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 investigation of shock-induced bubble collapse dynamics and fluid-solid interactions during shock-wave lithotripsy.

In this paper we investigate the bubble collapse dynamics under shock-induced loading near soft and rigid bio-materials, during shock wave lithotripsy. A novel numerical framework was developed, that employs a Diffuse Interface Method (DIM) accounting for the interaction across fluid-solid-gas interfaces. For the resolution of the extended variety of length scales, due to the dynamic and fine interfacial structures, an Adaptive Mesh Refinement (AMR) framework for unstructured grids was incorporated. This multi-material multi-scale approach aims to reduce the numerical diffusion and preserve sharp interfaces. The presented numerical framework is validated for cases of bubble dynamics, under high and low ambient pressure ratios, shock-induced collapses, and wave transmission problems across a fluid-solid interface, against theoretical and numerical results. Three different configurations of shock-induced collapse applications near a kidney stone and soft tissue have been simulated for different stand-off distances and bubble attachment configurations. The obtained results reveal the detailed collapse dynamics, jet formation, solid deformation, rebound, primary and secondary shock wave emissions, and secondary collapse that govern the near-solid collapse and penetration mechanisms. Significant correlations of the problem configuration to the overall collapse mechanisms were found, stemming from the contact angle/attachment of the bubble and from the properties of solid material. In general, bubbles with their center closer to the kidney stone surface produce more violent collapses. For the soft tissue, the bubble movement prior to the collapse is of great importance as new structures can emerge which can trap the liquid jet into induced crevices. Finally, the tissue penetration is examined for these cases and a novel tension-driven tissue injury mechanism is elucidated, emanating from the complex interaction of the bubble/tissue interaction during the secondary collapse phase of an entrapped bubble in an induced crevice with the liquid jet.

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.

Droplet nuclei caustic formations in exhaled vortex rings.

Vortex ring (VR) structures occur in light or hoarse cough configurations. These instances consist of short impulses of exhaled air resulting to a self-contained structure that can travel large distances. The present study is the first implementation of the second order Fully Lagrangian Approach (FLA) for three-dimensional realistic flow-fields obtained by means of Computational Fluid Dynamics (CFD) and provides a method to calculate the occurrence and the intensity of caustic formations. The carrier phase flow field is resolved by means of second order accurate Direct Numerical Simulation (DNS) based on a Finite Difference approach for the momentum equations, while a spectral approach is followed for the Poisson equation using Fast Fourier Transform (FFT). The effect of the undulations of the carrier phase velocity due to large scale vortical structures and turbulence is investigated. The evaluation of the higher order derivatives needed by the second order FLA is achieved by pre-fabricated least squares second order interpolations in three dimensions. This method allows for the simulation of the clustering of droplets and droplet nuclei exhaled in ambient air in conditions akin to light cough. Given the ambiguous conditions of vortex-ring formation during cough instances, three different exhale (injection) parameters n are assumed, i.e. under-developed ([Formula: see text]), ideal ([Formula: see text]) and over-developed ([Formula: see text]) vortex rings. The formation of clusters results in the spatial variance of the airborne viral load. This un-mixing of exhumed aerosols is related to the formation of localised high viral load distributions that can be linked to super-spreading events.

Influence of Diesel Fuel Viscosity on Cavitating Throttle Flow Simulations under Erosive Operation Conditions.

This work investigates the effect of liquid fuel viscosity, as specific by the European Committee for Standardization 2009 (European Norm) for all automotive fuels, on the predicted cavitating flow in micro-orifice flows. The wide range of viscosities allowed leads to a significant variation in orifice nominal Reynolds numbers for the same pressure drop across the orifice. This in turn, is found to affect flow detachment and the formation of large-scale vortices and microscale turbulence. A pressure-based compressible solver is used on the filtered Navier-Stokes equations using the multifluid approach; separate velocity fields are solved for each phase, which share a common pressure. The rates of evaporation and condensation are evaluated with a simplified model based on the Rayleigh-Plesset equation; the coherent structure model is adopted for the subgrid scale modeling in the momentum conservation equation. The test case simulated is a well-reported benchmark throttled flow channel geometry, referred to as "I-channel"; this has allowed for easy optical access for which flow visualization and laser-induced fluorescence measurements allowed for validation of the developed methodology. Despite its simplicity, the I-channel geometry is found to reproduce the most characteristic flow features prevailing in high-speed flows realized in cavitating fuel injectors. Subsequently, the effect of liquid viscosity on integral mass flow, velocity profiles, vapor cavity distribution, and pressure peaks indicating locations prone to cavitation erosion is reported.

Numerical investigations on bubble-induced jetting and shock wave focusing: application on a needle-free injection.

The formation of a liquid jet into air induced by the growth of a laser-generated bubble inside a needle-free device is numerically investigated by employing the compressible Navier-Stokes equations. The three co-existing phases (liquid, vapour and air) are assumed to be in thermal equilibrium. A transport equation for the gas mass fraction is solved in order to simulate the non-condensable gas. The homogeneous equilibrium model is used in order to account for the phase change process between liquid and vapour. Thermodynamic closure for all three phases is achieved by a barotropic Equation of State. Two-dimensional axisymmetric simulations are performed for a needle-free device for which experimental data are available and used for the validation of the developed model. The influence of the initial bubble pressure and the meniscus geometry on the jet velocity is examined by two different sets of studies. Based on the latter, a new meniscus design similar to shaped-charge jets is proposed, which offers a more focused and higher velocity jet compared to the conventional shape of the hemispherical gas-liquid interface. Preliminary calculations show that the developed jet can penetrate the skin and thus, such configurations can contribute towards a new needle-free design.

Modelling cavitation during drop impact on solid surfaces.

The impact of liquid droplets on solid surfaces at conditions inducing cavitation inside their volume has rarely been addressed in the literature. A review is conducted on relevant studies, aiming to highlight the differences from non-cavitating impact cases. Focus is placed on the numerical models suitable for the simulation of droplet impact at such conditions. Further insight is given from the development of a purpose-built compressible two-phase flow solver that incorporates a phase-change model suitable for cavitation formation and collapse; thermodynamic closure is based on a barotropic Equation of State (EoS) representing the density and speed of sound of the co-existing liquid, gas and vapour phases as well as liquid-vapour mixture. To overcome the known problem of spurious oscillations occurring at the phase boundaries due to the rapid change in the acoustic impedance, a new hybrid numerical flux discretization scheme is proposed, based on approximate Riemann solvers; this is found to offer numerical stability and has allowed for simulations of cavitation formation during drop impact to be presented for the first time. Following a thorough justification of the validity of the model assumptions adopted for the cases of interest, numerical simulations are firstly compared against the Riemann problem, for which the exact solution has been derived for two materials with the same velocity and pressure fields. The model is validated against the single experimental data set available in the literature for a 2-D planar drop impact case. The results are found in good agreement against these data that depict the evolution of both the shock wave generated upon impact and the rarefaction waves, which are also captured reasonably well. Moreover, the location of cavitation formation inside the drop and the areas of possible erosion sites that may develop on the solid surface, are also well captured by the model. Following model validation, numerical experiments have examined the effect of impact conditions on the process, utilizing both planar and 2-D axisymmetric simulations. It is found that the absence of air between the drop and the wall at the initial configuration can generate cavitation regimes closer to the wall surface, which significantly increase the pressures induced on the solid wall surface, even for much lower impact velocities. A summary highlighting the open questions still remaining on the subject is given at the end.

Smoothed particle hydrodynamics simulation of a laser pulse impact onto a liquid metal droplet.

The impact of a laser pulse onto a liquid metal droplet is numerically investigated by utilising a weakly compressible single phase model; the thermodynamic closure is achieved by the Tait equation of state (EoS) for the liquid metal. The smoothed particle hydrodynamics (SPH) method, which has been employed in the arbitrary Lagrangian Eulerian (ALE) framework, offers numerical efficiency, compared to grid related discretization methods. The latter would require modelling not only of the liquid metal phase, but also of the vacuum, which would necessitate special numerical schemes, suitable for high density ratios. In addition, SPH-ALE allows for the easy deformation handling of the droplet, compared to interface tracking methods where strong mesh deformation and most likely degenerate cells occur. Then, the laser-induced deformation of the droplet is simulated and cavitation formation is predicted. The ablation pattern due to the emitted shock wave and the two low pressure lobes created in the middle of the droplet because of the rarefaction waves are demonstrated. The liquid metal droplet is subject to material rupture, when the shock wave, the rarefaction wave and the free surface interact. Similar patterns regarding the wave dynamics and the hollow structure have been also noticed in prior experimental studies.

Turbulence and Cavitation Suppression by Quaternary Ammonium Salt Additives.

We identify the physical mechanism through which newly developed quaternary ammonium salt (QAS) deposit control additives (DCAs) affect the rheological properties of cavitating turbulent flows, resulting in an increase in the volumetric efficiency of clean injectors fuelled with diesel or biodiesel fuels. Quaternary ammonium surfactants with appropriate counterions can be very effective in reducing the turbulent drag in aqueous solutions, however, less is known about the effect of such surfactants in oil-based solvents or in cavitating flow conditions. Small-angle neutron scattering (SANS) investigations show that in traditional DCA fuel compositions only reverse spherical micelles form, whereas reverse cylindrical micelles are detected by blending the fuel with the QAS additive. Moreover, experiments utilising X-ray micro computed tomography (micro-CT) in nozzle replicas, quantify that in cavitation regions the liquid fraction is increased in the presence of the QAS additive. Furthermore, high-flux X-ray phase contrast imaging (XPCI) measurements identify a flow stabilization effect in the region of vortex cavitation by the QAS additive. The effect of the formation of cylindrical micelles is reproduced with computational fluid dynamics (CFD) simulations by including viscoelastic characteristics for the flow. It is demonstrated that viscoelasticity can reduce turbulence and suppress cavitation, and subsequently increase the injector's volumetric efficiency.

Parametric Investigations of the Induced Shear Stress by a Laser-Generated Bubble.

The present paper focuses on the simulation of the growth and collapse of a bubble in the vicinity of a wall. Both liquid and gas phases are assumed compressible, and their interaction is handled with the volume-of-fluid method. The main interest is to quantify the influence of the induced shear stress and pressure pulse in the vicinity of the wall for a variety of bubble sizes and bubble-wall distances. The results are validated against prior experimental results, such as the measurements of the bubble size, induced pressure field, and shear stress on the wall. The simulation predictions indicate that the wall in the vicinity of the bubble is subjected both to high shear stresses and large pressure pulses because of the growth and collapse of the bubble. In fact, pressure levels of 100 bar or more and shear stresses up to 25 kPa have been found at localized spots on the wall surface, at the region around the bubble. Moreover, the simulations are capable of providing additional insight to the experimental investigation, as the inherent limitations of the latter are avoided. The present work may be considered as a preliminary investigation in optimizing bubble energy and wall generation distance for ultrasound cleaning applications.

Experimental Study of Diesel-Fuel Droplet Impact on a Similarly Sized Polished Spherical Heated Solid Particle.

The head-to-head impact of diesel-fuel droplets on a polished spherical brass target has been investigated experimentally. High-speed imaging was employed to visualize the impact process for wall surface temperatures and Weber and Reynolds numbers in the ranges of 140-340 °C, 30-850, and 210-1135, respectively. The thermohydrodynamic outcome regimes occurring for the aforementioned ranges of parameters were mapped on a We-T diagram. Seven clearly distinguishable postimpact outcome regimes were identified, which are conventionally called the coating, splash, rebound, breakup-rebound, splash-breakup-coating, breakup-coating, and splash-breakup-rebound regimes. In addition, the effects of the Weber number and surface temperature on the wettability dynamics were examined; the temporal variations of the dynamic contact angle, dimensionless spreading diameter, and liquid film thickness forming on the solid particle were measured and are reported.

Unveiling the physical mechanism behind pistol shrimp cavitation.

Snapping shrimps use a special shaped claw to generate a cavitating high speed water jet. Cavitation formed in this way, may be used for hunting/stunning prey and communication. The present work is a novel computational effort to provide insight on the mechanisms of cavitation formation during the claw closure. The geometry of the claw used here is a simplified claw model, based on prior experimental work. Techniques, such as Immersed Boundary and Homogenous Equilibrium Model (HEM), are employed to describe the claw motion and cavitating flow field respectively. The simulation methodology has been validated against prior experimental work and is applied here for claw closure at realistic conditions. Simulations show that during claw closure, a high velocity jet forms, inducing vortex roll-up around it. If the closure speed is high enough, the intensity of the swirling motion is enough to produce strong depressurization in the vortex core, leading to the formation of a cavitation ring. The cavitation ring moves along the jet axis and, soon after its formation, collapses and rebounds, producing high pressure pulses.

Modelling of thrombin generation under flow in realistic left anterior descending geometries.

Currently there are no available methods for prediction of thrombotic complications in Coronary Artery disease. Additionally, blood coagulation tests are mainly performed in a steady system while coagulation in vivo occurs under flow conditions. In this work, a phenomenological model for coagulation up-to thrombin generation is proposed; the model is mainly based on the results of thrombin generation assays and therefore it can account for the variation of the coagulability that is observed in different individuals. The model is applied on 3 cases of left anterior descending arteries (LAD) with 50% maximum stenosis placed at a different location and have been statistically assessed as of different complication risk. The simulations showed that parameters of thrombin generation assays obtain different values when they refer to thrombin generation under realistic coronary flow conditions. The flow conditions prevailing locally because of the geometric differences among the arterial trees can lead to different initiation times and thrombin production rates and it also alters the spatial distribution of the coagulation products. Similarly, small changes of the coagulation characteristics of blood under identical flow conditions can allow or prevent the initiation of coagulation. The results indicate that combined consideration of geometry and coagulation characteristics of blood can lead to entirely different conclusions compared to independent assessment of each factor.

Derivation of flow related risk indices for stenosed left anterior descending coronary arteries with the use of computer simulations.

The geometry of the coronary vessel network is believed to play a decisive role in the initiation, progression and outcome of coronary artery disease (CAD) and the occurrence of acute coronary syndromes (ACS). It also determines the flow field in the coronary artery which can be linked to CAD evolution. In this work geometric 3D models of left anterior descending (LAD) coronary arteries associated with either myocardial infarction (MI) or stable (STA) CAD were constructed. Transient numerical simulations of the flow for each model showed that specific flow patterns develop in different extent in the different groups examined. Recirculation zones, present distal the stenosis in all models, had larger extent and duration in MI cases. For mild stenosis (up to 50%) areas with low time averaged wall shear stress TAWSS (<0.15Pa) as well as areas with high TAWSS (>3Pa) appeared only in MI models; in moderate and severe stenosis (>50%) these areas were present in all models but were significantly larger for MI than STA models. These differentiations were expressed via numerical indices based on TAWSS, oscillating shear index (OSI) and relative residence time (RRT). Additionally we introduced the coagulation activation index (CAI), based on the threshold behaviour of coagulation initiation, which exceeded the suggested threshold only for MI models with intermediate stenosis (up to 50%). These results show that numerical simulations of flow can produce arithmetic indices linked with the risk of CAD complications.

VOF simulations of the contact angle dynamics during the drop spreading: standard models and a new wetting force model.

INTRODUCTION: In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas-liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface. METHODOLOGY: The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an "adhesion-like" force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid-air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface. RESULTS: The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θadv=10°-70°) and hydrophobic (θadv=105°-120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements. CONCLUSION: It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We<˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.

A simplified mathematical model for thrombin generation.

A new phenomenological mathematical model based directly on laboratory data for thrombin generation and having a patient-specific character is described. A set of the solved equations for cell-based models of blood coagulation that can reproduce the temporal evolution of thrombin generation is proposed; such equations are appropriate for use in computational fluid dynamic (CFD) simulations. The initial values for the reaction rates are either taken from already existing model or experimental data, or they can obtained from simple reasoning under certain assumptions; it is shown that coefficients can be adjusted in order to fit a range of different thrombin generation curves as derived from thrombin generation assays. The behaviour of the model for different platelet concentration seems to be in good agreement with reported experimental data. It is shown that the reduced set of equations used represents to a good approximation a low-order model of the detailed mechanism and thus it can represent a cost-effective and-case specific mathematical model of coagulation reactions up to thrombin generation.

Flow patterns at stented coronary bifurcations: computational fluid dynamics analysis.

BACKGROUND: The ideal bifurcation stenting technique is not established, and data on the hemodynamic characteristics at stented bifurcations are limited. METHODS AND RESULTS: We used computational fluid dynamics analysis to assess hemodynamic parameters known affect the risk of restenosis and thrombosis at coronary bifurcations after the use of various single- and double-stenting techniques. We assessed the distributions and surface integrals of the time averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (t(r)). Single main branch stenting without side branch balloon angioplasty or stenting provided the most favorable hemodynamic results (integrated values of TAWSS=4.13·10(-4) N, OSI=7.52·10(-6) m(2), t(r)=5.57·10(-4) m(2)/Pa) with bifurcational area subjected to OSI values >0.25, >0.35, and >0.45 calculated as 0.36 mm(2), 0.04 mm(2), and 0 mm(2), respectively. Extended bifurcation areas subjected to these OSI values were seen after T-stenting: 0.61 mm(2), 0.18 mm(2), and 0.02 mm(2), respectively. Among the considered double-stenting techniques, crush stenting (integrated values of TAWSS=1.18·10(-4) N, OSI=7.75·10(-6) m(2), t(r)=6.16·10(-4) m(2)/Pa) gave the most favorable results compared with T-stenting (TAWSS=0.78·10(-4) N, OSI=10.40·10(-6) m(2), t(r)=6.87·10(-4) m(2)/Pa) or the culotte technique (TAWSS=1.30· 10(-4) N, OSI=9.87·10(-6) m(2), t(r)=8.78·10(-4) m(2)/Pa). CONCLUSIONS: In the studied models of computer simulations, stenting of the main branch with our without balloon angioplasty of the side branch offers hemodynamic advantages over double stenting. When double stenting is considered, the crush technique with the use of a thin-strut stent may result in improved immediate hemodynamics compared with culotte or T-stenting.

A new method of three-dimensional coronary artery reconstruction from X-ray angiography: validation against a virtual phantom and multislice computed tomography.

OBJECTIVE: To develop and implement a method for three-dimensional (3D) reconstruction of coronary arteries from conventional monoplane angiograms. BACKGROUND: 3D reconstruction of conventional coronary angiograms is a promising imaging modality for both diagnostic and interventional purposes. METHODS: Our method combines image enhancement, automatic edge detection, an iterative method to reconstruct the centerline of the artery and reconstruction of the diameter of the vessel by taking into consideration foreshortening effects. The X-Ray-based 3D coronary trees were compared against phantom data from a virtual arterial tree projected into two planes as well as computed tomography (CT)-based coronary artery reconstructions in patients subjected to coronary angiography. RESULTS: Comparison against the phantom arterial tree demonstrated perfect agreement with the developed algorithm. Visual comparison against the CT-based reconstruction was performed in the 3D space, in terms of the direction angle along the centerline length of the left anterior descending and circumflex arteries relative to the main stem, and location and take-off angle of sample bifurcation branches from the main coronary arteries. Only minimal differences were detected between the two methods. Inter- and intraobserver variability of our method was low (intra-class correlation coefficients > 0.8). CONCLUSION: The developed method for coronary artery reconstruction from conventional angiography images provides the geometry of coronary arteries in the 3D space.