Radical production inside an acoustically driven microbubble

Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller-Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.

Penetration of hydroxyl radicals in the aqueous phase surrounding a cavitation bubble

In the sonochemical degradation of nonvolatile compounds, the free radicals must be delivered into the aqueous solution from the cavitation bubble to initiate reduction-oxidation reactions. The penetration depth in the liquid becomes an important parameter that influences the radical delivery efficiency and eventual treatment performance. However, the transport of radicals in the liquid phase is not well understood yet. In this paper, we focus on the most reactive OH radical and numerically simulate its penetration behavior. This is realized by solving the coupled equations of bubble dynamics, intracavity chemistry, and radical dispersion in the aqueous phase. The results present both the local and global penetration patterns for the OH radicals. By performing simulations over a wide range of acoustic parameters, we find an undesirable phenomenon that the penetration can be adversely suppressed when strengthening the radical production. A mechanistic analysis attributes this to the excessively vigorous recombination reactions associated with high radical concentrations near the bubble interface. In this circumstance, the radicals are massively consumed and converted into molecular species before they can appreciably diffuse away. Our study sheds light on the interplay between radical production inside the bubble and dispersion in the outside liquid. The derived conclusions provide guides for sonochemical applications from a new perspective.

Production and dispersion of free radicals from transient cavitation Bubbles: An integrated numerical scheme and applications

As an advanced oxidation process with a wide range of applications, sonochemistry relies on acoustic cavitation to induce free radicals for degrading chemical contaminants. The complete process includes two critical steps: the radical production inside the cavitation bubble, and the ensuing dispersion of these radicals into the bulk solution. To grasp the physicochemical details in this process, we developed an integrated numerical scheme with the ability to quantitatively describe the radical production-dispersion behavior. It employs coupled simulations of bubble dynamics, intracavity chemical reactions, and diffusion-reaction-dominated mass transport in aqueous solutions. Applying this method to the typical case of argon and oxygen bubbles, the production mechanism for the main radicals is revealed. Moreover, the temporal-spatial distribution of the radicals in the liquid phase is presented. The results demonstrate that the enhanced radical production observed in oxygen bubbles can be traced to the initiation reaction O₂ + H₂O → OH+HO₂, which requires relatively low activation energy. In the outside liquid region, the dispersion of radicals is limited by robust recombination reactions. The simulated penetration depth of OH is around 0.2 μm and agrees with reported experimental measurements. The proposed numerical approach can be employed to better capture the radical activity and is instrumental in optimizing the engineering application of sonochemistry.

The importance of chemical mechanisms in sonochemical modelling

A state-of-the-art chemical mechanism is introduced to properly describe chemical processes inside a harmonically excited spherical bubble placed in water and saturated with oxygen. The model uses up-to-date Arrhenius-constants, collision efficiency factors and takes into account the pressure-dependency of the reactions. Duplicated reactions are also applied, and the backward reactions rates are calculated via suitable thermodynamic equilibrium conditions. Our proposed reaction mechanism is compared to three other chemical models that are widely applied in sonochemistry and lack most of the aforementioned modelling issues. In the governing equations, only the reaction mechanisms are compared, all other parts of the models are identical. The chemical yields obtained by the different modelling techniques are taken at the maximum expansion of the bubble. A brief parameter study is made with different pressure amplitudes and driving frequencies at two equilibrium bubble sizes. The results show that due to the deficiencies of the former reaction mechanisms employed in the sonochemical literature, several orders of magnitude differences of the chemical yields can be observed. In addition, the trends along a control parameter can also have dissimilar characteristics that might lead to false optimal operating conditions. Consequently, an up-to-date and accurate chemical model is crucial to make qualitatively and quantitatively correct conclusions in sonochemistry.

GPU accelerated numerical investigation of the spherical stability of an acoustic cavitation bubble excited by dual-frequency

The spherical stability of an acoustic cavitation bubble under dual-frequency excitation is investigated numerically. The radial dynamics is described by the Keller-Miksis equation, which is a second-order ordinary differential equation. The surface dynamics is modelled by a set of linear ordinary differential equation according to Hao and Prosperetti (1999), which takes into account the effect of vorticity by boundary layer approximation. Due to the large amount of investigated parameter combinations, the numerical computations were carried out on graphics processing units. The results showed that for bubble size between R_E=2μm and 4μm, the combination of a low and a high frequency, and the combination of two close but not equal frequencies are important to prevent the bubble losing its shape stability, while reaching the chemical threshold (R_max/R_E=3) (Kalmár et al., 2020). The phase shift between harmonic components of dual-frequency excitation has no effect on the shape stability.

GPU accelerated study of a dual-frequency driven single bubble in a 6-dimensional parameter space: The active cavitation threshold

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (R_max-R_E)/R_E, where R_E is the equilibrium size of the bubble and R_max is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (R_max-R_E)/R_E=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (R_max-R_E)/R_E=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.

Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.

A strict formulation of a nonlinear Helmholtz equation for the propagation of sound in bubbly liquids. Part II: Application to ultrasonic cavitation

This paper addresses one of the greatest challenges in sonochemistry that has impaired scaling up ultrasonic processes, which is the lack of models capable of predicting the pressure distribution in sonoreactors. This work studies the effect of acoustic pressure on the transmission of sound thought cavitating bubbly liquids by utilizing the nonlinear Helmholtz equation that was demonstrated on the paper part I. The model showed that the wave number and the attenuation can be estimated from the bubble dynamics of inertial bubbles and the local bubble density. The linear model of Commander and Prosperetti is encompassed by the nonlinear model. The model was employed to predict the pressure distribution below an ultrasonic horn tip achieving a relatively close prediction of the experimental data and certainly an accurate qualitative description of the distribution of the pressure field in spite of the simplifications of the model and the assumptions of unknown variables such as the bubble density, bubble distribution and the vessel boundary conditions.

Relationship between the radial dynamics and the chemical production of a harmonically driven spherical bubble

The sonochemical activity and the radial dynamics of a harmonically excited spherical bubble are investigated numerically. A detailed model is employed capable to calculate the chemical production inside the bubble placed in water that is saturated with oxygen. Parameter studies are performed with the control parameters of the pressure amplitude, the forcing frequency and the bubble size. Three different definitions of collapse strengths (extracted from the radius vs.time curves) are examined and compared with the chemical output of various species. A mathematical formula is established to estimate the chemical output as a function of the collapse strength; thus, the chemical activity can be predicted without taking into account the chemical kinetics into the bubble model. The calculations are carried out by an in-house code exploiting the high processing power of professional graphics cards (GPUs). The results shown that chemical activity can be approximated qualitatively from the values of relative expansion. This could be helpful in order to optimise chemical output of sonochemical reactors either from measurement data or simulations as well.

Study of non-spherical bubble oscillations under acoustic irradiation in viscous liquid

The effect of dissipation on the shape stability of a harmonically excited bubble is investigated. The employed liquid is the highly viscous glycerine. The rate of the dissipation is controlled through the alteration of viscosity of the liquid by varying its temperature. The mean radius of the bubble during its radial oscillation is described by the Keller-Miksis equation. Two approaches are used to describe the surface oscillations. The first model solves the surface dynamics equations of each mode together with the transport equation of the vorticity in the liquid domain. The second model approximates the transport equation, which is a partial differential equation, with a boundary layer approximation reducing the required computational resources significantly. The comparison of the surface models shows qualitative agreement at low dissipation rate; however, at high viscosity the application of the full transport equation is mandatory. The results show that an increasing rate of dissipation can significantly extend the shape stable domains in the excitation frequency-pressure amplitude parameter plane. Nevertheless, the collapse strength is decreasing due to the highly damped oscillations. It has been found that an optimal range of dissipation rate in terms of temperature can be defined expressing a good compromise between the collapse strength and surface stability. The computations are carried out by an in-house GPU accelerated initial value problem solver.

Phase structuring in metal alloys: Ultrasound-assisted top-down approach to engineering of nanostructured catalytic materials

High intensity ultrasound (HIUS) is a novel and efficient tool for top-down nanostructuring of multi-phase metal systems. Ultrasound-assisted structuring of the phase in metal alloys relies on two main mechanisms including interfacial red/ox reactions and temperature driven solid state phase transformations which affect surface composition and morphology of metals. Physical and chemical properties of sonication medium strongly affects the structuring pathways as well as morphology and composition of catalysts. HIUS can serve as a simple, fast, and effective approach for the tuning of structure and surface properties of metal particles, opening the new perspectives in design of robust and efficient catalysts.

Effect of Cavitation Bubble Collapse on the Modification of Solids: Crystallization Aspects

This review examines the concepts how cavitation bubble collapse affects crystalline structure, the crystallization of newly formed structures, and recrystallization. Although this subject can be discussed in a broad sense across the area of metastable crystallization, our main focus is discussing specific examples of the inorganic solids: metal, intermetallics, metal oxides, and silicon. First, the temperature up to which ultrasound heats solids is discussed. Cavitation-induced changes in the crystal size of intermetallic phases in binary AlNi (50 wt % of Ni) alloys allow an estimation of local temperatures on surfaces and in bulk material. The interplay between atomic solid-state diffusion and recrystallization during bubble collapses in heterogeneous systems is revealed. Furthermore, cavitation triggered red/ox processes at solid/liquid interfaces and their influence on recrystallization are discussed for copper aluminum nanocomposites, zinc, titanium, magnesium-based materials, and silicon. Cavitation-driven highly nonequilibrium conditions can affect the thermodynamics and kinetics of mesoscopic phase formation in heterogeneous systems and in many cases boost the macroscopic performance of composite materials, notably in catalytic alloy and photocatalytic semiconductor oxide properties, corrosion resistance, nanostructured surface biocompatibility, and optical properties.

Nucleus factory on cavitation bubble for amyloid β fibril

Structural evolution from monomer to fibril of amyloid β peptide is related to pathogenic mechanism of Alzheimer disease, and its acceleration is a long-running problem in drug development. This study reveals that ultrasonic cavitation bubbles behave as catalysts for nucleation of the peptide: The nucleation reaction is highly dependent on frequency and pressure of acoustic wave, and we discover an optimum acoustical condition, at which the reaction-rate constant for nucleation is increased by three-orders-of magnitudes. A theoretical model is proposed for explaining highly frequency and pressure dependent nucleation reaction, where monomers are captured on the bubble surface during its growth and highly condensed by subsequent bubble collapse, so that they are transiently exposed to high temperatures. Thus, the dual effects of local condensation and local heating contribute to dramatically enhance the nucleation reaction. Our model consistently reproduces the frequency and pressure dependences, supporting its essential applicability.