Nanocapillary Core-Annular Flows of Immiscible Active and Non-Active Liquids Trigger External-Drive-Free Nanofluidic Liquid Transport

In this paper, we develop analytical solutions for investigating the nanocapillary core-annular transport of an active liquid and an immiscible non-active liquid. The active liquid contains active particles that show vortex defects, which trigger a circular polarization field, eventually enabling the generation of an induced pressure-driven flow inside the active fluids in the presence of an axial gradient in the activity (or the concentration of the active particles). Here we consider two separate scenarios. For the first (second) case, the active liquid occupies the core (annular) region while the non-active liquid occupies the annular (core) region. Our main finding is that for both of these cases, the active flow drives the non-active flow and can achieve a significant volume flow rate (of the non-active flow) in the presence of an appropriate strength of activity (or concentration of the active particles); therefore, such significant nanofluidic transport of the driven fluid occurs with no external driving (such as an external pressure gradient or an applied axial electric field). Also, for both of these cases, a greater thickness of the active liquid layer increases the flow strength across the entire nanocapillary but causes a nonmonotonic variation of the volume flow rate of the non-active liquid. Furthermore, for the case where the active liquid occupies the core, a larger active:non-active liquid viscosity ratio significantly enhances the overall transport; however, for the other case, the viscosity ratio has no effect. Finally, we provide our analytical results for the case where there is a finite slip at the nanocapillary walls. We find that depending on the scenario (active liquid occupying the core or the annular region), different signs of the slip lengths have different influences on the overall magnitude and direction of the velocity field in the system and the flow rate in the driven liquid.