Shear-thinning rheology and geometric asymmetry govern droplet dynamics in branched microchannels

Droplet formation and breakup in branched microchannels with asymmetric constrictions were investigated using shear-thinning xanthan gum solutions as the continuous phase and soybean oil as the dispersed phase. Experiments at concentrations of 400-1500 ppm were complemented by validated three-dimensional simulations to assess the influence of the power-law index (n) on droplet dynamics. Time-resolved analyses revealed periodic upstream pressure oscillations whose amplitude increased as n decreased, linking rheology directly to droplet size and formation frequency. Normalized droplet length data from all cases collapsed onto a single power-law curve when rescaled by the effective capillary number, providing a universal representation of breakup dynamics. With increasing n, droplet volumes grew while front-tip velocities declined, demonstrating the coupled effect of rheology on both size and transport. Velocity fields further confirmed flatter core profiles in shear-thinning systems, characteristic of power-law fluids, in contrast to the parabolic distributions observed for Newtonian flows. Collectively, the results establish how shear-thinning rheology and downstream asymmetry interact to control droplet breakup and partitioning, offering design principles for predictive scaling in multiphase microfluidics.