Regime-resolved scaling of droplet formation in flow-focusing microfluidic devices

Droplet generation in microfluidic flow-focusing devices is governed by competing hydrodynamic and interfacial forces whose character varies across flow regimes. Most existing scaling correlations for drop size treat individual regimes in isolation rather than within a common framework. This work addresses that gap through a systematic scaling analysis, yielding regime-specific correlations and a unified expression of the form Ld/wd≈K Cac α Wed β, where the exponents α and β encode the relative contributions of the continuous-phase capillary number Cac and the dispersed-phase Weber number Wed to the drop size Ld, scaled by the channel width wd. In the squeezing and dripping regimes, drop size depends solely on Cac (α=−1/3 and β=0), while in the jetting regime, both parameters contribute (α=−1/3 and β=1/6). These predictions are compared against three-dimensional volume of fluid-based simulations and published experimental data, with the closest agreement in the squeezing regime and progressively larger deviations in dripping and jetting. Regime maps in Cac–Cad space reveal that decreasing the viscosity ratio μr below unity or increasing the density ratio ρr above unity promotes earlier transitions to dripping and jetting. A phenomenological scaling relation between the interfacial extensional stress τxx and junction angle θ is derived, rationalizing the previously reported optimum at θ=90° for maximizing τxx and enhancing dripping efficiency. A shape deformation index is also introduced to characterize interface evolution; its cyclic period directly yields the drop formation frequency, which increases monotonically with Cac and peaks in jetting. These results provide a physically motivated organizing framework for interpreting droplet formation across regimes and for the rational design of flow-focusing microfluidic devices.