Parsimonious inertial cavitation rheometry via bubble collapse time

TL;DR

The paper introduces parsimonious inertial microcavitation rheometry (pIMR), a rapid framework to characterize local viscoelastic properties of soft materials by focusing on the time to first laser-induced cavity collapse. Building on a Keller–Miksis bubble dynamics model with viscoelastic stress contributions, it combines a modified Rayleigh collapse time approach with an energy-balance analysis to derive a tractable, approximate collapse time that incorporates bubble pressure, surface tension, compressibility, and material rheology. By fitting collapse-time predictions to a batch of LIC experiments, pIMR identifies the simplest constitutive model and corresponding parameters (G, μ, τ1) with dramatically reduced post-processing time (seconds rather than hours) and demonstrates applicability to viscous fluids (water-PEG) and soft hydrogels (PAAm). The work significantly lowers the computational and optical requirements for high-rate materials characterization, enabling near real-time, localized rheometry and offering a pathway to hybrid approaches that couple pIMR speed with IMR accuracy for more complex material behaviors.

Abstract

The rapid and accurate characterization of soft, viscoelastic materials at high strain rates is of interest in biological and engineering applications. Examples include assessing the extent of tissue ablation during histotripsy procedures and developing injury criteria for the mitigation of blast injuries. The inertial microcavitation rheometry technique (IMR, Estrada et al., 2018) allows for the characterization of local viscoelastic properties at strain rates up to 1E8 per second. However, IMR now typically relies on bright-field videography of a sufficiently translucent sample at >1 million frames per second and a simulation-dependent fit optimization process that can require hours of post-processing. Here, we present an improved IMR-style technique, called parsimonious inertial microcavitation rheometry (pIMR), that parsimoniously characterizes surrounding viscoelastic materials. The pIMR approach uses experimental advancements to estimate the time to first collapse of the laser-induced cavity within approximately 20 ns and a theoretical energy balance analysis that yields an approximate collapse time based on the material viscoelasticity parameters. The pIMR method closely matches the accuracy of the original IMR procedure while decreasing the computational cost from hours to seconds while potentially reducing reliance on ultra-high-speed videography. This technique can enable nearly real-time characterization of soft, viscoelastic hydrogels and biological materials with a numerical criterion assessing the correct choice of model. We illustrate the efficacy of the technique on batches of tens of experiments for both soft hydrogels and fluids.

Figures (7)

• Figure 1: Schematic representation of the spherical bubble considered in the bubble dynamics and approximate collapse time models. The nearly incompressible, viscoelastic material surrounding the bubble is modeled as a finite deformation, standard linear solid (SLS) described by a ground-state elastic shear modulus $G$, a viscous shear modulus $\mu$, and a relaxation time scale $\tau_1$. When $\tau_1\to{0}$, the SLS model becomes a Kelvin--Voigt model.
• Figure 2: The experimental setup to generate, record, and profile single laser-induced microcavitation (LIC) bubble events in soft materials. The setup uses a combination of a class-4, frequency-doubled Q-switched 532nm Nd:YAG pulsed laser, a high-speed imaging camera, and a spatial light modulator. The time of the first bubble collapse is estimated according to the shock wave, which was visualized by shadowgraph and ghost imaging techniques.
• Figure 3: Combined effect of viscoelasticity, bubble content pressure, weak compressibility, and surface tension on the bubble collapse time in a Kelvin--Voigt material with $\{ G = 10kPa, \mu = 0.1Pas \}$ across typical range of $R_{\max}$ and $\Lambda_{\max}$ in LIC experiments.
• Figure 4: Comparison of measured vs. predicted collapse time for the 80% (v/v) concentration water-PEG mixture characterized, with $n = 20$ samples. The collapse time during LIC is larger than the predicted value for an inviscid material, suggesting the dominance of viscosity over elasticity during the collapse process.
• Figure 5: Bubble dynamics corresponding to representative experiment data (hollow squares) and the inverse characterization solutions: (a) water-PEG 8000 mixture, (b) PAAm gel with 5/0.03% (v/v) acrylamide/bisacrylamide concentration.