Viscosity ratio as a governing factor in microdroplet generation and size modulation

This study utilizes numerical methods to systematically investigate the effect of viscosity ratio on the formation dynamics and size modulation of microdroplets within cross-shaped microchannels with a contraction structure. It demonstrates that varying the viscosity ratio between the dispersed and continuous phases gives rise to three droplet formation modes: dripping, transition, and jetting. In contrast to standard cross-junction microchannels, the contraction geometry significantly enhances local shear stress and pressure differentials, resulting in a non-monotonic dependence of droplet size on viscosity ratio—exhibiting an initial decrease followed by a subsequent increase. Specifically, in the dripping mode, a higher dispersed phase viscosity reduces internal vorticity and deformation resistance, increases pressure-driven forces beyond the interfacial tension, and thereby accelerates droplet breakup to yield smaller droplets. Conversely, in the jetting mode, the high viscosity of the dispersed phase impedes deformation, elongates the breakup cycle, and ultimately increases droplet size. The flow field analysis reveals the underlying force competition mechanism that dynamically governs the droplet breakup process across regimes. Additionally, theoretical scaling relations are proposed for predicting droplet size, which is derived from the capillary number and viscosity ratio, and validated against simulation data.