Dean vortices-induced enhancement of mass transfer through an interface separating two immiscible liquids

Two-fluid Dean vortex flow in a coiled pipe with vanishing torsion, and its effect on the mass transfer through the liquid-liquid interface of two immiscible fluids are studied numerically. The liquids are stratified by gravity, with the denser one occupying the lower part of the pipe. The Navier-Stokes equations in both fluid layers are solved numerically by the finite volume method. The results reveal a detailed structure of the transverse flow (the Dean vortices) in coiled pipes with the dimensionless curvature 0.1. Both cocurrent and countercurrent axial flows in the fluid layers are considered. Using the flow fields predicted, the mass transfer equation is solved. It is shown that the mass transfer of a passive scalar (say, a protein with the Schmidt number of the order of 10³) through the interface can be significantly enhanced by the Dean vortices, so that the mass transfer rate can be increased by three to four times. This makes the Dean vortex flow an effective tool for mass transfer enhancement at the liquid-liquid interface. It is shown that the Dean flow provides a stronger mising than the Taylor-Couette flow. It is also shown that there exists an optimal axial flow rate in terms of this enhancement. The optimal flow corresponds to the value of the Dean number of about 180. In the countercurrent flow case the Dean vortices can split, which has a negative effect on the mass transfer enhancement. Both the cocurrent and countercurrent axial flows yield a similar enhancement effect on the interfacial mass transfer rate. The problem is related to the search for novel bioseparator devices.