Impact dynamics of flexible hydrogels on solid substrates of different wettabilities

Abstract

In this work, 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, yielding an elastic number El variation of five orders of magnitude. Transient spreading morphology and impact force were simultaneously resolved using synchronized high-speed imaging and piezoelectric force sensing. At low elastic numbers ($El < 1$), impacting hydrogels exhibit a hybrid poroelastic response: a liquid-rich contact foot is expelled from the polymer network and spreads independently, while the bulk drop undergoes viscoelastic contact-line pinning into a pancake geometry at maximum deformation. At high elastic numbers ($El > 1$), contact foot spreading is suppressed, and deformation is accurately described by a neo-Hookean energy balance, yielding a maximum spreading factor independent of substrate wettability. Further, we show that the normalized peak impact force $F^*$ collapses to a constant value consistent with the Wagner limit for $El < 1$ and follows a power-law scaling $F^* \sim El^{0.38}$ for $El > 1$, in close agreement with both Hertzian and neo-Hookean predictions, and independent of substrate wettability. Furthermore, we highlight that post-impact retraction is suppressed across nearly the entire parameter space due to adsorbed polymer chains anchoring the receding gel network to the substrate, producing circumferential ridge instabilities; rebound occurs only when elastic restoring forces overcome the work of adhesion.