Mechanisms Driving Fluid Transfer during Confinement-Guided Coalescence Between Drops

Generation of arrays of immobilized microfluidic droplets with variation in reagent concentration from drop-to-drop is important for a variety of biochemical and screening assays. Our laboratory showed that such gradients in chemical concentration can be achieved by coalescing diluting plugs with drops immobilized in a microfluidic parking network (Sun et al., Lab Chip, 2011). In this study, we investigate the key hydrodynamic mechanisms responsible for generation of concentration gradients in static droplet arrays, with the goal of qualitatively predicting the dilution profiles observed in experiments. We conduct simulations based on a phenomenological model that includes diffusion, advection due to circulating flow within moving plugs, enhanced material transfer due to coalescence events and gutter-flow-induced advection (GFIA), and geometry. Consistent with our model predictions, our experiments verify that gutter flows alter circulation patterns within the trap and significantly increase the rate of dilution compared to experiments where gutter flows are intentionally limited.  Furthermore, we find that the strength of GFIA is inversely related to capillary number. Our results impact the design and operation of SDAs for creating broad and predictable concentration gradients.