Origins of periodic and chaotic dynamics in microfluidic loop devices

TL;DR

This paper investigates the origins of periodic and chaotic droplet dynamics in microfluidic loop devices, proposing a conservation principle-based explanation and a method to identify periodicity, validated through experiments, simulations, and analytical models.

Contribution

It introduces a droplet spacing conservation principle and a technique to identify periodicity in microfluidic droplet systems, advancing understanding of their complex behaviors.

Findings

Periodic behavior arises from droplet conservation principles.

Aperiodic behavior occurs during transitions between periodic states.

Analytical expressions predict transition regions based on system parameters.

Abstract

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.