outperform symmetric ones in flux efficiency depending on viscosity ratios.

Contribution

It introduces a novel analysis showing that asymmetric flow configurations maximize flux, contrasting with traditional symmetric solutions in two-phase flow.

Findings

Asymmetric flow configurations outperform symmetric ones in flux maximization.

The optimal flow configuration depends on the viscosity ratio, with side-by-side being best for ratios ≤ 4.60.

Eccentric core-annular flow can achieve 51% more flux than symmetric solutions at high viscosity ratios.

Abstract

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.