Bubble Number Density Research Articles

The influence of Fe[sbnd]Ti oxide microlites on bubble nucleation in rhyolitic melts

We conducted a set of high-temperature decompression experiments to constrain the mechanisms of heterogeneous bubble nucleation in high-silica rhyolitic melt that contained 4.6–4.8 wt% H2O. The melt was seeded with two different size fractions of magnetite crystals: 1–2 μm crystals and large crystals of 32–135 μm (long axis). The number density of bubbles (BND) that nucleated on the small crystals was found to increase from 106.5 to 108.7 cm−3 as H2O increasingly supersaturated (ΔP) in the melt from 3 to 23 MPa. At ΔP >23 MPs, however, the number of bubbles nucleated equals the number of small magnetite and no more nucleated with increased ΔP. At the same conditions, the number of bubbles that nucleated on the large crystals increases, from <1 bubble per crystal at ΔP = 3 MPa to 14 ± 4 bubbles per crystal at 58 MPa. We thus find that ΔP has a significant influence on the mechanisms of heterogenous nucleation, but the observed increases in BND are much greater than would be predicted solely from the increase in ΔP. The discrepancy can be reconciled if there are different sites on the crystals that become activated at greater ΔP, leading to greater numbers of bubbles nucleating. The cumulative BND nucleated on small crystals, however, is capped by the number of crystals present. The BND values generated at ΔP >23 MPa in our experiments overlap with those found in ~80 % of naturally occurring pumice. Assuming our experiments are representative of natural pumice, this suggests that explosively erupted magmas either become significantly volatile supersaturated before heterogeneously nucleating bubbles, or that the number of nucleation sites in natural magmas greatly exceed 109 cm−3.

Melt embayments record multi-stage magma decompression histories

Over the last decade, the melt embayment has proven its merit as a robust petrological tool capable of recording magma decompression rates for explosive eruptions. However, the models developed and applied to extract this information from embayments have not accounted for the complexity and nonlinearity of magma flow in the conduit. We present Embayment Decompression in Two Stages (EDiTS): a numerical model for extracting magma decompression rates from measured volatile diffusion profiles preserved in crystal-hosted embayments, approximating magma acceleration using two constant-rate decompression paths. This model solves for three unknown parameters: initial (deeper) and final (shallower) decompression rates, as well as the pressure where a transition occurs. We successfully benchmark EDiTS against existing numerical diffusion models, and use controlled multi-stage decompression experiments on natural quartz-hosted embayments to test the ability of our model to recover known decompression paths. We find that EDiTS is able to closely approximate the known two-stage path in the mixed-volatile (H2O + CO2) experiment, while a constant-rate modeling approach is unable to simultaneously fit H2O and CO2 gradients. However, in the H2O-saturated experiment, there is no unique solution to the resulting gradient, with both constant-rate and two-stage models reproducing the measured profile, and EDiTS notably overestimating the known total ascent time by several hours. Using decompression experiments, we show that constant-rate models can provide misleadingly good fits to embayment H2O gradients produced by more complex decompression histories, and thus the measurement and modeling of multiple diffusing species, when available, can provide crucial constraints. We then apply EDiTS to re-evaluate mixed-volatile embayment datasets from explosive silicic arc and caldera-forming eruptions from five volcanic centers (Yellowstone, WY, USA; Bandelier, NM, USA; Long Valley, CA, USA; Taupo, NZ; Mount St. Helens, WA, USA), where all systems contain initial CO2. In contrast to the minutes to hours of total ascent time extracted from embayment volatile profiles using constant-rate models, our two-stage model resolves slower initial ascent times that span several to >10 h. Final ascent rates are 1–2 orders of magnitude faster than the initial extracted rates, in agreement with theoretical conduit flow model predictions. Application of EDiTS to embayments from the May 18th, 1980 eruption of Mount St. Helens results in an initial stage of ascent on the order of hours consistent with the timing of magma arrival at the surface from the seismically-inferred storage region (7–9 km) ~3.5 h after the initial blast, and a final stage of ascent (<1–5 min) in close agreement with time-integrated bubble number densities. Our combined numerical, experimental, and natural results suggest that, with the application of more advanced models, the melt embayment can provide a complete picture of magma decompression timescales from the deep conduit to the surface.

Enhancing strength and irradiation tolerance of Mg alloy via co-addition of Mn and Ca elements

The Mg alloys with combination of high strength and excellent irradiation resistance are currently required for research reactors. In this work, the novel Mg-3Mn-0.5Ca alloy with a high strength of over 300 MPa has been fabricated via co-addition of Mn and Ca elements. Moreover, the Xe ion implantation (300 °C/4.5 × 1015 ions/cm2) is conducted for pure Mg, Mg-3Mn and Mg-3Mn-0.5Ca alloys. Microstructure characterization shows that the number density of dislocation loops is comparable between Mg-3Mn and pure Mg, while the phase boundary of nano-Mn particles could act as the sink to absorb more Xe atoms, resulting in the abundant formation of Xe bubbles in the matrix of irradiated Mg-3Mn alloy. With further minor addition of Ca element, the formation of Xe bubbles and dislocation loops in Mg-3Mn-0.5Ca alloy has been obviously suppressed, and the abundant grain boundaries (GBs) due to grain refinement then act as the sink region for Xe precipitation. The limited number density of Xe bubbles leads to the extremely low swelling ratio in Mg-3Mn-0.5Ca alloy, ∼0.08 %. The result above suggests that the Mn and Ca co-addition could enhance the mechanical properties and irradiation tolerance of Mg alloys, simultaneously. The present low-alloying strategy would provide a new design reference for novel nuclear materials.

Bubbles Counting Using Organic Pollutants Degradation as a Probe

Relying on the fact that both of chemical and physical impacts of sonication are in strong relation to the number of acoustic cavities, the present paper introduces an innovative technique for the estimation of the number of active bubbles using the degradation of nonvolatile pollutants in the bulk liquid as a probe. The internal (gas pages) and external (liquid) bubble sonochemistry were simulated to track the radicals generation and use for nonvolatile pollutants degradation (in the liquid phase). To this end, COPASI® chemical kinetics software has been used for optimizing the acoustic bubble number density by linking the instantaneous bubble gas reaction (described by a bubble dynamic model accounting for the radical dissolution mechanism) and the aqueous free radicals degradation kinetics [i.e. concentration vs. time] of several nonvolatile organics (phenol, 4-chlorophenol, dyes…). Based on this strategy, the number density of active bubbles was determined for different operating circumstances (i.e. acoustic intensity, frequency, liquid temperature and saturation gas type). The performance of our method was evaluated by comparing our findings to those available in the literature, where an excellent agreement was established. Our technique showed that the number density monotonously goes up with increasing ultrasound frequency from 200 to 1140kHz, regardless of the experimental conditions used in this investigation. The opposite behavior has been obtained with the increase of the liquid temperature and acoustic intensity. Additionally, it has been noticed that the variation in the number of cavities with respect to the nature of saturating gas is frequency-dependent. At a frequency of 200kHz, the number of bubbles is in the order: O2>Ar>air. However, over this frequency (>200kHz), the number of acoustic bubbles is in the order: O2>air>Ar. On the other hand, it has been shown that below a frequency of ~860kHz, the variation of void fraction (ε) is synchronized with change in number density (N); nevertheless, over this value (>860kHz), these two parameters (N, ε) are no longer closely connected. As a result, in this case (>860kHz), the evaluation of number density from the total volume fraction of bubbles could not be directly performed without more information regarding the bubbles population, (e.g. size distribution, bubble-bubble interactions, bubbles deformation…etc.). Finally, the current proposed technique is flexible and can determine the number density of active bubbles for a wide range of operating conditions and circumstances.

Effect of pre-existing dislocations and precipitates on microstructure evolution in W-0.5ZrC alloy during in-situ He+ & H2+ dual-beam synergistic irradiation

Bubble evolution in different defect sinks has a crucial effect on the properties of materials for fusion reactor. Here, transmission electron microscopy (TEM) was used to in-situ investigate bubble evolution in different defect sinks, including pre-existing dislocations and precipitates in W-0.5ZrC alloy during He+ & H2+ dual-beam synergistic irradiation at 900 °C. The average size and volume number density of bubbles with increasing irradiation dose were obtained, revealing not only the significant effect of different types of defect sinks, but also the obvious impact of the same type of defect sinks in different states. It was found that linear pre-existing dislocations promoted bubble growth while inhibited nucleation. Pre-existing dislocations characterized by curved form exhibited strong inhibition effect on bubble nucleation, while pre-existing dislocations with staggered-mesh form, not only inhibited bubble growth but also suppressed nucleation compare to the linear pre-existing dislocations. ZrC precipitates had minimal effect on bubble growth, but could decrease the bubble nucleation. Dispersed small precipitates could better reduce the bubble nucleation sites in the early stage of irradiation. Once the absorption capacity of small precipitate was saturated, bubble growth might accelerate sharply. The presence of hydrogen made the linear pre-existing dislocation maintain high mobility. The current research results are of great significance for understanding the irradiation behavior of tungsten alloys and optimizing the preparation process.

Effects of the diffusion path on the effective diffusion coefficient of hydrogen isotope in tungsten with helium bubbles

In irradiated tungsten (W), the formation of numerous helium (He) bubbles has a significant impact on the diffusion behaviors of hydrogen (H) isotopes. To investigate the influence of the microstructure of He bubbles on the diffusion behaviors of deuterium (D), we utilize the reconstructed experimental data, the phase-field method, and the steady-state diffusion equation to calculate the effective diffusion coefficients of D based on four possible diffusion paths, i.e., D atoms diffuse in the bulk W, inside the He bubbles, and along the outer and inner surface of He bubbles. Simulation results based on the reconstructed depth-dependent distribution of He bubbles reveal that the diffusion paths remarkably affect the effective diffusion coefficient of D. By varying the radius and number density of He bubbles, the effective diffusion coefficient of D undergoes significant changes. Subsequently, we fit an empirical formula of the effective diffusion coefficient of D as a function of the radius and number density of He bubbles for different diffusion paths of D based on simulation data. Besides, the growth behaviors of He bubbles are simulated by the phase-field model, and the effective diffusion coefficient of D as a function of the evolutionary time for different diffusion paths is also discussed. At last, we investigate the influence of the D concentration and temperature on the effective diffusion coefficient of D along different diffusion paths. These results indicate that the effective diffusion coefficient of D increases with decreasing the D concentration and increasing the temperature for four diffusion paths. The current study provides a reference for investigating the diffusion behaviors of D in W in the presence of He bubbles, and may benefit the efforts of developing low D retention W-based materials.

Investigating the temperature dependence of helium bubble dynamics in plasma exposed tungsten via in-situ TEM annealing

In-situ TEM annealing and imaging were performed on tungsten samples pre-exposed at either 573 K or 1013 K in a pure helium plasma to a fluence of 1025 m−2. To investigate the thermal evolution of helium bubbles, the samples were imaged for annealing temperatures up to 998 K in steps of 100 K. It is found that annealing temperatures had little effect on the bubble dynamics for the lower temperature exposure of 573 K. Elongated bubble structures remained in the sample throughout the annealing process and there is minimal change in both the average bubble size and cross-sectional number density. However, annealing had a significant effect on the higher temperature exposure of 1013 K. Bubbles were found to be trapped in large clusters and increasing annealing temperature caused a significant increase in the average bubble size accompanied by a decrease in the cross-sectional bubble number density. The experimental observations are supported by theoretical calculations that show a simultaneous increase in the average number of He atoms per bubble in the higher exposure temperature sample but an overall decrease in He atoms retained within bubbles as the annealing temperature increased. These trends in bubble dynamics with annealing temperature suggest that Ostwald ripening dominates, whereby bubble growth is determined by the different pressures of different bubble sizes, rather than through bubble migration and coalescence.

Effects of Submerged Entry Nozzle Bottom Shape on the Size Distribution of Argon Bubbles in a Steel Continuous Casting Slab Strand Using Multiple‐Size‐Group Approach

Herein, the effects of the bottom shape of the submerged entry nozzle (SEN) on the molten steel flow and size distribution of argon bubbles are analyzed in a steel continuous casting slab strand using multiple‐size‐group approach. The type of nozzle bottom includes the well bottom, flat bottom, and mountain bottom. Most of argon bubbles are larger than 4.5 mm inside the SEN and the mold at the three types of nozzles. The frequency distribution of bubbles inside the SEN increases from 28.29% to 32.65% and 35.74% for 5.0–5.5 mm bubbles and decreases from 53.71–50.49% and 47.38% for 5.5–6.0 mm bubbles with the nozzle bottom varied from the flat to mountain and well shape, respectively. The number density of argon bubbles with 4.0–5.5 mm diameter in the mold decreases and increases for 5.5–6.0 mm bubbles with the nozzle bottom varying from the well to flat and mountain shape, respectively. In addition, the results of the industrial trials show that inclusions adhesion and aggregation at the bottom of the nozzle are eliminated using the flat bottom SEN casting. Meanwhile, the mechanism of SEN clogging under the different types of nozzle bottoms is analyzed.

Evaluating the Role of Titanomagnetite in Bubble Nucleation: Rock Magnetic Detection and Characterization of Nanolites and Ultra‐Nanolites in Rhyolite Pumice and Obsidian From Glass Mountain, California

AbstractWe document the presence, composition, and number density (TND) of titanomagnetite nanolites and ultra‐nanolites in aphyric rhyolitic pumice, obsidian, and vesicular obsidian from the 1060 CE Glass Mountain volcanic eruption of Medicine Lake Volcano, California, using magnetic methods. Curie temperatures indicate compositions of Fe2.40Ti0.60O4 to Fe3O4. Rock‐magnetic parameters sensitive to domain state, which is dependent on grain volume, indicate a range of particle sizes spanning superparamagnetic (&lt;50–80 nm) to multidomain (&gt;10 μm) particles. Cylindrical cores drilled from the centers of individual pumice clasts display anisotropy of magnetic susceptibility with prolate fabrics, with the highest degree of anisotropy coinciding with the highest vesicularity. Fabrics within a pumice clast require particle alignment within a fluid, and are interpreted to result from the upward transport of magma driven by vesiculation, ensuing bubble growth, and shearing in the conduit. Titanomagnetite number density (TND) is calculated from titanomagnetite volume fraction, which is determined from ferromagnetic susceptibility. TND estimates for monospecific assemblages of 1,000 nm–10 nm cubes predict 1012 to 1020 m−3 of solid material, respectively. TND estimates derived using a power law distribution of grain sizes predict 1018 to 1019 m−3. These ranges agree well with TND determinations of 1018 to 1020 m−3 made by McCartney et al. (2024), and are several orders of magnitude larger than the number density of bubbles in these materials. These observations are consistent with the hypothesis that titanomagnetite crystals already existed in extremely high number‐abundance at the time of magma ascent and bubble nucleation.

Evaluating the Role of Titanomagnetite in Bubble Nucleation: Novel Applications of Low Temperature Magnetic Analysis and Textural Characterization of Rhyolite Pumice and Obsidian From Glass Mountain, California

AbstractNucleation of H2O vapor bubbles in magma requires surpassing a chemical supersaturation threshold via decompression. The threshold is minimized in the presence of a nucleation substrate (heterogeneous nucleation, &lt;50 MPa), and maximized when no nucleation substrate is present (homogeneous nucleation, &gt;100 MPa). The existence of explosively erupted aphyric rhyolite magma staged from shallow (&lt;100 MPa) depths represents an apparent paradox that hints at the presence of a cryptic nucleation substrate. In a pair of studies focusing on Glass Mountain eruptive units from Medicine Lake, California, we characterize titanomagnetite nanolites and ultrananolites in pumice, obsidian, and vesicular obsidian (Brachfeld et al., 2024, https://doi.org/10.1029/2023GC011336), calculate titanomagnetite crystal number densities, and compare titanomagnetite abundance with the physical properties of pumice to evaluate hypotheses on the timing of titanomagnetite crystallization. Titanomagnetite crystals with grain sizes of approximately 3–33 nm are identified in pumice samples from the thermal unblocking of low‐temperature thermoremanent magnetization. The titanomagnetite number densities for pumice are 1018 to 1020 m−3, comparable to number densities in pumice and obsidian obtained from room temperature methods (Brachfeld et al., 2024, https://doi.org/10.1029/2023GC011336). This range exceeds reported bubble number densities (BND) within the pumice from the same eruptive units (average BND ∼4 × 1014 m−3). The similar abundances of nm‐scale titanomagnetite crystals in the effusive and explosive products of the same eruption, together with the lack of correlation between pumice permeability and titanomagnetite content, are consistent with titanomagnetite formation having preceded the bubble formation. Results suggest sub‐micron titanomagnetite crystals are responsible for heterogeneous bubble nucleation in this nominally aphyric rhyolite magma.

Reconciling petrologic magma ascent speedometers for the June 12th, 1991 eruption of Mt. Pinatubo, Philippines

We investigate whether decompression rates derived from three often-disparate petrologic techniques (microlites, bubbles, and melt embayments) can be reconciled or integrated for a more complete understanding of magma ascent in the conduit. We focus on the well-studied and -documented earliest Plinian eruptions (June 12, 1991) of Mount Pinatubo. Using a newly developed two-stage decompression-diffusion model, volatile profiles in quartz-hosted embayments reveal an initial stage of decompression nearly two orders of magnitude slower than final rates. In applying time-integrated models of microlite and bubble nucleation and growth, initial decompression rates from embayments are supported by microlite modeling results, whereas final rates are in close agreement with bubble number densities. This consistency and continuity between speedometers supports the sensitivity of different petrologic recorders to specific regions of the conduit system and highlights the fidelity of embayments as recorders of decompression throughout the entire conduit. Ascent timescales derived from Pinatubo embayments range from hours to days, coinciding with the visual onset of lava effusion leading to explosive activity.

The effect of cavitation-induced pressure on bubble cloud density in histotripsy

Tissue ablation in histotripsy is achieved by generating clouds of cavitation or boiling bubbles in the tissue. The rate of tissue ablation increases for clouds with a greater number density of nucleated bubbles. Therefore, controlling density may offer a mechanism to improve treatment efficacy. Experiments demonstrate several trends in density with ultrasound frequency, transducer f-number, and other variables. This presentation will describe one potential mechanism governing the density of cavitation bubbles nucleated during a focused ultrasound pulse. In particular, the rapid expansion of a cavitation bubble generates a partial cancellation of the incident pressure in the vicinity of the bubble, mitigating potential nucleation of other bubbles. We demonstrate this effect through a single-bubble numerical model, and further evaluate dependences of the pressure field with nuclei size, pressure amplitude, pulse frequency, and medium properties. The single-bubble model is further extended to consider the evaluate the effect of transducer focusing, and the combined pressure fields of multiple bubbles during cavitation nucleation. The predictions from simulation show good agreement with experimentally reported trends with frequency and transducer f-number, supporting the role of the mechanism in limiting the nucleation density in histotripsy.

Experimental emulation of 10B(n, α)7Li reaction-induced microstructural evolution of Al-B4C neutron absorber used in the dry storage of spent nuclear fuel

Al-B4C neutron absorber in spent fuel dry storage could suffer significant radiation damage at elevated temperature (∼150–300 °C) mainly via 10B(n, α)7Li reactions. Several recent studies reported significant bubble formation in the absorber, however only from wet storage environment at near ambient temperature (< ∼90 °C). In this study, we irradiated a commercially widely used Al-B4C absorber of interest utilizing 120-keV helium ion-beam accelerator with twelve different conditions; three different doses (0.01, 0.1, and 1 dpa) combined with four different temperatures (room temperature, 150, 270, and 400 °C). This was to investigate the irradiation-induced microstructural evolution of the absorber in dry storage environment in expedited manner instead of time-consuming neutron irradiation test. The effects of irradiation dose and temperature on helium bubble nucleation and growth were investigated by image analysis on BF-TEM images, which showed a typical tendency of increasing bubble size with increasing temperature at the expense of decreasing bubble number density. Helium bubble morphology at grain boundaries was quite similar with the ones reported from the previous studies on the surveillance coupons used in the wet environment, elliptic helium bubbles around B4C particles. Notable difference was the prominent formation of numerous helium bubbles even from the lowest dose (0.01 dpa) at slightly elevated temperature (150 °C), perhaps due to higher irradiation temperature than that of spent fuel pool. This study may experimentally confirm that significant bubble formation and growth in the absorber could be the case from the early stage of the dry storage, even without the participation of hydrogen produced from the absorber corrosion. Particularly in the case of non-clad Al-B4C absorber, possible B4C particle detachment may need to be concerned since the bubble coalescence was concentrated at the interface between Al alloy matrix and B4C particle which would be microcracked under neutron irradiation.

Demonstration of Helide formation for fusion structural materials as natural lattice sinks for helium

Fusion power holds promise as an ultimate energy source. However, achieving true sustainability in fusion energy requires addressing the embrittlement of polycrystalline materials in fusion reactors caused by helium, which leads to premature failure, often within a year. Here we experimentally demonstrate that nanodispersoids with constitutional vacancy-like atomic-scale free volume can securely store helium, not only at the matrix-dispersoid interface but also within their bulk lattices, which suggests their effectiveness in delaying critical helium damage of the polycrystalline matrix. The selected model nano-heterophase, fayalite Fe2SiO4, possesses moderately strong lattice sinks for helium while undergoing lattice distortions upon helium absorption. These distortions cause observable changes in peak intensities of X-ray diffraction (XRD) patterns, distinct from changes resulting from other factors like radiation damage. By comparing grazing incidence XRD patterns with ab initio computed patterns, we show that such nano-heterophases can store up to ∼10 at% helium within their bulk lattice, forming a “helide compound.” Incorporating just 1 vol% of Fe2SiO4 reduces helium bubble size and number density by >20 % and >50 %, respectively. These findings suggest that 1–2 vol% of appropriate nano-heterophases can accommodate a few thousand appm of bulk helium, expected to be generated over a 10-year operational period.

Outgassing behaviour during highly explosive basaltic eruptions

AbstractExplosivity of basaltic eruptions is related to the efficiency in which exsolved gas can separate from the melt during ascent, which is controlled by magma permeability. However, basaltic pyroclasts from eruptions of varying explosivity can show similar permeability, indicating a possible complex relationship between permeability, outgassing and eruptive style. Here, we provide 3D measurements of basaltic pyroclasts using X-ray microtomography. We investigate the role of permeability and outgassing on magma ascent dynamics by using a numerical conduit model. Among the permeable parameters, bubble number density and friction coefficient largely affect explosivity. However, for fast ascending basaltic magmas, gas-melt coupling is maintained independent of magma permeability. In this case, magma storage conditions may determine eruptive style, driving rapid magma ascent, crystallisation and bubble nucleation, producing a highly explosive eruption. Monitoring parameters which reveal pre-eruptive conditions may assist hazard mitigation, particularly for basaltic systems which exhibit a wide range in eruptive style.

A model of coupled oscillation of bubble cluster in liquid cavity wrapped by viscoelastic medium

Considering the interactions between bubbles in a multi-bubble system in a liquid micro-cavity, a spherical bubble cluster in a liquid cavity is modeled in order to describe the dynamical effect of the viscoelastic medium outside the liquid cavity on the oscillation of bubbles, and the coupled equations of bubbles are obtained. Subsequently, the acoustic response characteristics of bubbles are investigated by analyzing the radial oscillation, the stability of the non-spherical shape of bubbles and the threshold of inertial cavitation. The results show that the confinement of the cavity and the bubble cluster facilitates the suppression of bubble oscillation, however, it might enhance the nonlinear properties of bubbles to a certain extent. From the acoustic response curve at 1 MHz, it is found that the main resonance peaks shift leftward with the increase of the bubble number, which means a minor resonant radius can be obtained. The nonlinear stability of bubbles in a confined environment is mainly determined by acoustic pressure amplitude and frequency, the initial bubble radius, and bubble number density, while the effect of the cavity radius is enhanced with the increase of the driving pressure. There is a minimum unstable driving acoustic pressure threshold, depending on the initial bubble radius, and the unstable regions are mainly located in a range of less than 4 μm. With the increase in bubble number density, the strip-type stable region scattered of the unstable region in the map is gradually transformed into a random patch-like distribution, which indicates that the bubble oscillation under high acoustic pressure is more sensitive to the parameters, and it is very susceptible to interference, produces unstable oscillation and then collapses. When the bubble equilibrium radius is in a range greater than 4 μm, the influences of frequency and bubble number density on the inertial thresholds are particularly significant.

Structural stability analysis of spherical bubble clusters in acoustic cavitation fields

The upwelling growth and evolution of spherical bubble clusters appearing at one-quarter wavelength from the water surface in ultrasonic cavitation fields at frequencies of 28 kHz and 40 kHz are studied by high-speed photography. Due to the interactions among bubbles, the stable bubble aggregation occurs throughout the rise of the bubble cluster, whose vertical pressure difference leads to a more significant spreading in the upper part of the cluster in the standing-wave field. At 28 kHz, the rising speed is about 0.6 m/s, controlled by the primary acoustic field. After a violent collapse of the bubble clusters, the aggregating structure begins to hover near the water surface. The size and stability of the structure are affected by the frequency and pressure of the primary acoustic field. If two clusters are close to each other, the clusters deviate from the spherical shape, even trailing off, and eventually merge into a single bubble cluster. By considering the influence of water-air boundary, based on the mirror principle, a spherical bubble cluster model is developed to explore the structure stability of the clusters, and the modified dynamics equations are obtained. The effects of driving acoustic pressure amplitude, bubble number density, water depth, and bubble equilibrium radius on the optimal stable radius of the spherical bubble cluster are numerically analyzed by using the equivalent potentials at 28 kHz and 40 kHz. The results show that the optimal stabilizing radius of spherical bubble cluster is in a range of 1–2 mm, and it tends to decrease slightly with the increase of the driving acoustic pressure and bubble number density. It is worth noting that the nonlinearity is enhanced by increasing acoustic pressure, which may promote the stability of the cluster structure. The smaller the unstable equilibrium radius, the easier it is to grow, and the stable size at 40 kHz is slightly smaller than that at 28 kHz. Generally, spherical clusters first appear in a high-pressure region and then move to a low-pressure region. If the acoustic pressure drops below a certain critical value, bubble clusters disappear. The theoretical analysis is in good agreement with the experimental observation. The analysis of the growth and structural stability of spherical bubble cluster is helpful in understanding the behavioral modulation of bubbles.

He bubbles inhibition and abnormal hardening in GH3535 alloy by niobium element addition

GH3535 and 2 wt.% Nb-modified GH3535 (Nb-GH3535) alloys were irradiated with 1.2 MeV He ion at fluences of 1 × 1016, 3 × 1016 and 1 × 1017 ions/cm2 at 750 °C. Microstructural changes, including the formation of He bubbles and superlattice phases, as well as the irradiation-induced hardening, were investigated by TEM and nanoindentation. Notably, Nb-GH3535 exhibited a smaller size and lower number density of He bubbles, especially at higher fluences, indicating the inhibitory effect of Nb on bubble evolution. First-principles calculations revealed that the presence of Nb inhibits the combination of He atoms and vacancies, reducing their diffusion rate and consequently impeding the nucleation and growth of He bubbles. Furthermore, the addition of Nb facilitates the irradiation-induced precipitation of the superlattice phase, leading to a higher degree of total hardening in Nb-GH3535 alloy.

Sound attenuation in high mach number oscillating bubble media

We study theoretically and numerically sound attenuation in bubble-containing media when the bubbles are freely oscillating at high Mach numbers. This paper expands one of the main forms of bubble-related acoustic damping factors by extending the previous theories to higher Mach numbers, further improves the theories of nonlinear sound propagation in bubble-containing media. A nonlinear sound propagation model incorporating second-order liquid compression terms is developed, expressing the sound velocity and density in the medium as a function of the driving pressure, and taking into account the higher-order liquid compression effects on sound propagation. The correctness of the proposed model is verified by comparing with a linear model and a nonlinear model containing only low-order Mach number terms. When the bubble oscillates at a high Mach number, radiation damping, which is directly related to Mach number, becomes the main damping component affecting sound attenuation. The higher the driving amplitude, the stronger the nonlinear effect, and the greater the impact of high-order liquid compression effects on the sound attenuation, the more necessary it is to use the proposed model to calculate the sound attenuation. For high Mach numbers, varying the bubble radius and bubble number density, respectively, the difference between the proposed model and the model containing only low-order Mach number terms in capturing the pressure-dependent attenuation is calculated. Due to stronger radiation damping in smaller bubbles, the effect of compressibility becomes more important. The smaller the bubble radius, the greater the half-quality factor of the curve related to the difference in attenuation calculated by the two models, the more necessary it is to calculate the pressure-dependent attenuation using the proposed model. Here, the half-quality factor is defined as the corresponding frequency bandwidth when the curve falls from the maximum value to 22 times. Without considering the coupling effect between bubbles, the half-quality factor of the curve is not affected by the bubble number density.

Experimental validation of the mechanism and condition for the onset of significant void in subcooled flow boiling

In evaluating the axial void fraction profile in the subcooled boiling region in heated channels, accurate determination of the point of onset of significant void (POSV) is of critical importance. Recently, it has been reported that the POSV can be predicted with high accuracy if the onset of significant void (OSV) is assumed to be caused by a sudden decrease in the interfacial area due to global bubble coalescence (GBC) leading to the formation of large bubbles. Therefore, in this work, experimental investigations were carried out to measure the void fraction, bubble size and bubble number density. The experimental results were utilized to validate the mechanism causing the OSV in subcooled flow boiling. The experimental results were in qualitative and quantitative agreement with the model based on the GBC concept. Thus, it was validated that the sudden decrease in condensation rate due to large bubble formation is the main cause of OSV. It was also confirmed that the GBC occurs when the local void fraction near the heated wall reaches about 0.3, analogous to the flow regime transition from bubbly flow to slug flow in adiabatic gas-liquid two-phase flows.