Liquid-liquid counter-current flow in microchannels

In large-scale process equipment, counter-current flow is achieved by exploiting differences in fluid densities. Thus almost all counter-current operations involve a gas and a liquid. In the realm of microfluidics, however, the small scales render gravity and inertia irrelevant. Is is still possible to operate in counter-current mode? As experiments involving counter-current liquid-liquid extraction have been performed successfully in microchannels, the answer must be yes. Interfacial tension must play an important role in maintaining the flow, despite opposing pressure gradients in the two phases. How exactly the balance of forces work out is now well understood. Moreover, the stability of such flows to perturbations and therefore their range of operability in the parameter space of flow rates and fluid viscosities is unknown. The goal of this project is to analyse this two-phase flow, using suitable asymptotic approximations, and to answer these open questions which are relevant to several microfluidic devices.