Collaborative Research: Integrated Experiments and Modeling for Spatial, Finite, and Fast Rheometry of Graded Hydrogels using Inertial Cavitation

Until recently, inertial cavitation—the rapid, unstable growth and collapse of bubbles—has been best known as a damaging agent in environments such as pumps, coatings, and bodily tissues. Current advances in medicine aim to harness inertial cavitation to cut tissues noninvasively using ultrasound, but this goal is limited by available data. A present challenge is that tissues and various soft material systems are complex, with interfaces and stiffness gradients along different internal directions. This award supports characterizing, modeling, and predicting the mechanical response of non-uniform soft materials subject to rapid bubble collapse and oscillation. This knowledge could be used, for example, to speed up assessment during ultrasound-based surgery and provide critical insight into mitigating injury from rapid forces. Thus, the research will not only promote the progress of science but will also advance national health, prosperity, and welfare. This project will further train students working across disciplines of fluid and solid mechanics, and materials science. The team will encourage scientific learning in a broad early-learner audience via the development of two children's books written in multiple languages and outreach activities about soft material mechanics. A single test probing ultra-high-rate and finite deformation regimes of materials simultaneously has been elusive. Prior work has established inertial cavitation rheometry as a promising candidate, but the technique restrictively assumes spherical symmetry. This project aims to leverage quantities surrounding asphericity—regarded as a problem in the original technique—as a critical metric for assessing local material gradients. A multi-perspective, ultra-high-rate microscopy platform for characterizing graded, ultraviolet-light-tunable hydrogels using bubble kinematics, and full-field deformations determined via embedded speckle plane-based digital image correlation comprise the experimental setup. Concurrently, numerical methods leveraging (a) full-field kinematic fields with simulation and (b) bubble shape perturbation information with a modified 1D-perturbation model of the governing equations of motion and conservation will establish a suite of baseline problems. Together, critical measurable quantities in the inverse calibration problem will be used to establish a fast reduced-order model for describing both material behavior and gradients therein. This approach will provide a methodology for producing linearly graded hydrogels, a database of ultra-high-rate, finite viscoelastic hydrogel behavior, upgraded inverse-calibration procedures leveraging spherical perturbations and simulations, and a reduced-order approach for fast rheology without, with, or with-coupled property gradients. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.