Characterizing viscoelastic materials via ensemble-based data assimilation of bubble collapse observations

Area of Science:

• Rheology
• Fluid Dynamics
• Biomaterials Science

Background:

• Accurate measurement of viscoelastic material properties at high strain rates is crucial for modeling biological and medical systems.
• Bubble cavitation generates extreme strain rates, making bubble dynamics sensitive to material properties, offering a pathway for rheometry.
• Previous methods like least-squares shooting have demonstrated bubble-dynamic rheometry, but require generalization to handle model and initial condition uncertainties.

Purpose of the Study:

• To generalize bubble-dynamic rheometry by incorporating ensemble-based data assimilation for improved efficiency and scalability.
• To assess the performance of different data assimilation techniques (EnKF, IEnKS, En4D-Var) in estimating material properties like viscosity and shear modulus.
• To apply these enhanced methods to experimental data and investigate potential unaccounted mechanisms in the current models.

Main Methods:

• Ensemble-based data assimilation techniques, including ensemble Kalman filter (EnKF), iterative ensemble Kalman smoother (IEnKS), and a hybrid ensemble-based 4D-Var (En4D-Var), were employed.
• These methods were tested on synthetic data to evaluate their accuracy in estimating the viscosity and shear modulus of a Kelvin-Voigt material.
• The validated methods were applied to experimental bubble cavitation data from Estrada et al. (2018).

Main Results:

• Ensemble-based data assimilation significantly reduces computational cost for bubble cavitation models.
• En4D-Var and IEnKS demonstrated superior estimation of material moduli compared to EnKF on synthetic data.
• Application to experimental data yielded comparable material property estimates to prior work, with added uncertainty quantification.

Conclusions:

• Ensemble-based data assimilation provides a more efficient and scalable framework for bubble-collapse rheometry.
• The En4D-Var method provided lower viscosity estimates in some cases, suggesting potential model limitations.
• Observed discrepancies indicate possible inelastic material behavior or damage mechanisms during bubble collapse not captured by the current Kelvin-Voigt model.