Hydrodynamic interaction of a tandem of Newtonian drops sedimenting in elastoviscoplastic materials

We report the results of a computational study investigating the gravity-driven motion and hydrodynamic interaction of a tandem of viscous drops sedimenting in an elastoviscoplastic material, modelled via the Saramito–Herschel–Bulkley constitutive equation. To solve the governing equations, we employ finite volume formulation coupled with a volume of fluid method. We validate our numerical setup via comparison with reported experimental results, finding satisfactory agreement in terms of terminal shapes and velocities. For a specific unequal pair of drops, we capture a critical initial separation distance that determines whether the pair coalesces or separates consistently with previous experimental findings. We observe that for small enough initial distances, the two drops are connected through a shear bridge that decreases the effective viscosity of the material in front of the trailing drop, promoting approach and coalescence. Elastic effects are found to be crucial to justify the deviation from the theoretical results obtained with inelastic viscoplastic models, both before and after the merging. We accurately predict distinct experimental phenomena, such as the formation of teardrop-shaped drops and the flow reversal behind them (negative wake). Furthermore, we conduct a comprehensive parametric analysis to examine how geometric parameters such as drop size and relative size and initial separation, along with material properties including interfacial tension, yield stress, and elastic modulus, influence interaction dynamics. These factors determine whether droplets approach or repel each other or maintain a stable separation distance.