Penetration of laser-induced jets into soft elastic substrates: simplified model and experiments

We study the penetration dynamics of laser-induced bullet jets into soft elastic substrates, via experiments and a simplified energy-based model that predicts the time-dependent jet penetration depth based on jet kinematics and substrate elasticity. Our model provides solutions in two variants: one using a prescribed jet velocity and another predictive formulation based on stand-off (i.e., bubble-to-free surface distance). High-speed experiments in gelatin, as a representative soft elastic material, reveal that small stand-off distances enhance bubble collapse asymmetry and produce coherent jets, while larger stand-offs suppress penetration. Model predictions show reasonable agreement with experimental data: the velocity- and stand-off-based formulations reasonably capture penetration trends. A range of experiments with bullet and re-entrant jets confirm the model's applicability across diverse jet-gelatin interactions. The model's minimal form and predictive accuracy offer a simplified foundation for optimizing cavitation-based technologies in biomedical applications, including needle-free injections, soft robotic actuation, and bioprinting.