Forces and energy of viscoelastic droplets impacting a wall

The energy partition and impact force of viscoelastic Phan–Thien–Tanner (PTT) droplets on solid surfaces are investigated numerically across two decades of Weissenberg and Weber numbers and dynamic contact angles spanning hydrophilic to hydrophobic wetting. Simulations use xanthan-gum solutions at three polymer concentrations and the Kistler dynamic contact-angle model. Viscous dissipation overwhelmingly dominates the energy budget, with elastic energy storage well below 1 % (instantaneous maximum ≈0.06%), extending the Newtonian half-rule for kinetic-energy partitioning to the viscoelastic regime. The inertia-driven first peak force is essentially independent of surface wettability, whereas the retraction-driven second peak force appears only on neutral or hydrophobic surfaces and below a critical elasticity number of approximately 50. We introduce an effective Reynolds number built on the rate-dependent PTT shear viscosity evaluated at the impact shear rate. Plotted against this effective Reynolds number, the first peak forces from all three fluids and three wettabilities collapse onto a single master curve with an inertial plateau, a shear-thinning viscous correction, and a capillary correction in the Weber number. Replacing the Ohnesorge number by its effective counterpart recovers one-to-one agreement with the recent Newtonian energy-budget theory. The second peak force follows an empirical power law in the effective Reynolds number that approaches the Newtonian asymptote at high values but is not universal across fluids (per-fluid R2 ≈ 0.2 for the weakest solution near the existence boundary), reflecting the sensitivity of the retraction-driven Worthington jet to interface topology. Together these results provide a physics-informed prediction framework for the peak impact forces of viscoelastic drops.