(98w) Origins of Periodic and Chaotic Dynamics in Microfluidic Loop Device

The binary decision making of droplets in a microfluidic loop device produces complex spatio-temporal dynamics. It has been shown that a train of droplets entering the loop at fixed inlet spacing could exit the loop at periodic or chaotic time intervals. We observed that periodic behavior is an outcome of carrier phase mass conservation principle, which translates into a droplet spacing quantization rule. This rule implies that the summation of exit spacing is equal to an integral multiple of inlet spacing. This principle also enables identification of periodicity in experimental systems with input scatter. We find that the origin of chaotic behavior is through intermittency, which arises when drops enter and leave the junctions at the same time. We derive an analytical expression to estimate the occurrence of these chaotic regions as a function of system parameters. A network model is used to study the dynamic behavior of different inlet feeding frequencies. Using this model, a bifurcation map is generated. It is observed that the chaotic regions are observed in between islands of periodic behavior. We propose key insights regarding the behavior of droplets at bifurcations and show that these insights are not only important for the design of droplet based fluidic devices but more broadly, has relevance in understanding how decision making leads to multi-stability and memory storage in  biological networks