Interaction between droplets and co-flow interface in a microchannel: Droplet migration and interfacial deformation

We report hydrodynamic interaction between droplets and the interface of a pair of co-flowing immiscible streams in a microchannel revealing droplet migration and interfacial deformation. We find small droplets of confinement ratio, i.e., ratio of drop size to the suspending stream width, β<1, exhibit lateral migration - while smaller droplets of β<0.5 migrate towards the co-flow interface, unexpectedly larger droplets of 0.5<β<1 drift away from the interface. The size-based contrasting migration behavior is attributed to the interplay between the hitherto unexplored wall-directed negative lift force and the well-established center-directed noninertial lift force. We also find large droplets of β>1 cause deformation waves in an initially stable and flat interface that propagate downstream akin to traveling peristaltic waves. Numerical simulations reveal that interfacial deformation is a consequence of the distinctive pressure jumps across the co-flow interface at the upstream and downstream of a droplet. Our study reveals the amplitude of the deformation wave associated with a droplet grows spatially downstream but remains the same for a train of droplets crossing a fixed location, indicating convective instability. The effects of co-flow interfacial tension, viscosity contrast, confinement ratio, and droplet spacing on the deformation wave amplitude and its variation along the flow direction are studied. The experimental results are verified using a simple theoretical model. Our study presents an unexplored droplet-driven interfacial deformation wave that may find relevance in droplet microfluidics.