Investigation of the ultrasound-induced collapse of air bubbles near soft materials.

A numerical investigation into the ultrasound-induced collapse of air bubbles near soft materials, utilizing a novel multi-material diffuse interface method (DIM) model with block-structured adaptive mesh refinement is presented. The present work expands from a previous five-equation DIM by incorporating Eulerian hyperelasticity. The model is applicable to any arbitrary number of interacting fluid and solid material. A single conservation law for the elastic stretch tensor enables tracking the deformations for all the solid materials. A series of benchmark cases are conducted, and the solution is found to be in excellent agreement against theoretical data. Subsequently, the ultrasound-induced bubble-tissue flow interactions are examined. The bubble radius was found to play a crucial role in dictating the stresses experienced by the tissue, underscoring its significance in medical applications. The results reveal that soft tissues primarily experience tensile forces during these interactions, suggesting potential tensile-driven injuries that may occur in relevant treatments. Moreover, regions of maximal tensile forces align with tissue elongation areas. It is documented that while early bubble dynamics remain relatively unaffected by changes in shear modulus, at later stages of the penetration processes and the deformation shapes, exhibit notable variations. Lastly, it is demonstrated that decreasing standoff distances enhances the interaction between bubbles and tissue, thereby increasing the stress levels in the tissue, although the behavior of the bubble dynamics remains largely unchanged.

Prediction of shock heating during ultrasound-induced bubble collapse using real-fluid equations of state.

Numerical simulations of collapsing air bubbles considering complex and more accurate equations of state (EoS) for estimating the properties of both the liquid and gas are presented. The necessity for utilising such EoSs in bubble collapse simulations is illustrated by the unphysical (spurious) liquid temperature jump formed in the vicinity of the bubble-air interface when simplified EoSs are used. The solved fluid flow equations follow the mechanical equilibrium multiphase method of Kapila. The solver is coded in the AMReX platform, enabling high-performance computation with parallel processing and Adaptive Mesh Refinement for speeding up simulations. It is initially demonstrated that the frequently used Stiffened Gas (SG) EoS overpredicts the liquid temperature at high compression. More sophisticated EoS models, such as the International Association for the Properties of Water and Steam (IAPWS), the Modified Noble Abel Stiffened Gas (MNASG) and a modified Tait EoS introduced here, are also implemented into the flow solver and their differences are highlighted for bubble collapse cases for the first time. Subsequently, application of the developed model to cases of practical interest is showcased. More specifically, simulations of bubble collapse near a solid wall are presented for conditions simulating shock wave lithotripsy (SWL). It is concluded that for such cases, a maximum increase of 25 K of the liquid temperature in contact along the solid wall is caused during the collapse of the air bubble due to shock wave focusing effects. It is also highlighted that the maximum liquid heating varies depending on the initial bubble-wall stand-off distance.

Numerical study of real gas effects during bubble collapse using a disequilibrium multiphase model.

An explicit density-based solver of the Euler equations for inviscid and immiscible gas-liquid flow media is coupled with real-fluid thermodynamic equations of state supporting mild dissociation and calibrated with shock tube data up to 5000 K and 28 GPa. The present work expands the original 6-equation disequilibrium method by generalising the numerical approach required for estimating the equilibrium pressure in computational cells where both gas and liquid phases co-exist while enforcing energy conservation for all media. An iterative numerical procedure is suggested for taking into account the properties of the gas content as derived from highly non-linear real gas equations of state and implemented in a tabulated form during the numerical solution. The developed method is subsequently used to investigate gaseous bubble collapse cases considering both spherical and 2D asymmetric arrangements as induced by the presence of a rigid wall. It is demonstrated that the predicted maximum temperatures are strongly influenced by the equations of state used; the real gas model predicts a temperature reduction in the bubble interior up to 41% space-averaged and 50% locally during the collapse phase compared to the predictions obtained with the aid of the widely used ideal gas approximation.