Numerical study of the effect of liquid compressibility on acoustic droplet vaporization

In acoustic droplet vaporization (ADV), a cavitated bubble grows and collapses depending on the pressure amplitude of the acoustic pulse. During the bubble collapse, the surrounding liquid is compressed to high pressure, and liquid compressibility can have a significant impact on bubble behavior and ADV threshold. In this work, a one-dimensional numerical model considering liquid compressibility is presented for ADV of a volatile microdroplet, extending our previous Rayleigh-Plesset based model [Ultrason. Chem. 71 (2021) 105361]. The numerical results for bubble motion and liquid energy change in ADV show that the liquid compressibility highly inhibits bubble growth during bubble collapse and rebound, especially under high acoustic frequency conditions. The liquid compressibility effect on the ADV threshold is quantified with varying acoustic frequencies and amplitudes.     

A new pressure formulation for gas-compressibility dampening in bubble dynamics models

We formulated a pressure equation for bubbles performing nonlinear radial oscillations under ultrasonic high pressure amplitudes. The proposed equation corrects the gas pressure at the gas–liquid interface on inertial bubbles. This pressure formulation, expressed in terms of gas-Mach number, accounts for dampening due to gas compressibility during the violent collapse of cavitation bubbles and during subsequent rebounds. We refer to this as inhomogeneous pressure, where the gas pressure at the gas–liquid interface can differ to the pressure at the centre of the bubble, in contrast to homogenous pressure formulations that consider that pressure inside the bubble is spatially uniform from the wall to the centre. The pressure correction was applied to two bubble dynamic models: the incompressible Rayleigh–Plesset equation and the compressible Keller and Miksis equation. This improved the predictions of the nonlinear radial motion of the bubble vs time obtained with both models. Those simulations were also compared with other bubble dynamics models that account for liquid and gas compressibility effects. It was found that our corrected models are in closer agreement with experimental data than alternative models. It was concluded that the Rayleigh–Plesset family of equations improve accuracy by using our proposed pressure correction.     

The Asymmetric Collapse of Bubbles in Compressible Liquid

The analytical solution ora bubble collapse close to a solid boundary in a compressible water is investigatedby means of a perturbation method to first order in the bubble wall Mach number. It is shown, in this paper, that itis the Rayleigh-Plesset equation for incompressible liquid to zero order solution or similar to the Gilmore equation forcompressible water to first order solution when the effect of solid boundary is negligibly small enough, i.e., sufficientlyfar away from the bubble center.     

A comparison of broadband models for sand sediments

Chotiros and Isakson [J. Acoust. Soc. Am. 116(4), 2011-2022 (2004)] recently proposed an extension of the Biot-Stoll model for poroelastic sediments that makes predictions for compressional wave speed and attenuation, which are in much better accord with the experimental measurements of these quantities extant in the literature than either those of the conventional Biot-Stoll model or the rival model of Buckingham [J. Acoust. Soc. Am. 108(6), 2796-2815 (2000)]. Using a local minimizer, the Nelder-Mead simplex method, it is shown that there are generally at least two choices of the Chotiros-Isakson parameters which produce good agreement with experimental measurements. Since one postulate of the Chotiros-Isakson model is that, due to the presence of air bubbles in the pore space, the pore fluid compressibility is greater than that of water, an alternative model based on a conjecture by Biot [J. Acoust. Soc. Am. 34(5), 1254-1264 (1962)], air bubble resonance, is considered. While this model does as well or better than the Chotiros-Isakson model in predicting measured values of wave speed and attenuation, the Rayleigh-Plesset theory of bubble oscillation casts doubt on its plausibility as a general explanation of large dispersion of velocity with respect to frequency.     

声场中水力空化泡的动力学特性

以水为工作介质,考虑了液体黏性、表面张力、可压缩性及湍流作用等情况,对文丘里管反应器中空化泡在声场作用下的动力学行为特性进行了数值研究.分析了超声波频率、声压及喉径比对空化泡运动特性以及空化泡崩溃时所形成泡温以及压力脉冲的影响.结果表明,超声将水力空化泡运动调制成稳态空化,有利于增强空化效果. 关键词： 超声波 水力空化 湍流 气泡动力学     

超声珩磨区实际气体的单空泡动力学分析

为进一步揭示功率超声振动的珩磨机理,以珩磨液为工作介质,研究了功率超声珩磨环境中实际气体的单空泡动力学特性。基于Rayleigh-Plesset方程,应用实际气体绝热方程和范德瓦尔斯方程对其进行了修正,建立了功率超声珩磨环境中实际气体的单空泡动力学方程以及实际气体单空泡共振频率方程。并运用4~5阶RungeKutta法模拟了不同超声条件(声压幅值、空泡初始半径、振动频率)对泡壁的运动以及运动速度的影响。结果表明:较高的声压幅值,空泡理论共振半径R'0与初始半径R0的比值为102数量级以及较低的超声频率有利于超声珩磨磨削区空化效应的发生。     

匀强磁场对水中气泡运动的影响

基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

The Rayleigh-Plesset equation in terms of volume with explicit shear losses

The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh-Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh-Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh-Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.     

Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei

Numerical modelling of acoustic cavitation threshold in water is presented taking into account non-condensable bubble nuclei, which are composed of water vapor and non-condensable air. The cavitation bubble growth and collapse dynamics are modeled by solving the Rayleigh-Plesset or Keller-Miksis equation, which is combined with the energy equations for both the bubble and liquid domains, and directly evaluating the phase-change rate from the liquid and bubble side temperature gradients. The present work focuses on elucidating acoustic cavitation in water with a wide range of cavitation thresholds (0.02–30 MPa) reported in the literature. Computations for different nucleus sizes and acoustic frequencies are performed to investigate their effects on bubble growth and cavitation threshold. The numerical predictions are observed to be comparable to the experimental data in the previous works and show that the cavitation threshold in water has a wide range depending on the bubble nucleus size.     

Thermodynamic of collapsing cavitation bubble investigated by pseudopotential and thermal MRT-LBM

The thermodynamic of cavitation bubble collapsing is a complex fundamental issue for cavitation application and prevention. The pseudopotential and thermal multi-relaxation-time lattice Boltzmann method (MRT-LBM) is adopted to investigate the thermodynamic of collapsing cavitation bubble in this paper. The simulation results satisfy the maximum temperature equation of the bubble collapse, which derived from the Rayleigh-Plesset (R-P) equation. The validity of thermal MRT-LBM in simulating the collapse process of cavitation bubble is verified. It shows that the temperature evolution of vapor-liquid phase is well captured. Furthermore, the two-dimensional (2D) temperature, velocity and pressure field of the bubble near a solid wall are analyzed. The maximum temperature inside the bubble and wall temperature under different position offset parameters are discussed in details.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.     

声场中气泡运动的混沌特性

以水为工作介质,考虑了液体的可压缩性,研究了声场中气泡的运动特性,模拟了声波频率、声压幅值、气泡初始半径以及液体的表面张力和黏滞系数的变化对气泡运动状态的影响. 分析了空化处理效果与气泡运动状态之间关系. 结果表明:气泡运动处于混沌状态,是提高声空化降解有机污染物能力的最重要因素. 关键词： 声空化 混沌 相图 功率谱图     

Mixture segregation by an inertial cavitation bubble

Pressure diffusion is a mass diffusion process forced by pressure gradients. It has the ability to segregate two species of a mixture, driving the densest species toward high pressure zones, but requires very large pressure gradients to become noticeable. An inertial cavitation bubble develops large pressure gradients in its vicinity, especially as the bubble rebounds at the end of its collapse, and it is therefore expected that a liquid mixture surrounding such a bubble would become segregated. Theory developed in an earlier paper shows that this is indeed the case for sufficiently large molecules or nano-particles. The main theoretical results are recalled and a possible implication of this segregation phenomenon on the well-known cavitation-enhanced crystals nucleation is proposed.     

Observations of the collapses and rebounds of millimeter-sized lithotripsy bubbles

Bubbles excited by lithotripter shock waves undergo a prolonged growth followed by an inertial collapse and rebounds. In addition to the relevance for clinical lithotripsy treatments, such bubbles can be used to study the mechanics of inertial collapses. In particular, both phase change and diffusion among vapor and noncondensable gas molecules inside the bubble are known to alter the collapse dynamics of individual bubbles. Accordingly, the role of heat and mass transport during inertial collapses is explored by experimentally observing the collapses and rebounds of lithotripsy bubbles for water temperatures ranging from 20 to 60 °C and dissolved gas concentrations from 10 to 85% of saturation. Bubble responses were characterized through high-speed photography and acoustic measurements that identified the timing of individual bubble collapses. Maximum bubble diameters before and after collapse were estimated and the corresponding ratio of volumes was used to estimate the fraction of energy retained by the bubble through collapse. The rebounds demonstrated statistically significant dependencies on both dissolved gas concentration and temperature. In many observations, liquid jets indicating asymmetric bubble collapses were visible. Bubble rebounds were sensitive to these asymmetries primarily for water conditions corresponding to the most dissipative collapses.     

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.     

Variation of measured sound speeds in gaseous and liquid air with temperature and pressure

Based on sound speeds in gaseous and liquid air measured by Younglove and Frederick [Int. J. Thermophys. 13(6), 1033-1041 (1992)], empirical equations for the computation of sound speeds in the above media at relatively smaller temperature and pressure ranges were derived. For gaseous air, over a temperature range from 200 to 300 K and pressure from 0.614 to 10.292 MPa, the maximum deviation between the measured sound speeds and those computed with the empirical equation is 56 ppm. For liquid air, over the ranges from 90 to 110 K for temperature and from 0.763 to 13.823 MPa for pressure, the corresponding deviation is 173 ppm.     

Numerical modelling of ultrasonic waves in a bubbly Newtonian liquid using a high-order acoustic cavitation model

To address difficulties in treating large volumes of liquid metal with ultrasound, a fundamental study of acoustic cavitation in liquid aluminium, expressed in an experimentally validated numerical model, is presented in this paper. To improve the understanding of the cavitation process, a non-linear acoustic model is validated against reference water pressure measurements from acoustic waves produced by an immersed horn. A high-order method is used to discretize the wave equation in both space and time. These discretized equations are coupled to the Rayleigh-Plesset equation using two different time scales to couple the bubble and flow scales, resulting in a stable, fast, and reasonably accurate method for the prediction of acoustic pressures in cavitating liquids. This method is then applied to the context of treatment of liquid aluminium, where it predicts that the most intense cavitation activity is localised below the vibrating horn and estimates the acoustic decay below the sonotrode with reasonable qualitative agreement with experimental data.