  Droplets moving in a microfluidic loop device exhibit both periodic and
chaotic behaviors based on the inlet droplet spacing. We propose that the
periodic behavior is an outcome of a dispersed phase conservation principle.
This conservation principle translates into a droplet spacing conservation
equation. Additionally, we define a simple technique to identify periodicity in
experimental systems with input scatter. Aperiodic behavior is observed in the
transition regions between different periodic behaviors. We propose that the
cause for aperiodicity is the synchronization of timing between the droplets
entering and leaving the system. We derive an analytical expression to estimate
the occurrence of these transition regions as a function of system parameters.
We provide experimental, simulation and analytical results to validate the
proposed theory.
