A new framework for confined high-speed gas–liquid microfluidics: Developing region effect on instability

Predicting droplet generation dynamics in confined coaxial jets in droplet microfluidics can be challenging, especially for gas–liquid systems. This is particularly true when trying to assess the droplet size and generation rate based on perturbation and instrument parameter analysis. Extensive measurements of jet radii across a wide range of flow conditions suggest that the commonly held assumption that the jet is fully developed over most of its length and at droplet breakup might not be accurate for gas–liquid systems. In contrast, the entrance or developing region appears to have a substantial influence on the instability of these systems, and jet breakup frequently occurs before the jet radius reaches its fully developed value. A scaling analysis was employed to examine the developing region of confined coaxial jets. The results revealed that the length of the developing region is primarily determined by the difference between the Capillary numbers of the inner and outer flows, with a larger difference leading to a shorter distance required for the jet to converge toward its fully developed radius. The scaling results further indicate that the developing region can be divided into an inertia-controlled region near the inlet and a viscosity-controlled region downstream, referred to as region II, which occupies the major portion of the developing region. Based on the scaling results, a pseudo-fully developed assumption was introduced for region II, and a dispersion relation specifically for the developing region was proposed. The unknown coefficients arising from the scaling formulation were determined using experimentally measured regime boundaries, allowing the dispersion relation to consistently account for variations in channel geometry. Compared to existing dispersion relations derived under fully developed assumptions, this improved approach significantly enhances the accuracy of predicting jet breakup frequencies, as validated by experimental measurements.