Origin of periodic and chaotic dynamics due to drops moving in a microfluidic loop device.

Droplets moving in a microfluidic loop device exhibit both periodic and chaotic behaviors based on the inlet droplet spacing. We observe that the 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. We provide experimental, simulation, and analytical results to validate the origin of periodic and chaotic behavior.