Energy efficiency and process control are critical challenges in scaling sonochemical applications. To address this, we introduce a numerical optimisation framework focused on designing pre-seeded bubble clusters driven by impulse ultrasound to minimise energy consumption. The methodology efficiently handles the large parameter space (bubble sizes) by combining fast, reduced-order modelling of spherical bubbles and chemical kinetics with expensive multi-phase hydrodynamic simulations (ALPACA). The technique is demonstrated on two test cases: ammonia (NH3) and hydrogen (H2) synthesis, to analyse the effects of different reaction mechanisms. In both cases, the optimal size distribution of a chain of 16 bubbles is found with as few as three multi-phase flow simulations.

The present work numerically investigates the energy intensity of ultrasonic H2 production from a spherical argon bubble isolated in liquid water. The bubble is excited by a single sine impulse pressure wave, exhibiting dynamics characterised by a relatively slow expansion phase followed by a rapid collapse and damped free oscillations. The dissipated acoustic energy during the radial motion of the bubble is calculated as the sum of energy losses due to three mechanisms: viscous, thermal, and radiative. In the collapse phase, the bubble acts as a microreactor, triggering reactions as temperatures reach thousands of Kelvin. The temporal evolution of the bubble dynamics, internal temperature, chemical kinetics, and H2 yield is estimated through detailed numerical simulations. Key operational parameters investigated include the ultrasonic frequency, pressure amplitude, ambient radius, static pressure, water temperature, and accommodation coefficient of phase change. Under optimal operating conditions, the energy demand is estimated to be 1970 MJ/kg.

A widely cited experimental dataset (Cleve et al. , J. Fluid Mech. , 2019, vol. 875, pp. 597–621) on non-spherical acoustic cavitation dynamics provides a valuable benchmark for model validation, yet its use is hindered by large uncertainties in the two key parameters: the equilibrium bubble radius and the acoustic pressure amplitude. This study introduces a robust parameter-identification framework to resolve these discrepancies and enable meaningful comparison with models. Using an in-house graphics processing unit-accelerated solver for solving the second-order perturbation model developed by Shaw ( Phys. Fluids , 2006, vol. 18, issue 7, p. 072104), the dataset is systematically re-examined. A Fourier coefficient-based error metric is developed to quantify the pronounced mismatch between simulations and measurements. The proposed method reliably corrects the vast majority of the experimental parameters, yielding excellent agreement between numerical predictions and observations. The outcome is a validated dataset with accurately identified parameters that can serve as a reliable benchmark for validating advanced computational fluid dynamics simulations and theoretical models. In addition, the approach offers a general tool for future experiments where direct measurements of local acoustic pressure remain difficult.

Bubbles play a crucial role in various engineering and scientific applications, ranging from sonochemistry and ultrasonic water treatment to medical procedures and cavitation erosion. The simulation of complex bubble dynamics phenomena such as acoustically driven non-spherical oscillations requires both the accurate calculation of inertia and capillary forces. This paper presents a comprehensive study using the ALPACA compressible multiphase flow solver to simulate both spherical and non-spherical bubble dynamics. The study begins with the validation of ALPACA for standard multiphase test cases, including static, dynamic, and capillary waves, demonstrating its ability to avoid spurious currents and to handle surface tension-driven phenomena with adequate resolution. Subsequently, ALPACA is employed to simulate acoustically excited bubbles using a 2D axisymmetric setup. The results reveal that ALPACA can accurately predict spherical dynamics with at least first-order convergence. Furthermore, it is capable of reproducing dominant surface mode oscillations of larger amplitudes. The main novelty of our work is the direct numerical simulation of non-spherical bubble dynamics and the validation of ALPACA against measurement of acoustically driven non-spherical oscillations.

This study evaluates the accuracy of coupled-spherical-bubble models in acoustic fields by comparing them to direct numerical simulations (DNS). The coupled-spherical-bubble approach refers to the method of modeling multi-bubble systems, where the spherical bubble dynamics are governed by a simplified equation and these equations are coupled through the pressure emissions of the bubbles. Tested spherical models are the Keller-Miksis and Gilmore equation, and pressure emission models include the incompressible, quasi-acoustic and Kirkwood-Bethe hypothesis. Emphasis is placed on peak bubble pressure during collapse and the accuracy of pressure emission models. First, a single bubble in a spherical standing wave is analyzed. Among the simplified approaches, the Gilmore model provides closer agreement with DNS at Mach numbers approaching unity in water. In high-viscosity glycerol spherical models break down independently of the Mach number. Pressure wave emissions are accurately tracked by all tested models that assume a finite propagation velocity; however, shock wave emissions at high compression ratios can only be tracked by the Kirkwood-Bethe model. In the second part, a bubble pair is subjected to an ultrasonic pulse, and spherical volume oscillations and pressure emissions of bubbles are compared using various coupled-spherical-bubble approaches. DNS results show that jetting during collapse reduces gas compression, leading spherical models to overpredict internal pressure. While spherical models are effective for isolated bubbles in ideal conditions, DNS is essential for accurately capturing inter-bubble interactions. Nevertheless, spherical models provide good accuracy in the case of a bubble collapse without jetting, even when perfect sphericity is not preserved.

The present paper investigates the energy intensity of ammonia production by a freely oscillating microbubble placed in an infinite liquid domain. The spherical bubble initially contains a mixture of nitrogen and hydrogen. The bubble is expanded from its equilibrium size to a specific maximum radius via an isothermal expansion. The work needed to expand the bubble is its potential energy calculated by the sum of the work done by the internal gas, the work needed to displace the mass of the surrounding liquid, and the work needed to increase the area of the bubble against the surface tension. During the radial pulsation of the freely oscillating bubble, the internal temperature can reach several thousands of kelvin inducing chemical reactions. The chemical yield is computed by solving a set of ordinary differential equations describing the radial dynamics of the bubble (Keller—Miksis equation), the temporal evolution of the internal temperature (first law of thermodynamics), and the concentrations of the chemical species (reaction mechanism). The control parameters during the simulations were the equilibrium bubble size, the initial expansion ratio, the ambient pressure, and the initial concentration ratio of nitrogen and hydrogen. In the best-case scenario, the energy requirement in terms of GJ/t is 18.4 times higher than the best available facility of the Haber—Bosch process (assuming that the hydrogen is produced via the electrolysis of water).

This study numerically explores the suppression of bubble jet formation in oscillating microbubble pairs under excitation with an ultrasonic pulse, focusing on the conditions that lead to bubble collapse without jetting. Bubble jets (i.e., liquid jets penetrating the bubble) are typically observed in collapsing bubble pairs. However, jet formation can be avoided when the distance between the bubbles is kept within a specific range. We investigate identical-sized bubble pairs aligned along an axis and subjected to a single-cycle ultrasound pulse. Simulations are conducted using the axisymmetric assumption with the ALPACA compressible multiphase flow solver. Our findings revealed that the domain where jet formation is suppressed becomes smaller as the bubble compression increases. This is demonstrated by decreasing the bubble size and the excitation frequency, which allows for greater bubble growth. These results indicate that while jet suppression is feasible for bubble pairs with high compression ratios, it becomes increasingly sensitive to distance.

This study investigates the theoretical energy intensity of ammonia production via sonochemical reactions in non-Newtonian test fluids. A single, freely oscillating microbubble containing nitrogen and hydrogen is modelled using the Keller–Miksis equation, the first law of thermodynamics, and a detailed reaction mechanism. The goal is to assess whether modifying fluid properties can improve the energy intensity compared to conventional methods. Key parameters—including bubble size, ambient pressure, gas composition, and rheological properties—are varied systematically. The total energy input includes bubble expansion work, hydrogen production via electrolysis, and gas compression energy. The lowest energy intensity achieved is 682.6 GJ/t, which is 17.5 times higher than the Haber–Bosch process using renewable hydrogen. Compared to previous studies in water, a 5.3% improvement is observed, attributed primarily to the increased sound speed. The non-Newtonian rheology had only minor influence, suggesting that future efforts should focus on optimizing acoustic parameters and fluid compressibility rather than rheological properties.

Reinforcement Learning (RL) is employed to develop control techniques for manipulating acoustic cavitation bubbles. This paper presents a proof of concept in which an RL agent is trained to discover a policy that allows precise control of bubble positions within a dual-frequency standing acoustic wave field by adjusting the pressure amplitude values. The agent is rewarded for driving the bubble to a target position in the shortest possible time. The results demonstrate that the agent exploits the nonlinear behaviour of the bubble and, in specific cases, identifies solutions that cannot be addressed using the linear theory of the primary Bjerknes force. The RL agent performs well under domain randomization, indicating that the RL approach generalizes effectively and produces models robust against noise, which could arise in real-world applications.

A detailed GPU-based parameter study is performed on the nonlinear shape deformation of acoustically excited bubbles using a second-order perturbation theory developed by Shaw (2006). The parameter scan is utilized for an extensive validation study based on a detailed measurement study conducted by Cleve et al. (2019). Out of the ten measurements, six exhibit an excellent match with the simulation results. For the discrepancies of the remaining four, the authors identified two causes. First, the parameter identification of the measurement is prone to significant error; second, the dynamics of the surface wave oscillation is out of the validity limit of the employed model.

The present paper investigates the energy efficiency of hydrogen production by a freely oscillating microbubble placed in an infinite domain of liquid water. The spherical bubble initially contains a mixture of argon and water vapour. The bubble is expanded from its equilibrium size to a specific maximum radius via an isothermal expansion. The work needed to expand the bubble is its potential energy calculated by the sum of the work done by the internal gas, the work needed to displace the mass of the surrounding liquid, and the work needed to increase the area of the bubble against the surface tension. During the radial pulsation of the freely oscillating bubble, the internal temperature can reach several thousands of degrees of Kelvin inducing chemical reactions. The chemical yield is computed by solving a set of ordinary differential equations describing the radial dynamics of the bubble (Keller-Miksis equations), the temporal evolution of the internal temperature (first law of thermodynamics), and the concentration of the chemical species (reaction mechanism). The control parameters during the simulations were the equilibrium bubble size, initial expansion ratio, ambient pressure and temperature, the accommodation coefficient of the evaporation/condensation and the surface tension. In the best-case scenario, the energy requirement is 4072.3 MJ/kg.

The present paper studies the energy intensity of ammonia production by a freely oscillating microbubble placed in an infinite domain of liquid. The initial content of the bubble is a mixture of hydrogen and nitrogen. The bubble is expanded isothermically to a maximum radius, then it is "released" and oscillates freely. The input energy is composed of the potential energy of the bubble at the maximum radius, the energy required to produce hydrogen, and the pumping work in case a vacuum is employed. The chemical yield is computed by solving the underlying governing equations: the Keller-Miksis equation for the radial dynamics, the first law of thermodynamics for the internal temperature and the reaction mechanism for the evolution of the concentration of the chemical species. The control parameters during the simulations are the equilibrium bubble size, initial expansion ratio, ambient pressure, the initial concentration ratio of hydrogen and the material properties of the liquid. At the optimal parameter setup, the energy intensity is 90 .17 GJ / t that is 2 .31 times higher than the best available technology, the Haber-Bosch process. In both cases, the hydrogen is generated via water electrolysis.

The present paper investigates the energy efficiency of ammonia production by a freely oscillating microbubble placed in an infinite domain of liquid. The spherical bubble initially contains a mixture of nitrogen and hydrogen. The bubble is expanded from its equilibrium size to a specific maximum radius via an isothermal expansion. The work needed to expand the bubble is its potential energy calculated by the sum of the work done by the internal gas, the work needed to displace the mass of the surrounding liquid, and the work needed to increase the area of the bubble against the surface tension. During the radial pulsation of the freely oscillating bubble, the internal temperature can reach several thousands of degrees of Kelvin inducing chemical reactions. The chemical yield is computed by solving a set of ordinary differential equations describing the radial dynamics of the bubble (Keller-Miksis equations), the temporal evolution of the internal temperature (first law of thermodynamics), and the concentration of the chemical species (reaction mechanism). The control parameters during the simulations were the equilibrium bubble size, initial expansion ratio, ambient pressure, and the initial concentration ratio of nitrogen and hydrogen. In the best -case scenario, the energy requirement in terms of GJ/t is 6.8 times higher than the best available facility of the Haber-Bosch process (assuming that the hydrogen is produced via the electrolysis of water).

This paper presents a control technique capable of driving a harmonically driven nonlinear system between two distinct periodic orbits. A vital component of the method is a temporary dual-frequency driving with tunable driving amplitudes. Theoretical considerations revealed two necessary conditions: one for the frequency ratio of the dual-frequency driving and another one for torsion numbers of the two orbits connected by bifurcation curves in the extended dual-frequency driving parameter space. Although the initial and the final states of the control strategy are single-frequency driven systems with distinct parameter sets (frequencies and driving amplitudes), control of multistability is also possible via additional parameter tuning. The technique is demonstrated on the symmetric Duffing oscillator and the asymmetric Toda oscillator.

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 bidirectionally 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 highperformance GPU computations of massive parameter studies.

A detailed parameter study is made of chemically active spherical bubbles. The calculations apply an up-to-date chemical mechanism for pure oxygen initial content, taking into account pressure dependency, duplication of chemical reactions, and proper third-body efficiency coefficients. The chemical yield is defined as the amount of substance at the maximum bubble radius, and the dissipated power is approached in a relatively new method. The parameter study focuses on finding the parameter combinations where maximum yield and maximum energy efficiency arise for various chemical species (O3, OH radical, H2 and H2O2). Results show that the locations of maximum yield and efficiency points differ significantly, depending on the chemical species. Usually, neither chemical yield nor efficiency values arise at maximum pressure amplitude and minimum driving frequency (as one would presumably expect).

A közelmúlt környezeti-, társadalmi- és gazdasági változásai ráirányították a figyelmet a globális ellátási láncok sérülékenységére. Különösen azokban az esetekben igaz ez, amikor a külső befolyásoló tényezők válságszerűek, hiszen a válságok – természetükből adódóan – újszerű kezelést, megoldást kívánnak. Az ellátási lánc menedzsment tudományterülete jelenleg éppen olyan periódusban van, amikor ezeket az újszerű megoldásokat szükséges felszínre hozni, hiszen a korábbi gyakorlatok már nem feltétlenül képesek szavatolni az ellátási láncok szakadásmentes és kiszámítható működését a megváltozott feltételrendszerben. Tanulmányunkban összefoglaljuk a közelmúlt azon traumáit, amelyek közvetlen vagy közvetett hatást gyakoroltak a globális ellátási láncokra. E tekintetben nem a közvetlen vagy közvetett jellemzőre koncentráltunk, hanem az ellátási láncokra gyakorolt hatás mértékére. A globális befolyásoló hatások számbavételén túl vizsgáljuk az egyes jelenségek logisztikai, ellátási lánc szervezési következményeit, melyek okán várhatóan számos vállalat átalakítja üzleti modelljét. Tanulmányunkban a szcenárió-elemzés módszertanát alkalmazva megfogalmazzuk az átalakulás lehetséges jövőbeli dimenzióit, szem előtt tartva ezek gyakorlati alkalmazhatóságát, hiszen olyan kihívásokra igyekeznek választ adni, melyekkel a közeljövőben a vállalatoknak szembesülni kell ellátási láncaik megszervezése és működtetése során.

This chapter introduces state-of-the-art modelling techniques of chemical kinetics inside a single spherical oscillating bubble placed in an infinite domain of liquid water. The initial content of the bubble is pure oxygen and water vapor. The reaction mechanism that governs chemical kinetics inside the bubble takes into account many aspects that are usually neglected in previous sonochemical investigations. First, at the collapse state of a bubble, the pressure inside can reach several hundreds of atmospheres; thus, the incorporation of the pressure dependence of reactions in which a third body plays a role is mandatory. Second, third body efficiencies are also taken into account. Third, the backward reactions are computed via thermodynamic equilibrium conditions. Fourth, reactions that have non-Arrhenius temperature dependence can be described by two sets of Arrhenius constants. These reactions are identified and modelled properly. As more experimental data have been accumulated over the decades, the Arrhenius constants of certain reactions have been changed even by orders of magnitude. Therefore, it is also important to employ up-to-date values of the Arrhenius constants. The behavior of the proposed model is demonstrated with reaction condition sets (pressure amplitude, frequency and bubble size) typically used during the experiments. The production of important chemical species (e.g., hydrogen or free radicals) are investigated from energy efficiency points of view (yield in mole per unit dissipated power of the bubble).

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.