A Local Dispersion Approach to Gas-Liquid Microfluidic Flow Instability and Droplet Formation

A theoretical model is proposed to describe the instability, regime transition, and predict the droplet generation frequency in gas-liquid droplet microfluidic systems. Gas-liquid microfluidics, unlike traditional liquid-liquid systems, achieve higher throughput and smaller droplets but introduce greater instability, resulting in high dispersion in droplet size and frequency. Therefore, a theoretical model for the instability of high-speed gas-liquid microfluidic systems is essential for better understanding, controlling, and reducing dispersion in these systems. Apparently, the Rayleigh-Plateau and Ganan-Calvo models cannot be adopted due to the presence of confined external flow and co-flow. Furthermore, Gas-liquid systems feature a longer development region in the flow direction, often extending beyond the jet length, making traditional liquid-liquid dispersion relations inapplicable. Consequently, the locality of the dispersion relation must be considered. In light of this, a scaling method was applied to derive a model for jet diameter development in the flow direction. Experimentally obtained boundaries between jetting and dripping regimes were used as data points and fitted to establish the local dispersion relation for gas-liquid systems. Using the theory of open flow instability, this dispersion relation allows for the prediction or experimental validation of characteristics such as regime and frequency.