Modelling the effect of acoustic waves on the thermodynamics and kinetics of phase transformation in a solution: Including mass transportation

Effects of acoustic waves on a phase transformation in a metastable phase were investigated in our previous work [S. R. Haqshenas, I. J. Ford, and N. Saffari, “Modelling the effect of acoustic waves on nucleation,” J. Chem. Phys. 145, 024315 (2016)]. We developed a non-equimolar dividing surface cluster model and employed it to determine the thermodynamics and kinetics of crystallisation induced by an acoustic field in a mass-conserved system. In the present work, we developed a master equation based on a hybrid Szilard-Fokker-Planck model, which accounts for mass transportation due to acoustic waves. This model can determine the kinetics of nucleation and the early stage of growth of clusters including the Ostwald ripening phenomenon. It was solved numerically to calculate the kinetics of an isothermal sonocrystallisation process in a system with mass transportation. The simulation results show that the effect of mass transportation for different excitations depends on the waveform as well as the imposed boundary conditions and tends to be noticeable in the case of shock waves. The derivations are generic and can be used with any acoustic source and waveform

Modelling the effect of acoustic waves on the thermodynamics and kinetics of crystal nucleation from a solution

A phase transformation in a metastable solution can be affected when it is subjected to high-intensity acoustic waves. Despite the extensive experimental evidence, the nature of this phenomenon has been little studied theoretically. This work aims to tackle this issue and develop the theoretical basis for investigating the thermodynamics and kinetics of crystallisation induced by an acoustic field. In the first part of thesis, we investigated the effect of acoustic waves on the thermodynamics of crystallisation by the aid of the Gibbs droplet model in a generic format. We have developed a new model based on non-equimolecular clusters which can overcome some of the shortcomings of the conventional form of the classical nucleation theory (CNT) in describing the thermodynamics of small clusters. The model is validated by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data. Our results demonstrate a close agreement with experimental data, better than predictions by CNT. In the second part, we studied the kinetics of phase transformation in an acoustic field. We developed a master equation based on a hybrid Szilard-Fokker Planck model, which accounts for mass transportation due to acoustic waves. This model is employed to determine the kinetics of nucleation and the early stage of growth of clusters including the Ostwald ripening phenomenon in an isothermal sonocrystallisation process and is solved numerically for different scenarios in a system with and without mass transportation. Our results show that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to CNT. Furthermore, we calculated mass transportation for different excitations modelled as plane waves propagating in a semi-infinite medium which tends to be rather noticeable only in the case of shock waves. The derivations are generic and can be used with any acoustic source and waveform

Modelling the effect of acoustic waves on the thermodynamics and kinetics of phase transformation in a solution: Including mass transportation

Effects of acoustic waves on a phase transformation in a metastable phase were investigated in our previous work [S. R. Haqshenas, I. J. Ford, and N. Saffari, “Modelling the effect of acoustic waves on nucleation,” J. Chem. Phys. 145, 024315 (2016)]. We developed a non-equimolar dividing surface cluster model and employed it to determine the thermodynamics and kinetics of crystallisation induced by an acoustic field in a mass-conserved system. In the present work, we developed a master equation based on a hybrid Szilard-Fokker-Planck model, which accounts for mass transportation due to acoustic waves. This model can determine the kinetics of nucleation and the early stage of growth of clusters including the Ostwald ripening phenomenon. It was solved numerically to calculate the kinetics of an isothermal sonocrystallisation process in a system with mass transportation. The simulation results show that the effect of mass transportation for different excitations depends on the waveform as well as the imposed boundary conditions and tends to be noticeable in the case of shock waves. The derivations are generic and can be used with any acoustic source and waveform

Modelling the effect of acoustic waves on nucleation

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory

Modelling the effect of acoustic waves on nucleation

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory

Modelling the Physics of Bubble Nucleation in Histotripsy

This work aims to establish a theoretical framework for the modeling of bubble nucleation in histotripsy. A phenomenological version of the classical nucleation theory was parametrized with histotripsy experimental data, fitting a temperature-dependent activity factor that harmonizes theoretical predictions and experimental data for bubble nucleation at both high and low temperatures. Simulations of histotripsy pressure and temperature fields are then used in order to understand spatial and temporal properties of bubble nucleation at varying sonication conditions. This modeling framework offers a thermodynamic understanding on the role of the ultrasound frequency, waveforms, peak focal pressures, and duty cycle on patterns of ultrasound-induced bubble nucleation. It was found that at temperatures lower than 50 °C, nucleation rates are more appreciable at very large negative pressures such as -30 MPa. For focal peak-negative pressures of -15 MPa, characteristic of boiling histotripsy, nucleation rates grow by 20 orders of magnitude in the temperature interval 60 °C-100 °C

Benchmarking preconditioned boundary integral formulations for acoustics.

The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The discretization of its weak formulation leads to a dense system of linear equations, which is typically solved with an iterative linear method such as GMRES. The application of BEM to simulating wave propagation through large-scale geometries is only feasible when compression and preconditioning techniques reduce the computational footprint. Furthermore, many different boundary integral equations exist that solve the same boundary value problem. The choice of preconditioner and boundary integral formulation is often optimized for a specific configuration, depending on the geometry, material characteristics, and driving frequency. On the one hand, the design flexibility for the BEM can lead to fast and accurate schemes. On the other hand, efficient and robust algorithms are difficult to achieve without expert knowledge of the BEM intricacies. This study surveys the design of boundary integral formulations for acoustics and their acceleration with operator preconditioners. Extensive benchmarks provide valuable information on the computational characteristics of several hundred different models for multiple reflection and transmission of acoustic waves

Boundary integral formulations for acoustic modelling of high-contrast media

The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density, wavespeed and frequency. In particular, high contrast in density and wavespeed across a material interface leads to an ill-conditioned discretisation matrix. Therefore, the convergence of Krylov methods to solve the linear system is slow. Here, specialised boundary integral formulations are designed for the case of acoustic scattering at high-contrast media. The eigenvalues of the resulting system matrix accumulate at two points in the complex plane that depend on the density ratio and stay away from zero. The spectral analysis of the Calderón preconditioned PMCHWT formulation yields a single accumulation point. Benchmark simulations demonstrate the computational efficiency of the high-contrast Neumann formulation for scattering at high-contrast media

Unmyelinated Peripheral Nerves Can Be Stimulated in Vitro Using Pulsed Ultrasound

Appreciation for the medical and research potential of ultrasound neuromodulation is growing rapidly, with potential applications in non-invasive treatment of neurodegenerative disease and functional brain mapping spurring recent progress. However, little progress has been made in our understanding of the ultrasound–tissue interaction. The current study tackles this issue by measuring compound action potentials (CAPs) from an ex vivo crab walking leg nerve bundle and analysing the acoustic nature of successful stimuli using a passive cavitation detector (PCD). An unimpeded ultrasound path, new acoustic analysis techniques and simple biological targets are used to detect different modes of cavitation and narrow down the candidate biological effectors with high sensitivity. In the present case, the constituents of unmyelinated axonal tissue alone are found to be sufficient to generate de novo action potentials under ultrasound, the stimulation of which is significantly correlated to the presence of inertial cavitation and is never observed in its absence

The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

A phenomenological implementation of Classical Nucleation Theory (CNT) is employed to investigate the connection between high intensity focused ultrasound (HIFU) pressure and temperature fields with the energetic requirements of bubble nucleation. As a case study, boiling histotripsy in tissue-mimicking phantoms is modelled. The physics of key components in the implementation of CNT in HIFU conditions such as the derivation of nucleation pressure thresholds and approximations regarding the surface tension of the liquid are reviewed and discussed. Simulations show that the acoustic pressure is the ultimate trigger for millisecond bubble nucleation in boiling histotripsy, however, HIFU heat deposition facilitates nucleation by lowering nucleation pressure thresholds. Nucleation thus occurs preferentially at the regions of highest heat deposition within the HIFU field. This implies that bubble nucleation subsequent to millisecond HIFU heat deposition can take place at temperatures below 100 °C as long as the focal HIFU peak negative pressure exceeds the temperature-dependent nucleation threshold. It is also found that the magnitude of nucleation pressure thresholds decreases with decreasing frequencies. Overall, results indicate that it is not possible to separate thermal and mechanical effects of HIFU in the nucleation of bubbles for timescales of a few milliseconds. This methodology provides a promising framework for studying time and space dependencies of the energetics of bubble nucleation within a HIFU field