Transient Cavities Research Articles

A numerical investigation of non-spherical rebounding bubbles

The motion of buoyant transient cavities with non-condensible contents is investigated numerically using a boundary-integral method. The bubble contents are described by an adiabatic gas law. Motion is considered in the neighbourhood of a rigid boundary, in an axisymmetric geometry. We investigate whether the non-condensible contents will resist the formation of jets. It is found that jets form upon collapse and, in general, completely penetrate the bubble before it rebounds, but circumstances are identified under which the non-spherical bubble will rebound prior to this occurrence. In these cases the bulk of the jet growth occurs upon rebound. Furthermore, the interaction between the buoyancy force causing jet formation upwards, and the Bjerknes attraction of the rigid boundary causing jet formation towards it, is investigated and general principles discussed which allow the behaviour to be interpreted. The concept of the Kelvin impulse is utilized.

Igneous emplacement in a transpressive shear zone: Ox Mountains igneous complex

The central and southwestern Ox Mountains Inlier in western Ireland, comprises amphibolite facies metasediments and metavolcanic rocks which have been deformed by a major sinistral shear zone. Granitoid emplacement occurred in two distinct styles in the Ox Mountains shear zone. The older pluton, the Ox Mountains granodiorite was emplaced syn-kinematically with respect to the main sinistral, transpressional events in its wall rocks. It was emplaced as a series of compositionally distinct sheets in the central part of the shear zone system thus suggesting the formation of transient, dilational sites occurred in response to the transpressive deformation. The younger, Lough Talt and Easky Lough adamellites were emplaced as individual intrusions in dilational cavities produced by reactivated movements on a discrete zone within the Ox Mountains inlier. The different intrusive styles are considered to be a product of the tectonic regimes operating during emplacement. Intrusion into transient dilational cavities may be one method by which granitoid magmas are emplaced into fault zones undergoing active contractional deformation.

Periventricular Leukomalacia: Ultrasonic and Neuropathological Correlations

Ultrasound scans of a preterm neonate (27 weeks gestation) at seven weeks of age showed periventricular echo-free cavities, but these were no longer visible at 15 weeks, three weeks before the infant died. At autopsy, a linear glial scar, extending from the periventricular white-matter into the white axis of the parasagittal gyrus, was found in the area occupied by the periventricular cysts. The larger cavity was reduced to a slit-like excavation in the midst of glial tissue. Unsuspected focal infarcts in the cerebral cortex were also found. This observation demonstrates that transient echo-free cavities represent foci of cystic necrosis, which are subject to secondary collapse. In the authors' experience, the linear extension of periventricular leukomalacia (PVL) into the core of parasagittal gyri is a frequent feature of PVL, and one which cannot easily be accounted for by the usual explanations of border-zone ischaemic softening.

Erratum: transient pulsations of small gas bubbles in water [J. Acoust. Soc. Am. 84, 985-998 (1988)] [corrected and republished

Transient behavior of small gas bubbles in a liquid set into violent motion by ultrasonic pressure waves is of interest because of widespread use of microsecond pulses in diagnostic ultrasound. Such pulses contain only a few pressure cycles and the transient pulsations of bubbles set in motion by such pulses would determine the bubble-ultrasound interaction. A computer study has been made to obtain a global representation of the pulsation amplitudes R (t) of small gas bubbles (nuclei) in water during the first few cycles of a cw ultrasonic pressure. One objective was to obtain a better understanding of cavitation phenomena where many nuclei with initial radii Rn from 0.1-20 microns are set in motion at pressures ranging from 0.5-5 bars and at frequencies from 0.5-10 MHz. Results allowed construction of surfaces showing the relative bubble amplitude R/Rn as a function of Rn and of the time t/TA, where TA is the acoustic period. One finding is that, in the range of peak pressures found in diagnostic pulses, transient cavities would be generated during the first pressure cycle from nuclei with initial radii as small as a few microns (micron). Nuclei that grow into transient cavities in the first pressure cycle are here called "prompt" nuclei. At a specified pressure, the size range of radii Rn in which they occur decreases with increasing frequency. At 5 bars, the range of Rn for prompt nuclei is 0.166-11.35 microns at 0.5 MHz and vanishes at 10 MHz.

Transient pulsations of small gas bubbles in water

Transient behavior of small gas bubbles in a liquid set into violent motion by ultrasonic pressure waves is of interest because of widespread use of microsecond pulses in diagnostic ultrasound. Such pulses contain only a few pressure cycles and the transient pulsations of bubbles set in motion by such pulses would determine the bubble–ultrasound interaction. A computer study has been made to obtain a global representation of the pulsation amplitudes R(t) of small gas bubbles (nuclei) in water during the first few cycles of a cw ultrasonic pressure. One objective was to obtain a better understanding of cavitation phenomena where many nuclei with initial radii Rn from 0.1–20 μm are set in motion at pressures ranging from 0.5–5 bars and at frequencies from 0.1–10 MHz. Results allowed construction of surfaces showing the relative bubble amplitude R/Rn as a function of Rn and of the time t/TA, where TA is the acoustic period. One finding is that, in the range of peak pressures found in diagnostic pulses, transient cavities would be generated during the first pressure cycle from nuclei with initial radii as small as a few microns (μm). Nuclei that grow into transient cavities in the first pressure cycle are here called ‘‘prompt’’ nuclei. At a specified pressure, the size range of radii Rn in which they occur decreases with increasing frequency. At 5 bars, the range of Rn for prompt nuclei is 0.166–11.35 μm at 0.5 MHz and vanishes at 10 MHz.

Protein-ligand dynamics: A 96 picosecond simulation of a myoglobin-xenon complex

A 96 picosecond dynamics trajectory of myoglobin with five xenon-probe ligands in internal cavities is examined to study the effect of protein motions on ligand motion and internal cavity fluctuations. Average structural and energetic properties indicate that the simulation is well behaved. The average protein volume is similar to the volume of the X-ray model and the main-chain atom root-mean-square deviation between the X-ray model and the average dynamical structure is 1.25 Å. The protein volume oscillates 3 to 4% around the volume of the X-ray structure. These fluctuations lead to changes in the internal free volume and in the size, shape and location of atom-sized cavity features. Transient cavities produced in the simulation have a crucial role in the movement of two of the ligands. One of the ligands escapes to the protein surface, whilst a second ligand travels through the protein interior. Complex gating processes involving several protein residues are responsible for producing the necessary pores through which the ligand passes between transient cavities or packing defects.

Transient cavities near boundaries Part 2. Free surface

Calculations of the growth and collapse of transient vapour cavities near a free surface when buoyancy forces may be important are made using the boundary-integral method described in Part 1. Bubble shapes, particle paths, pressure contours and centroid motion are used to illustrate the calculations. In the absence of buoyancy forces the bubble migrates away from the free surface during the collapse phase, yielding a liquid jet directed away from the free surface. When the bubble is sufficiently close to the free surface, the nonlinear response of the free surface produces a high-speed jet (‘spike’) that moves in the opposite direction to the liquid jet and, in so doing, produces a stagnation point in the fluid between the bubble and the free surface. For sufficiently large bubbles, buoyancy forces may be dominant, so that the bubble migrates towards the free surface with the resulting liquid jet in the same direction. The Kelvin impulse provides a reasonable estimate of the physical parameter space that determines the migratory behaviour of the collapsing bubbles.

Evidence for free radicals produced in aqueous solutions by diagnostic ultrasound

Recent theoretical calculations have shown that small gas nuclei in water exposed to microsecond ultrasonic pulses above an intensity threshold may grow into transient cavities that collapse violently, leading to the formation of .OH radicals and .H atoms. We have detected these free radicals in aqueous solutions exposed to microsecond pulsed ultrasound using spin trapping and electron spin resonance (ESR). The public health implications of our results are discussed.

Transient pulsations of cavitation bubbles

Transient behavior of small gas bubbles in a liquid set into violent motion by ultrasonic pressure waves is of interest because of widespread use of microsecond pulses in diagnostic ultrasound. Such pulses contain only a few pressure cycles and the transient pulsations of bubbles set in motion by such pulses would determine the bubble‐ultrasound interaction. A computer study has been made to obtain a global representation of the pulsation amplitudes R(t) of small gas bubbles (nulcei) in water during the first few cycles of a cw ultrasonic pressure. One objective was to obtain a better understanding of cavitation phenomena where many nuclei with initial radii from 0.1 to 20 μm are set in motion at pressures ranging from 0.5–5 bars and at frequencies from 0.5–10 MHz. Results allowed construction of surfaces showing the relative bubble amplitude R/Rn, as a function of Rn, and of the time t/TA, where TA is the acoustic period. One finding is that, in the range of peak pressures found in diagnostic pulses, transient cavities would be generated during the first pressure cycle from nuclei with initial radii as small as a few microns (μm). [Research supported by NIH.]

Transient cavities near boundaries. Part 1. Rigid boundary

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.

A geometric model for excavation and modification at terrestrial simple impact craters

A geometric model for the excavation and modification of simple crater development is presented. Modification is modelled by considering the relative dimensions and geometries of the final crater and the transient cavity formed by excavation and displacement. The input parameters required are the rim crest diameter of the final crater, the depth to autochthonous basement, the rim crest height and the outer rim slope. The model calculates the diameter of the final crater at the original ground plane, the dimensions of the transient cavity and the rim crest volume difference between the final and transient cavities. This volume is considered to be the material which slumped off the unstable, overheightened transient cavity wall during modification and corresponds to the observed volume of the breccia lens within the final crater. Excavation is approximated by a steady state Z model, with the diameter of excavation equivalent to the previously modelled diameter of the transient cavity at the original ground plane, the center of flow taken as 1 projectile diameter, and Z = 2.5–3.0. The Z model predicts such parameters as the depth and volume of excavation, which can be compared with observational data. The applicability of the model has been tested with data from Meteor and Brent craters. In the case of Meteor, the modelled final crater diameter at the original ground plane is within 26 m of the observed value and the modelled breccia lens and the rim crest volumes of the final true crater are within 9.5% and 2.5%, respectively, of observed values. The results of the Z model for Meteor crater, with Z = 2.8 ± 0.1, give results consistent with observational data on the depth and volume of excavation. The correspondence for the more degraded Brent crater is less precise, as there is greater uncertainty in the input parameters. It is possible, however, to match the model parameters with the breccia lens volume and published estimates of original dimensions. The modelled excavated volumes for Meteor and Brent are 58% and 55%, respectively, of the transient cavity volume below the original ground plane. In the absence of additional observational data for further testing, it is concluded that the model may provide first‐order spatial information on the formation of simple craters.

A mechanism for the generation of cavitation maxima by pulsed ultrasound.

A train of 1-MHz pulses can generate maxima of cavitation activity [V. Ciaravino, H. G. Flynn, and M. W. Miller, Ultrasound Med. Biol. 7, 159-166 (1981)] at pulse lengths of 6 and 60 ms and at pressure amplitudes, PA, between 5.4 and 9.4 bars (or intensities between 10 and 30 W/cm2). Generation of maxima at PA between these limits on pressure amplitude implies that the increase in cavitation activity originates from gas nuclei with radii lying in a critical size range centered at about 0.08 micron. The mechanism proposed for this phenomenon suggests that nuclei in this critical range are unstabilized nuclei generated in one pulse and surviving to the next with an appreciable fraction of the survivors lying in the critical range. Transient cavities that grow from such small nuclei are shown to behave as isolated mechanical systems that on reaching maximum size collapse as imploding spheres. The maximum pressures reached in such imploding cavities would then approximate those calculated for the spherical collapse of cavities. The occurrence of the observed maxima is ascribed to the spherical collapse of transient cavities.

Evidence for free radical production by ultrasonic cavitation in biological media

The statement is often made that free radicals will be produced during the violent collapse of transient cavities in liquids, that may result from the passage of ultrasonic waves in the low megahertz frequency range. Evidence for such free radicals is mostly indirect. We have insonated some argon-saturated aqueous solutions of biological molecules (trypsin, Dulbecco's Minimum Essential Medium, fetal bovine serum, and human blood plasma) and whole human blood, all containing a spin trapping compound, at 1 MHz, continuous wave, 6.6 W/cm 2 (SPTA) for 15 min at 4–8°C. Electron spin resonance spectra of the samples were recorded 10 and 30 min. after cessation of insonation. The spectra included those of spin adducts formed with ·OH and ·H radicals, which were absent in the cases of the sham treated controls. Thus, we have demonstrated the formation of the highly reactive ·OH and ·H radicals in the insonated media, even in the presence of natural radical scavengers in the mammalian derived products.

Generation of transient cavities in liquids by microsecond pulses of ultrasound

Calculations reported here show that small gas nuclei in a liquid acted on by microsecond ultrasonic pulses may grow into transient cavities that collapse violently. The maximum pressures and temperatures generated by such collapsing cavities are found in these calculations to be of the order of 1000 to 70 000 bars and 1000 ° to 20 000 °K.

Cometary and meteorite swarm impact on planetary surfaces

The velocity flow fields, energy partitioning, and ejecta distributions resulting from impact of porous (fragmented) icy cometary nuclei with silicate planetary surfaces at speeds from 5 to 45 km/s are different than those resulting from the impact of solid ice or silicate meteorites. The impact of 1 g/cm3 ice spheres onto an atmosphereless anorthosite planetary surface induces cratering flows that appear similar to those induced by normal density anorthosite meteorite impact. Both of these impactors lead to deep transient crater cavities for final crater diameters less than ∼1 to ∼10 km and for escape velocities ≲105cm/s. Moreover the fraction of internal energy partitioned into the planetary surface at the cratering site is 0.6 for both ice and anorthosite impactors at 15 km/s. As the assumed density of the hypothetical cometary nucleus or fragment cloud from a nucleus decreases to 0.01 g/cm3, the fraction of the impact energy partitioned into planetary surface internal energy decreases to less than 0.01, and the flow field displays a toroidal behavior in which the apparent source of the flow appears to emanate from a disc or ringlike region rather than from a single point, as in the explosive cratering case. The edges of the crater region are in several cases depressed and flow downward, whereas the center of the crater region is uplifted. Moreover, the resultant postimpact particle velocity flow in some cases indicates the formation of concentric ridges, a central peak, and a distinct absence of a deep transient cavity. In contrast, transient cavities are a ubiquitous feature of nearly all previous hypervelocity impact calculations. The calculations of the flow fields for low density (0.01 g/cm3) impactors exhibited surface interface (comet‐planet) instabilities. These are attributed to both the Rayleigh‐Taylor and Helmholtz instability conditions, and we believe that these occur in all flows involving volatile low‐density (0.01 g/cm3) projectiles. It is speculated that these hydrodynamic instabilities can give rise to concentric rings in the inner crater region in large‐scale impacts on planetary surfaces, although other mechanisms for their production may also act. The ejecta mass loss versus planetary escape velocity was computed, and these results imply that the critical escape velocity, at which as much material is lost as is being accreted from a planet, ranges from 1.2 to 2.75 km/s for encounter speeds of 5 to 15 kms/s, with cometary impactors having a density of 0.01 to 1 g/cm3. These values compare to 0.83 and 1.5 km/s for silicate impactors, thereby indicating that it is more difficult for volatiles than silicates to be accreted onto objects with escape velocities similar to the Moon, Mercury, and Mars. For objects with escape velocities in the 0.1 to 1 km/s range the accretional efficiency for silicate and various porosity ices are similar, whereas for objects with escape velocities <0.1 km/s the accretional efficiency of icy impactors becomes significantly lower than for silicate impactors.

2H nuclear magnetic relaxation study of the rotation of adamantane in n-alkanes

Deuteron spin–lattice relaxation time has been measured for adamantane-d1 in several n-alkane solutions at variable temperature. It is found that solvent viscosity plays only a minor role in adamantane reorientation. This latter involves an activated Arrhenius process with a solvent-independent activation energy (1.3 kcal/mole in the 183–423 °K temperature range). It follows that adamantane rotation is mainly governed by microscopic collisional motions rather than by collective hydrodynamic effects and can be pictured by the concept of transient solvent cavities in which the solvent molecule reorients.

Formation of complex impact craters: Evidence from Mars and other planets

The simple-to-complex transition for impact craters on Mars occurs at diameters between about 3 and 8 km. Ballistically emplaced ejecta surround primarily those craters that have a simple interior morphology, whereas ejecta displaying features attributable to fluid flow are mostly restricted to complex craters. Size-dependent characteristics of 73 relatively fresh Martian craters, emphasizing the new depth/diameter ( d/ D) data of D. W. G. Arthur (1980, to be submitted for publication), test two hypotheses for the mode of formation of central peaks in complex craters. In particular, five features appear sequentially with increasing crater size: first flat floors (3–4 km), then central peaks and shallower depths (4–5 km), next scalloped rims ( ∂ km), and lastly terraced walls (∼8 km). This relative order indicates that a shallow depth of excavation and an unspecified rebound mechanism, not centripetal collapse and deep sliding, have produced central peaks and in turn have facilitated failure of the rim. The mechanism of formation of a shallow crater remains elusive, but probably operates only at the excavation stage of impact. This interpretation is consistent with two separate and complementary lines of evidence. First, field data have documented only shallow subsurface deformation and a shallow transient cavity in complex terrestrial meteorite craters and in certain surface-burst explosion craters; thus the shallow transient cavities of complex craters never were geometrically similar to the deep cavities of simple craters. Second, the average depths of complex craters and the diameters marking the transition from simple to complex craters on Mars and on three other terrestrial planets vary inversely with gravitational acceleration at the planetary surface, g, a variable more important in the excavation of a crater than in any subsequent modification of its geometry. The new interpretation is summarized diagrammatically for complex craters on all planets.

Interrelationship between creep deformation and creep rupture in 2¼Cr-1Mo steel

AbstractCreep deformation and rupture have been studied in 2¼Cr-IMo steel over the stress range 60-210 MN m⁻² at 565°C. Creep damage accumulates by the initiation and growth of extensive cavitation at the prior austenite grain boundaries. Cavity formation predominates during the initial transient and individual cavities appear to nucleate on grain boundary carbides. Quantitative analysis of the cavitation kinetics in relation to the creep deformation processes suggests that cavity growth is directly related to deformation occurring at the grain boundaries. It is inferred that the vacancy diffusion mechanism is inhibited and growth is limited by the local creep process occurring at the grain boundaries. At low stresses the latter is controlled by intra-granular recovery creep such that the overall rate of cavitation is proportional to the macroscopic strain rate. However, results obtained under biaxial shear conditions imply that the rate of cavitation is additionally dependent upon the normal boundary str...

The contribution of major impact processes to lunar crustal evolution

Large terrestrial impact craters provide structural models for the interpretation, of lunar craters and basins and petrological data for comparison with complex lunar breccias. The terrestrial examples illustrate the mixing processes operative in the production of impact melts and breccias and the considerable volumes of impact melt rocks in large impact craters. Three forms of craters are found on Earth, Moon, Mars and Mercury; Simple bowl-shaped craters (smallest), central uplift, and ring structures (largest). The variations in form are interpreted as different degrees of gravitational modification which immediately follow the initial excavation. On Earth the transient cavity excavated has diameter/depth ( D/d) near 3/1 in non-porous, essentially homogeneous rocks. From Orbiter and Apollo photographic data transient cavities in the most competent lunar materials have D/d of approximately 4/1. Experiments indicate ejecta come from as deep as two-thirds rds the transient cavity depth: disturbed material from greater depths remains as the crater lining. Application to the Imbrium basin indicates a portion of the ejecta at the Apollo 15 site may have come from as deep as 100 km, and from somewhat shallower depths at the Apollo 14 site. Ultramafic green and howarditic glasses are possible candidates for these materials of deep origin. Uplift of upper mantle in the centre of the basm would contribute to the Imbrian mascon.

Cavitation Dynamics

A program of research in acoustic cavitation that was started at the suggestion of F. V. Hunt and continued through his cooperation has resulted in an extensive study of the motions of small bubbles under the influence of acoustic pressure fields. The principal tool in this investigation has been a mathematical formulation made up of a set of integral equations, differential equations, and algebraic equations. Solutions of this formulation obtained through use of a digital computer have so far given considerable insight into the free pulsations of cavities, the thresholds for generation of transient cavities, and the temperatures and pressures that might be reached in the collapse of transient cavities. A brief survey of these results will be given. [This work was supported by Acoustics Programs, Office of Naval Research.]