Optimizing performance of liquid-liquid extraction in stratified flow in micro-channels

Several applications such as liquid-liquid extraction in micro-fluidic devices are concerned with the flow of two immiscible liquid phases. Two characteristic flow regimes are observed in these systems: the stratified flow and the slug flow. In this work, two phase (liquid-liquid) stratified flows in a rectangular geometry are first analyzed. The influence of physical properties, in particular the viscosity of the two liquids, on the velocity profiles is determined analytically. The flow profiles are classified in the parameter space of physical properties (viscosity ratio) and operating conditions (flow-rate ratio). Viscosity affects the shapes of the velocity profile and the dispersion of a solute in each phase. The question addressed is: can the viscosity of a fluid be exploited to improve extraction efficiency? This would then give us an extra degree of freedom to control and improve extraction efficiency when there can be more than one possible candidate for extractant. The mass transfer behavior in the liquid-liquid system is numerically simulated using both a finite-difference and a finite-volume method. This helps understanding of the role of various operating conditions as pressure drop, flow rate, etc on the behavior of the system. Our analysis can be used to establish guidelines for carrying out experiments. It is found that the effect of the difference in the shape of the flow profiles on mass transfer is not very significant for some modes of operation. The predictions of our model are compared with experimental results from the literature.