arXiv subjects

Mauro Rodriguez Jr

Publications and source records attributed to Mauro Rodriguez Jr.

5 recordsLinked to original sources

arXiv2026

Nonspherical gas bubble dynamics in viscoelastic soft materials

Nonspherical gas bubble dynamics in viscoelastic materials influence the stress transmission and energy dissipation of their surroundings and are difficult to predict. Their accurate prediction is essential in applications ranging from biomedical procedures to high-strain-rate rheological measurements. However, existing models do not sufficiently capture the nonspherical rotational dynamics. We formulate and superpose a rotational contribution to the perturbed deformation with a potential contribution. Linearised forward and inverse coordinate maps are formulated based on the deformation field which are used to compute velocities, accelerations, and stresses. The addition of the rotational degree of freedom satisfies the momentum balance equations and stress continuity at the bubble surface. The material surrounding the bubble is modelled with a Kelvin-Voigt constitutive model with Newtonian viscosity and quadratic strain-stiffening neo-Hookean elasticity. The model agrees with previous viscous fluids models when elastic effects are neglected and radial oscillations are small. When viscous effects are small relative to elastic, shear waves radiate from the bubble surface into the material. The resulting strain energy is delocalised and increases damping of the perturbation amplitude in time relative to potential-based models. We show agreement between the stability of the shape modes with previous ultrasound forced experiments and temporal evolution of different shape modes with previous laser-induced cavitation experimental data.

physics.flu-dyn↗

arXiv2026

Peristaltic pumping under poroelastic confinement

Low Reynolds number flow near a poroelastic interface can be found across scales in biological and engineered systems. We develop a 2D model of peristaltic flow confined under a poroelastic solid. In this geometry, the lower boundary is an infinite train of traveling waves which pump fluid along a channel. The upper boundary of the flow is a poroelastic half space. The flow and deformation are solved analytically by an asymptotic expansion in the peristaltic amplitude and depend nonlinearly on dimensionless poroelastic stiffness, permeability, and interfacial slip. We quantify the effect of material properties on the poroelastic fluid-structure interaction. Peristaltic flow through the channel is inhibited by poroelastic confinement owing to increased viscous dissipation across the interface and energy loss in deforming the elastic solid. Permeability and slip interact with the material stiffness to produce material dependent regimes of forward or backward interstitial flow within the poroelastic domain. The maximum Darcy flow is found to occur at permeability values that optimize the elastic matrix interaction.

physics.flu-dyn↗

arXiv2026

Microbubble surface instabilities in a strain stiffening viscoelastic material

Understanding the dynamics of instabilities along fluid-solid interfaces is critical for the efficacy of focused ultrasound therapy tools (e.g., histotripsy) and microcavitation rheometry techniques. Non-uniform pressure fields generated by either ultrasound or a focused laser can cause non-spherical microcavitation bubbles. Previous perturbation amplitude evolution models in viscoelastic materials either assume pure radial deformation or have inconsistent kinematic fields between the fluid and solid contributions. We derive a kinematically-consistent theoretical model for the evolution of surface perturbations. The model captures the non-linear kinematics of a strain-stiffening viscoelastic material surrounding a non-spherical bubble. The model is validated for (i) small, approximately linear radial oscillations and (ii) large inertial oscillations using laser-induced microcavitation experiments in a soft hydrogel. For the former, the bubble is allowed to reach mechanical equilibrium, and then surface perturbations are excited using ultrasound forcing. For the latter, the microbubble forms small bubble surface perturbations at its maximum radius that grow during collapse. The model's dominant surface perturbation mode scales linearly with equilibrium radius and matches experiments. Similarly, the model's perturbation amplitude evolution sufficiently constrains the rheometry problem and is experimentally validated.

physics.flu-dyn↗

arXiv2025

Hierarchical Bayesian constitutive model selection for high-strain-rate soft material characterization

The high-fidelity characterization of soft, tissue-like materials under ultra-high-strain-rate conditions is critical in engineering and medicine. Still, it remains challenging due to limited optical access, sensitivity to initial conditions, and experimental variability. Microcavitation techniques (e.g., laser-induced microcavitation) have emerged as a viable method for determining the mechanical properties of soft materials in the ultra-high-strain-rate regime (higher than 10^3 s^{-1}); however, they are limited by measurement noise and uncertainty in parameter estimation. A hierarchical Bayesian model selection method is employed using the Inertial Microcavitation Rheometry (IMR) technique to address these limitations. With this method, the parameter space of different constitutive models is explored to determine the most credible constitutive model that describes laser-induced microcavitation bubble oscillations in soft, viscoelastic, transparent hydrogels. The target data/evidence is computed using a weighted Gaussian likelihood with a hierarchical noise scale, which enables the quantification of uncertainty in model plausibility. Physically informed priors, including range-invariant, stress-based parameter priors, a model-redundancy prior, and a Bayesian Information Criterion motivated model prior, penalize complex models to enforce Occam's razor. Using a precomputed grid of simulations, the probabilistic model selection process enables an initial guess for the Maximum A Posteriori (MAP) material parameter values. Synthetic tests recover the ground-truth models and expected parameters. Using experimental data for gelatin, fibrin, polyacrylamide, and agarose, MAP simulations of credible models reproduce the data. Moreover, a cross-institutional comparison of 10% gelatin indicates consistent constitutive model selection.

physics.flu-dyn↗

arXiv2024

Low Reynolds number pumping near an elastic half space

Previous studies on peristalsis, the pumping of fluid along a channel by wave-like displacements of the channel walls, have shown that the elastic properties of the channel and the peristaltic wave shape can influence the flow rate. Motivated by the oscillatory flow of cerebrospinal fluid along compliant perivascular spaces, we consider a prescribed wave motion of a single boundary which pumps fluid at small Reynolds number near an elastic half space. We investigate the relationship between flow rate and elastic deformation as a function of the fluid and solid properties. We consider transverse and longitudinal motion of the driving peristaltic wave. We find that a transverse peristaltic wave produces net forward flow and induces elastic motion in which all material points oscillate uniformly. Conversely, a longitudinal peristaltic wave produces a net backward flow and drives elastic motion which is nonuniform in the elastic solid. We use dimensional values relevant to the flow of cerebrospinal fluid and find agreement with in vivo velocity data.

physics.flu-dyn↗