Bridging Liquid and Elastic Solid Impact Regimes Using Flexible Hydrogels

The impact dynamics of Newtonian liquid drops and rigid spheres have been extensively studied and are well understood. Bridging these two extremes requires investigating the impact of soft elastic (or viscoelastic) drops and spheres. To probe this, we perform experiments with spherical polyacrylamide (PAAm) hydrogel drops/spheres spanning a broad range of shear moduli and impact velocities on hydrophilic (plasma-treated glass) and hydrophobic (silane-coated) substrates. The transient post-impact spreading morphology and impact force are simultaneously resolved using synchronized high-speed imaging and piezoelectric force sensing. We find that the elastic number (El) is the critical control parameter governing the impact dynamics. At low elastic numbers (El < 1), impacting hydrogels exhibit a hybrid response: a liquid-rich contact foot containing dissolved polymer chains is expelled from the bulk drop and spreads independently, while the bulk drop itself undergoes viscoelastic contact-line pinning, adopting a pancake geometry at maximum deformation. In this regime, the maximum spreading factor is marginally higher on hydrophilic substrates than on hydrophobic ones. At high elastic numbers (El > 1), the formation of the contact foot is suppressed, and the deformation is well described by a neo-Hookean energy balance, yielding a maximum spreading factor that is independent of substrate wettability. Furthermore, we show that the normalized peak impact force F* saturates to a constant value consistent with the Wagner limit for El < 1, and follows a power-law scaling F*∼El^0.38 for El > 1, in close agreement with both Hertzian and neo-Hookean predictions. The peak force trends are independent of substrate wettability for both elastic number regimes. Our findings offer insight into how material and system properties can be effectively tuned to achieve optimal performance in three-dimensional (3D) bioprinting using biomaterial inks.