A Regime-Based Theoretical and Visualization Framework for Droplet Formation in Microfluidic Co-Flow Systems

Droplet formation in microfluidic co-flow systems is essential for producing controlled emulsions in biomedical, pharmaceutical, chemical, and materials applications. Despite extensive studies of a wide range of operating conditions, existing predictive and nondimensional relations are generally restricted to specific flow regimes and physical mechanisms. In this study, we develop a regime-based theoretical and visualization framework for predicting droplet generation across three representative co-flow regimes: dripping, narrowing jetting, and widening jetting. The proposed framework combines force-balance and mass-conservation principles to derive explicit analytical expressions for droplet size and droplet-generation frequency in terms of key dimensionless parameters, including the outer capillary number, viscosity ratio, and flow-rate ratio. For dripping, droplet size decreases with increasing outer capillary number. In narrowing jetting, droplet size decreases while generation frequency increases due to jet stretching and thinning. In widening jetting, droplet size increases with flow-rate ratio. In addition, the influence of the viscosity ratio weakens as the value increases. The models are validated against experimental data from the literature and show good agreement in predicting droplet size and frequency across multiple flow regimes and operating conditions. This work provides a physics-guided, regime-aware reduced-order framework for analyzing and designing microfluidic co-flow droplet-generation systems.