Motion and deformation of migrating compound droplets in shear-thinning fluids in a microcapillary tube

The deformation dynamics of a moving compound droplet inside a microcapillary tube is investigated in Newtonian and non-Newtonian ambient fluids. The numerical method used is a ternary phase-field model to determine the temporal evolution and the subsequent hydrodynamics of compound droplets traveling inside a microcapillary tube. By solving the axisymmetric momentum equations, the compound droplet movement is identified by tracing the spatiotemporal evolution of a pair of two deformable interfaces. Results indicate that the rheological properties of the continuous phase significantly influence the compound droplet characteristics. The position of the center of the mass of both inner and outer drops along the tube axis increases linearly in a Newtonian ambient fluid while it is nonlinear in a non-Newtonian medium, and the deviation from the linear behavior increases as the concentration of the polymer solution increases. These distinct behaviors occur after a particular normalized time (t*, which is normalized with R/Uavg in which R is the radius of the tube and Uavg is the average inlet velocity) during the early stages of droplet formation (t*∼1). The migration of the compound drop inside a Newtonian fluid approaches a relatively constant velocity after a specific time of the initial movement. Conversely, the movement velocity of both drops increases gradually until the pinch-off moment in non-Newtonian fluids, which means that a moving compound drop has an accelerative motion in all stages of movement in non-Newtonian fluids. The findings presented here are essential for employing compound droplets in droplet microfluidic systems for biological applications.