Universal Correlation for Droplet Fragmentation in a Microfluidic T-Junction

Despite extensive research on droplet dynamics at microfluidic T-junction, for different droplet lengths and Capillary numbers, there remains limited understanding of their dynamics at different viscosity ratio. In this study, we adopt a modeling framework in a three-dimensional (3D) configuration to numerically investigate the droplet dynamics as it passes through a symmetric T-junction with varying Capillary numbers, droplet lengths, and viscosity ratios. We present a 3D regime map for the first time to demarcate the droplet breakup and no breakup regimes. Herein, we propose a simple surface equation accounting for the critical Capillary number for breakup, in terms of viscosity ratio and dimensionless droplet length. The proposed universal relationship aligns well with experimental and computational findings from the existing literature. Furthermore, we reveal a new droplet breakup characteristic at high viscosity ratio and high Capillary number where the droplet spreads almost twice its initial value before splitting. Overall, this research provides comprehensive understanding of droplet dynamics at the T-junction and has significant implications for several related applications, including the large-scale synthesis of microdroplets using microchannel networks.