Velocity jump of Newtonian droplets in viscoelastic fluids: analytical and experimental study

This study presents a combined analytical and experimental investigation into the rising dynamics of Newtonian droplets in viscoelastic fluids, focusing on discontinuous transitions in droplet velocity. Although velocity jumps have been observed in gas bubbles, this work is the first systematic investigation of the phenomenon in Newtonian droplets. Analytically, a triple-perturbation approach is developed using Reynolds ( Re ), Deborah ( De ) and capillary ( Ca ) numbers as expansion parameters. The surrounding viscoelastic medium is modelled using the nonlinear-Giesekus constitutive equation. The analysis reveals that increasing Deborah number intensifies and reorients normal stresses – particularly the polar ( $\theta$ -direction) and hoop components – along the droplet interface. These stresses migrate rearward with increasing elasticity, resulting in localised elongational flows and concentrated radial stresses near the rear stagnation point, which indicates the onset of elastic instabilities. Experimentally, Newtonian droplets are introduced into a variety of exterior fluids: (i) quasilinear Boger fluids, which are constant-viscosity viscoelastic solutions that isolate elastic effects; and (ii) a strongly nonlinear viscoelastic solution, which exhibits both high elasticity and significant shear-thinning behaviour. Equivalent Newtonian fluids of matched viscosity are also used as controls. Viscoelastic fluids are solutions of polyacrylamide in the water–glycerine mixture. Across all experiments, the dimensionless ranges were $\textit{Re}\approx 6\times 10^{-4}{-}4.59$ , $\textit{De}\approx 0.057{-}0.802$ and $\textit{Ca}\approx 0.0026{-}0.638$ , framing the scope of applicability. The experimental observations challenge the classical expectation of smooth droplet motion and demonstrate that Newtonian droplets in viscoelastic environments can exhibit sharp, weak or no velocity jumps, depending on the balance between elasticity, viscosity and deformability.