Maximum Bubble Radius Research Articles

Modelling Lipid-Coated Microbubbles in Focused Ultrasound Applications at Subresonance Frequencies

We present a computational study of the behaviour of a lipid-coated SonoVue microbubble with initial radius 1 µm ≤ R0 ≤ 2 µm, excited at frequencies (200–1500 kHz) significantly below the linear resonance frequency and pressure amplitudes of up to 1500 kPa—an excitation regime used in many applications of focused ultrasound. The bubble dynamics are simulated using the Rayleigh–Plesset equation and the Gilmore equation, in conjunction with the Marmottant model for the lipid monolayer coating. Also, a new continuously differentiable variant of the Marmottant model is introduced. Below the onset of inertial cavitation, a linear regime is identified in which the maximum pressure at the bubble wall is linearly proportional to the excitation pressure amplitude and the mechanical index. This linear regime is bounded by the Blake pressure, and, in line with recent in vitro experiments, the onset of inertial cavitation is found to occur at an excitation pressure amplitude of approximately 130–190 kPa, depending on the initial bubble size. In the nonlinear regime the maximum pressure at the bubble wall is found to be readily predicted by the maximum bubble radius, and both the Rayleigh–Plesset and Gilmore equations are shown to predict the onset of sub- and ultraharmonic frequencies of the acoustic emissions compared with in vitro experiments. Neither the surface dilational viscosity of the lipid monolayer nor the compressibility of the liquid has a discernible influence on the quantities studied, but accounting for the lipid coating is critical for accurate prediction of the bubble behaviour. The Gilmore equation is shown to be valid for the bubbles and excitation regime considered, and the Rayleigh–Plesset equation also provides accurate qualitative predictions, even though it is outside its range of validity for many of the cases considered.

Considering solubility disparity and acoustic-cavitation susceptivity of neoteric solvents to accurately predict sono-recovery yield of value-added compounds

This work aimed to theoretically predict the sono-recovery yield of value-added compounds in various neoteric solvents through considering solubility difference and acoustic-cavitation variability. Preferentially, the solvent-solute compatibility was calculated by Hansen solubility parameters (HSPs), but unexpectedly the results showed that the HSPs prediction was not preferably consistent with the tendency of extraction yield. Subsequently, calculated correlations between maximum bubble radius (MBR) and solvent properties showed the following hierarchies: viscosity (−0.86**) > density (−0.83**) > surface tension (−0.64**), and MBR can be considered as a mirror of solvent properties to reflect the flavonoids yield (r = 0.75**) but that was inapplicable to phenolic acids (r = 0.33). Evidentially, micromorphological observation exhibited that significant modification of epidermis had an intense disposition to occur in the solvents with greater MBR such as methanol, water and ethyl acetate. No significant sonochemiluminescence (SCL) signal was captured including aqueous malic acid/choline chloride (ChCl), lactic acid/ChCl, sucrose/ChCl, methanol, ethyl lactate, and glycerol, but the addition of ChCl into alcohols can enhance the production of free radicals. The generation of free radicals was independent of MBR and their impacts on final compounds presented pluralist and limited effects. In addition, how to more accurately quantify the effects of free radicals on the final compounds is still a poser. Overall, This work constructed a bridge between theoretical calculation and laboratory data and demonstrated the fundamentality of maximum bubble radius in the biorefinery of value-added compounds.

Analysis of discharge regimes obtained by microsecond underwater electrical breakdown in regard to energy balance

This paper reports the analysis of the energy balance of micro-second pin-to-pin discharges in water as well as the bubble dynamics involved in the electrical breakdown. This approach, complementary to previous electrical and optical measurements, is of primary interest to better understand the phenomena leading to different discharge regimes despite having the same applied conditions. This work indicates that different discharge regimes are related to different energy distributions through thermal and mechanical components despite the same initial energy; as a consequence, the breakdown involves different maximum radius of the cavitation bubble as well as bubble dynamics. For the cathode regime the initial energy is mainly converted into thermal energy (70%) that involves the formation of a small vapor filled bubble (∼1 mm) followed by many rebounds. For the anode regime, the initial energy is evenly distributed into thermal and mechanical components (43%/57%) which results in a higher empty bubble (∼2 mm) that collapses. The bubble growth is directly related to the energy dissipated during the breakdown, following same power law but with different constant. This work validates the hypothesis of the thermal regime for cathode breakdown whereas the anode regime is mainly driven by mechanical effects. Despites these discrepancies, simulations using a modified Rayleigh–Plesset model show that the growth of the first bubble is controlled by inertial effects for both regimes.

An experimental and numerical study on the dynamical behaviors of the rebound cavitation bubble near the solid wall

The final collapse of the rebound cavitation bubble may be more violent than its initial, resulting in more severe damage to the nearby structures. To better understand the dynamical behaviors of the rebound cavitation bubble, the multi-period evolution of the cavitation bubble near the solid wall is investigated experimentally and numerically. Due to multiple factors affecting the rebound cavitation bubble behaviors, a compressible two-phase solver considering phase change and thermodynamic effect simultaneously is developed in OpenFOAM in this study. Validations are conducted by comparing the numerical results with corresponding experimental data. The essential and comprehensive dynamics of the rebound cavitation bubble is well reproduced and analyzed, which helps reveal the underlying physical mechanisms. The potential damage is numerically quantified by the pressure peak at the wall center. The quantitative effect of the dimensionless standoff distance γ on the pressure peaks is analyzed with four distinct stages identified. Moreover, the maximum rebound radius, corresponding to the amount of the initial energy during the rebound stage, and maximum temperature within the bubble at different γ are also discussed. The results show that the maximum rebound bubble radius increases first and then decreases with the increase of γ. In addition, the effect of the γ on the maximum temperature is given with three distinct stages identified.

Effect of frequency ratio and phase difference on the dynamic behavior of a cavitation bubble induced by dual-frequency ultrasound

The best cavitation can be obtained only with an appropriate frequency ratio and phase difference. To optimize dual-frequency ultrasonic cavitation and to analyze the influence of the frequency ratio and phase difference, a dynamic model of dual-frequency ultrasonic cavitation that considers energy and material exchange inside and outside the bubble was established. The results show that the negative-pressure amplitude of dual-frequency ultrasound is higher than that of single-frequency ultrasound for the same energy input. For a harmonic, the phase difference that results in a maximum of the negative-pressure amplitude of dual-frequency ultrasound is periodic for different frequency ratios. The phase difference that results in expansion–contraction oscillations of the bubble changes periodically as 1.5π → π → 0.5π → 0 → 1.5π for different frequency ratios. The maximum bubble radius and the maxima of the pressure, energy, and number of water vapor molecules inside the bubble all reduce spirally and the intensity of cavitation decreases with an increase of the frequency ratio. Compared with a harmonic, the maxima of the cavitation parameters are less affected by the phase difference for an ultraharmonic. Therefore, similar cavitation can be easier to obtain by employing an ultraharmonic, which is helpful in achieving stable cavitation.

Study of methods for controlling direction and velocity of liquid jets formed during subcooled boiling

The mechanism of submerged jets generation during subcooled surface and volumetric water boiling is studied experimentally and numerically. The boiling take place near the tip of the optical fiber through which the laser radiation is supplied. It is shown that the interaction of a collapsing bubble with the end face of the optical fiber leads to the symmetry breaking of the bubble, following by the water jet generation. The jet velocity depends on the collapse rate as well as on the ratio of the maximum bubble radius reached during the inflation stage to the fiber radius and, therefore, on the laser radiation intensity. Other problem parameters affecting characteristics of the generated jets are the temperature of the surrounding liquid and the fiber radius. Experiments with two perpendicular optical fibers demonstrate vector summation of the velocities of the jets generated by each individual fiber. Presented results might contribute to the development of new operating medical technologies for laser surgical treatment of a wide range of common diseases.

Numerical investigation of the interactions between a laser-generated bubble and a particle near a solid wall

The interactions between the bubbles and the particles near structures are important issues for the applications of the cavitation in the fluid machinery. To study the hidden microscopic mechanisms, a numerical method for simulating the laser-generated bubble between the solid wall and a particle is developed in this paper with considerations of the viscosities and the compressibility of the gas and the liquid phases, as well as the surface tension between them. The gas-liquid interface is tracked by the coupling level set and the volume of fluid (CLSVOF) method. The numerical results clearly reveal that the particle can influence the cavitation bubble behaviors. The potential damage of the nearby structures is numerically quantified in terms of the wall pressure, which helps better understand the synergetic effects of the particle on the cavitation. The effects of three dimensionless parameters on the wall pressure are also investigated, especially, on the peak pressure, namely, γ1 (defined as L1 / Rmax, where L1 is the distance from the center of the initial bubble to the solid wall and Rmax is the maximum bubble radius), γ2 (defined as L2 / Rmax, where L2 is the distance from the lower surface of the spherical particle to the initial bubble center) and θ (defined as Rp / Rmax, where Rp is the spherical particle radius). Further numerical results show that these parameters play a dominant role in determining the peak pressure. When γ1 1.00, the peak pressure is caused by the shock wave. With the increase of θ or decrease of γ2, the peak pressure increases. When γ2 > 2.00, the effect of the particle on the bubble behavior can be neglected.

A model for the fate of carbon dioxide from a simulated carbon storage seep

Offshore geological carbon storage (GCS) is a rapidly developing technology essential for meeting international climate goals. While the likelihood of leakage from a properly planned geological sequestration site is low, assurance that CO2 stays contained will require robust monitoring programs. While seismic imaging methods are used to monitor the geological reservoir, the ideal method for monitoring the water column above the reservoir depends on the fate and transport of CO2. Whether CO2 is likely to be present as a rising seep of bubbles or dissolved in the water column near the seafloor will determine the appropriate monitoring technology and lead to a better understanding of the environmental impact of a potential leak. In this study, high definition video of a laboratory release of a carbon dioxide bubble seep recorded the size distribution of bubbles as a function of flow rate and orifice diameter. The transport of CO2 from different bubble size distributions was then modeled using the Texas A&M Oil Spill Calculator modeling suite. Model results show that the most important factor determining the rise height and transport of CO2 from the simulated leak was the maximum initial bubble size. For a maximum bubble radius of 5 mm, 95% of CO2 in the simulated seep reached a height of 17.1 m above the seafloor. When the maximum bubble radius was limited to 3 mm, 95% of CO2 dissolved by 7.8 m above the seafloor. The modeled results were verified during a controlled release of CO2 in Oslo Fjord.

Propagation of Shock Wave at the Cavitation Bubble Expansion Stage Induced by a Nanosecond Laser Pulse

Abstract The objective of this paper is to reveal the attenuation characteristics of a shock wave after optical breakdown in water, with laser pulses of 12-ns duration. A high time-resolved shadowgraph method is applied to capture the temporal evolutions of the cavitation bubble wall and shock wave. The experiments are carried out on a single bubble generated far away from the free surface and the rigid walls with laser pulse energies of 22 mJ, 45 mJ, and 60 mJ. The results show that a high, time-resolved, wave front velocity of the shock wave is identified, and the maximum velocity can reach up to around 4000 m/s. An asymmetric shock wave is observed at the very start of the bubble expansion stage, and the process of the sharp attenuation of wave front velocity down to sound velocity is accomplished within 310 ns. The possible relationship of the cavitation bubble and the shock wave is discussed and a prediction model, using the maximum bubble radius and the corresponding time calculated by the Gilmore model, is proposed to calculate the location of the wave front.

The radiated acoustic pressure and time scales of a spherical bubble

Numerical simulations of violent bubble dynamics are often associated with numerical instabilities at the end of collapse, when a shock wave is emitted. Based on the Keller–Miksis equation, we show that this is caused by two time scales associated with the phenomenon. Nonsingular equations are thus formed based on asymptotic expansion theory and the time derivatives of the bubble radius are shown to have algebraic singularities in the Mach number. The period of oscillation is shown to divide into two asymptotic layers: a long and short time scale. The short time scale, on which significant acoustic radiation is emitted from the bubble, has been determined to be , where c is the speed of sound in the liquid, the maximum bubble radius, ρ the liquid density, the hydrostatic pressure of the liquid, the vapour pressure of the liquid and κ the polytropic index of the bubble gas. Using the scalings for this short time scale, the radiated acoustic pressure scale has been deduced to be , where is the radial distance from the bubble centre to the point of measurement. The results are validated by comparison with experimental results.

Predicting laser‐induced cavitation near a solid substrate

AbstractThe asymmetric collapse of cavitation bubbles near a solid substrate generates large wall shear stresses, the precise magnitude of which is still not known with certainty. By comparing numerical simulations and experiments of a laser‐induced cavitation bubble near a solid substrate, we demonstrate that an accurate measurement of the pressure pulse emitted during bubble inception and of the maximum bubble radius allow a unique initialisation of the simulation. This allows an accurate reproduction of the asymmetric collapse, with reliable predictions of the shear stress and pressure generated at the substrate.

Single–bubble dynamics in histotripsy and high–amplitude ultrasound: Modeling and validation

A variety of approaches have been used to model the dynamics of a single, isolated bubble nucleated by a microsecond length high–amplitude ultrasound pulse (e.g. a histotripsy pulse). Until recently, the lack of single–bubble experimental radius vs. time data for bubble dynamics under a well–characterized driving pressure has limited model validation efforts. This study uses radius vs. time measurements of single, spherical histotripsy–nucleated bubbles in water to quantitatively compare and validate a variety of bubble dynamics modeling approaches, including compressible and incompressible models as well as different thermal models. A strategy for inferring an analytic representation of histotripsy waveforms directly from experimental radius vs. time and cavitation threshold data is presented. We compare distributions of a calculated validation metric obtained for each model applied to 88 experimental data sets. There is minimal distinction (<1%) among the modeling approaches for compressibility and thermal effects considered in this study. These results suggest that our proposed strategy to infer the waveform, combined with simple models minimizing parametric uncertainty and computational resource demands accurately represent single–bubble dynamics in histotripsy, including at and near the maximum bubble radius. Remaining sources of parametric and model–based uncertainty are discussed.

Comparative Investigation of the Spherical Acoustic Microbubble Models in an Unbounded Liquid.

Microbubble oscillating associated with many applications in biomedical and engineering sectors. The spherical oscillations of a single microbubble submerged in a quiescent liquid exerted by an acoustic force can be governed either by the Rayleigh-Plesset (RP) equation or by the Keller-Miksis (KM) equation under different physical assumptions. In this paper, both models were numerically and analytically analyzed, and the systematic parametric study was performed. The viscosity and compressibility effects and linearization in both models were investigated with the aids of MATLAB and Maple tools.&nbsp; In KM, the effects of the linear and nonlinear equations of states (EOS) compared for updating density with time. At the minimum bubble radius, the liquid viscosity surrounding bubble surface expected to be decreased due to rising in temperature. This leads to effects the maximum bubble radius for upcoming cycles.

Effects of immersion depth on the dynamics of cavitation bubbles generated during ns laser ablation of submerged targets

On laser shock peening and underwater laser micromachining, previous studies have shown that the immersion depth of the sample significantly affects laser ablation of submerged targets; however, the underlying mechanisms are still obscure. In this work, we observe and study the formation, growth, and collapse of cavitation bubbles generated during nanosecond laser ablation of submerged titanium targets that are exposed at various immersion depths utilizing a stroboscopic shadowgraphy system. Our results show that the initial laser absorption and cavitation bubble formation after the laser incidence are not affected by the immersion depth. Nevertheless, when the immersion depth is less than the maximum radius of the generated cavitation bubble, the bubble shrinks asymmetrically during the collapse stage. Thus, the cavitation bubble is not fully compressed at the maximum implosion, and phenomena related to the violent implosive collapse, e.g., the second etching effect and the emission of strong shockwaves, are absent. We also propose a strategy to estimate the maximum radius of the laser-induced cavitation bubble, which helps to determine the optimal liquid depth for related engineering applications. Our results provide succinct explanations for the effects of immersion depth on pulsed laser ablation of submerged targets, which are important steps toward a deeper understanding of laser-materials’ interactions in liquid environments.

Study on the quantitative law of wall pressure caused by mini-charge underwater explosion bubble

The wall pressure caused by underwater explosion is always a key problem in the anti-explosion design of naval ships. Notably, the accurate wall pressure caused by underwater explosion bubble is one of the most difficult parts due to the significant nonlinear deformation of the bubble. In present study, the dynamics of an underwater explosion bubble near a rigid wall are captured by high-speed camera and the wall pressure in the wall center are measured by a pressure transducer. The wall pressure with standoff distance parameter γ=d/Rm from 0.38 to 1.54 are recorded, where d represents the vertical distance from the explosive charge center to the wall center, and Rm is the maximum radius of bubble. According to the previous study and the experimental data in this paper, when γ<1.2, the load on the wall center has obvious double-peak phenomenon, that is, the composition of the re-entrant jet load and the bubble collapse load. To obtain the quantitative law of wall pressure caused by mini-charge underwater explosion bubble, we proposed a mathematical model to describe the time-pressure curve when γ<1.2. And according to the conclusion in our previous study (Chen et al., 2018), based on the boundary element method (BEM), the space distribution of the wall pressure was obtained.

Collapse Dynamics of Hemispherical Cavitation Bubble in Contact with a Solid Boundary

The dynamics of electrochemically produced hemispherical bubble at solid-liquid interface is investigated experimentally. Time-resolved photography is applied to measure the position of bubble wall as a function of time. By means of stroboscope schlieren photography with 1 μs exposure time it is shown that the development of instabilities of the bubble shape are general feature of the bubble dynamics in contact with the solid boundaries. The acoustic transients emitted after cavitation bubble collapse were registered with the laser beam deflection technique. Duration of the transient of 50–60 ns enables to estimate maximum pressure as 2.5 kbar, when the maximum bubble radius is 1 mm.

Experimental investigation on the interface shape of bubble condensation for vertical upward steam jet at low mass flux

Steam direct contact condensation in subcooled water is widely used in various industries. The steam-water interface shape is an essential parameter for direct contact condensation. An experimental study was carried out to investigate the flow patterns and interface shape of bubbling regime with a vertical upward steam jet. Steam mass flux and water temperature were 8.34–50.13 kg/(m2∙s) and 40–85°C, respectively. Three flow patterns such as chugging, smooth grown bubble, and rough grown bubble were found based on the dynamic behavior of steam-water interface. The bubble collapse frequency and the maximum bubble radius at the bubble growth stage were calculated. The bubble collapse frequency increased rapidly when the smooth grown bubble regime was transformed into the rough grown regime. When the water temperature was between 40-80°C, the maximum bubble radius initially increased, and then decreased with the increase of steam mass flux. A transition criterion from the smooth grown bubble regime to the rough grown bubble regime was given based on the theoretical analysis and experimental data.

Collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall.

In the present paper, the collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall is experimentally investigated with a high-speed photography system. For a symmetrical setup, the two primary control parameters of the bubble collapsing behavior include the equivalent maximum bubble radius and the distance between the bubble and the edge of the rigid wall. Based on the bubble interface deformation during the collapsing process, three typical cases are identified for the categorization of the phenomenon with the influences of the parameters revealed. Through a quantitative analysis of the obtained high-speed photos, the motions of the bubble interface in different directions are given together with the calculations of the bubble centroid. The primary findings of the present paper could be summarized in terms of the bubble-edge distance as follows. When the bubble is close to the edge, the movement of the bubble interface near the edge will be restricted with a clear neck formation in the middle part of the bubble. For this case, the edge could delay the bubble collapsing time up to 22% of the Rayleigh collapsing time. When the bubble is of the medium distance to the edge, the differences of the expansion or shrinkage of the bubble interface among different directions will be reduced with an olive-shaped bubble formed during the collapsing process. For this range of parameters, the bubble moves rapidly toward the edge especially during the final collapsing stage. When the bubble is far away from the edge, the bubble will be a nearly spherical one.

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 (Rmax-RE)/RE, where RE is the equilibrium size of the bubble and Rmax 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 (Rmax-RE)/RE=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 (Rmax-RE)/RE=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.

Experimental studies of bubble dynamics inside a corner.

The dynamics of a bubble near a corner formed by two flat rigid boundaries (walls), is studied experimentally using a spark-generated bubble. The expansion, collapse, rebound, re-collapse and migration of the bubble, along with jetting and protrusion, are captured using a high-speed camera. Our experimental observations reveal the behaviour of the bubble in terms of the corner angle and the dimensionless standoff distances to the near and far walls in terms of the maximum bubble radius. The bubble remains approximately spherical during expansion except for its surface becoming flattened when in close proximity to a wall. When a bubble is initiated at the bisector of the two walls, the bubble becomes oblate along the bisector during the late stages of collapse. A jet forms towards the end of collapse, pointing to the corner. The closer the bubble to the two walls, the more oblate along the bisector the bubble becomes, and the wider the jet. A bubble initiated near one of the two walls is mainly influenced by the nearer wall. The jet formed is pointing to the near wall but inclined towards the corner. After the jet penetrates through the bubble surface, the bubble becomes a bubble ring, and a bubble protrusion forms following the jet. The bubble ring collapses and subsequently disappears, while the protrusion firstly expands, and then collapses and migrates to the corner.