T.G. Leighton

Bubble population phenomena in acoustic cavitation

Abstract Theoretical treatments of the dynamics of a single bubble in a pressure field have been undertaken for many decades. Although there is still scope for progress, there now exists a solid theoretical basis for the dynamics of a single bubble. This has enabled useful classifications to be established, including the distinction between stable cavitation (where a bubble pulsates for many cycles) and transient cavitation (where the bubble grows extensively over time-scales of the order of the acoustic cycle, and then undergoes an energetic collapse and subsequent rebound and then, potentially, either fragmentation, decaying oscillation or a repeat performance). Departures from sphericity, such as shape and surface oscillations and jetting, have also been characterized. However, in most practical systems involving high-energy cavitation (such as those involving sonochemical, biological and erosive effects), the bubbles do not behave as the isolated entities modelled by this single-bubble theory: the cavitational effect may be dominated by the characteristics of the entire bubble population, which may influence, and be influenced by, the sound field. The well established concepts that have resulted from the single-bubble theory must be reinterpreted in teh light of the bubble population, an appreciation of population mechanisms being necessary to apply our understanding of single-bubble theory to many practical applications of ‘power’ ultrasound. Even at a most basic level these single-bubble theories describe the response of the bubble to the local sound field at the position of the bubble, and that pressure field will be influenced by the way sound is scattered by neighbouring bubbles. The influence of the bubble population will often go further, a non-uniform sound field creating an inhomogeneous bubble distribution. Such a distribution can scatter, channel and focus ultrasonic beams, can acoustically shield regions of the sample, and elsewhere localize the cavitational activity to discrete ‘hot spots’. As a result, portions of the sample may undergo intense sonochemical activity, degassing, erosion, etc., whilst other areas remain relatively unaffected. Techniques exist to control such situations where they are desirable, and to eliminate this localization where a more uniform treatment of the sample is desired.

Ultrasonic propagation in cancellous bone: a new stratified model

The theoretical modeling of ultrasonic propagation in cancellous bone is pertinent to improving the ultrasonic diagnosis of osteoporosis. First, this paper reviews applications of Biots theory to this problem. Next, a new approach is presented, based on an idealization of cancellous bone as a periodic array of bone-marrow layers. Schoenbergs theory is applied to this model to predict wave properties. Bovine bone samples were tested in vitro using pulses centered at 1 MHz over various angles relative to the orientated cancellous structure. Two longitudinal modes (fast and slow waves) were observed for propagation parallel to the structure, but only one was observed for propagation normal to the structure. Angular-dependence of velocities was examined, and the fast wave was found to be strongly anisotropic. These results gave qualitative agreement with predictions of Schoenbergs theory. Although this new model is a simplification of the cancellous architecture, it has potential for future research.

Acoustic emission and sonoluminescence due to cavitation at the beam focus of an electrohydraulic shock wave lithotripter

The acoustic emission from cavitation in the field of an extracorporeal shock wave lithotripter has been studied using a lead zirconate titanate piezoceramic (PC4) hydrophone in the form of a 100-mm diameter focused bowl of 120-mm focal length. With this hydrophone directed at the beam focus of an electrohydraulic lithotripter radiating into water, it is possible to identify signals well above the noise level, at the 1-MHz resonance of the hydrophone, which originate at the beam focus. Light emission, attributed to sonoluminescence, is also shown to originate at the focal region of the lithotripter, and the signal obtained from a fast photomultiplier tube directed at the focus has similarities in structure and timing to the detected acoustic signals. The multiple shock emission resulting from a single discharge of an electrohydraulic source is shown to result in two separate bursts of cavitational activity separated by a period of 3-4 ms. The signal burst corresponding to the primary shock has a duration of about 600 microseconds with little noticeable structure. The signal burst associated with the secondary shock has a reproducible structure with two distinct peaks separated by about 200 microseconds depending on the shock amplitude. THe timing and structure of each burst is shown to be in reasonable agreement with the theoretical predictions made by Church (1989) based on the Gilmore model of bubble dynamics. In particular, it is shown that it is possible to obtain precise measurements of the time delay between the separate peaks within the signal burst detected following the secondary shock and this may, as predicted, provide a method of determining the size of bubbles remaining after the primary shock.

Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics

For several decades the propagation characteristics of acoustic pulses (attenuation and sound speed) have been inverted in attempts to measure the size distributions of gas bubbles in liquids. While this has biomedical and industrial applications, most notably it has been attempted in the ocean for defence and environmental purposes, where the bubbles are predominantly generated by breaking waves. Such inversions have required assumptions, and the state–of–the–art technique still assumes that the bubbles undergo linear, steady–state monochromatic pulsations in the free field, without interacting. The measurements always violate, to a greater or lesser extent, these assumptions. The errors incurred by the use of such assumptions have been difficult to quantify, but are expected to be most severe underneath breakers in the surf zone, where the void fraction is greatest. Very few measurements have been made in this important region of the ocean. This paper provides a method by which attenuation can be predicted through clouds of bubbles which need not be homogeneous, nor restricted to linear steady–state monochromatic pulsations. To allow inversion of measured surf zone attenuations to estimate bubble populations with current computational facilities, this model is simplified such that the bubble cloud is assumed to be homogeneous and the bubbles oscillating in steady state (although still nonlinearly). The uses of the new methods for assessing the errors introduced in using state–of–the–art inversions are discussed, as are their implications for oceanographic and industrial nonlinear bubble counters, for biomedical contrast agents, and for sonar target detection in the surf zone.

From seas to surgeries, from babbling brooks to baby scans: the acoustics of gas bubbles in liquids

Ultrasound is passed through liquids and tissue both for diagnostic reasons, and in order to produce a material change. The most familiar diagnostic application is the external foetal scanning that is routine in many pregnancies. However many more sites are now benefiting from ultrasonic scanning. This is evidenced by the presence of probes for use whilst inserted into the vagina, rectum and oesophagus; and the increase in the maximum insonification frequency from 30 MHz to one of 80 MHz, for use on shallow sites in dermatological and opthalometric work (where enhanced spatial resolution is required, but the increased absorption at these frequencies is not debilitating). Even in foetal scanning, new techniques are being explored (Figure 1) with, for example, the use of small bubbles to act as contrast agents. Non-imaging diagnostic methods have also developed, for example in the use of ultrasound to investigate bone health and osteoporosis.

An experimental study of the sound emitted from gas bubbles in a liquid

An undergraduate-level experiment is described for studying the sound emitted from bubbles formed by blowing gas through nozzles located within the bulk of a liquid. Hydrophone records give the frequency, pressure amplitude, and decay characteristics of the sound produced by a single bubble. The measured frequency agreed with the natural oscillation frequency of the bubble (the Minnaert frequency); the pressure amplitude gives the amplitude of oscillation of the bubble wall; the decay time broadly agrees with the value expected for radiative acoustic damping and thermal damping. The underwater sounds produced by natural brooks were recorded and found predominantly to consist of a succession of Minnaert-like oscillations, thereby allowing the bubble-size distributions to be obtained from the sound spectra.

Primary Bjerknes forces

When a bubble in a liquid is subjected to a periodic sound field, the resulting bubble oscillations can interact with the sound field, giving rise to the primary Bjerknes force. A simple undergraduate-level derivation, and a graphical illustration of the underlying processes, are given.

A Study of Bubble Activity Generated in Ex Vivo Tissue by High Intensity Focused Ultrasound

Cancer treatment by extracorporeal high-intensity focused ultrasound (HIFU) is constrained by the time required to ablate clinically relevant tumour volumes. Although cavitation may be used to optimize HIFU treatments, its role during lesion formation is ambiguous. Clear differentiation is required between acoustic cavitation (noninertial and inertial) effects and bubble formation arising from two thermally-driven effects (the vapourization of liquid into vapour, and the exsolution of formerly dissolved permanent gas out of the liquid and into gas spaces). This study uses clinically relevant HIFU exposures in degassed water and ex vivo bovine liver to test a suite of cavitation detection techniques that exploit passive and active acoustics, audible emissions and the electrical drive power fluctuations. Exposure regimes for different cavitation activities (none, acoustic cavitation and, for ex vivo tissue only, acoustic cavitation plus thermally-driven gas space formation) were identified both in degassed water and in ex vivo liver using the detectable characteristic acoustic emissions. The detection system proved effective in both degassed water and tissue, but requires optimization for future clinical application.

The spatial distribution of cavitation induced acoustic emission, sonoluminescence and cell lysis in the field of a shock wave lithotripter

This study examines the spatial distribution of various properties attributed to the cavitation field generated by a shock wave lithotripter. These properties include acoustic emission and sonoluminescence, which result from violent bubble collapse, and the degree of cell lysis in vitro, which appears to be related to cavitation. The acoustic emission detected with a 1 MHz, 12 cm diameter focused hydrophone occurs in two distinct bursts. The immediate signal is emitted from a small region contained within the 4 MPa peak negative pressure contour. A second, delayed, burst is emitted from a region extending further along the beam axis. The delay between these two bursts has also been mapped, and the longest delay occurs at positions close to the regions of maximum peak negative pressure. Sonoluminescence from both single and multiple shocks occurs in a broader region than the acoustic emission but the measurement technique does not allow time resolution of the signal. Cell lysis occurs in a relatively small region that correlates closely with the immediate acoustic emission for a shock propagating in a gelatine solution.

Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water

A free-Lagrange numerical method is implemented to simulate the axisymmetric jetting collapse of air bubbles in water. This is performed for both lithotripter shock-induced collapses of initially stable bubbles, and for free-running cases where the bubble initially contains an overpressure. The code is validated using two test problems (shock-induced bubble collapse using a step shock, and shock–water column interaction) and the results are compared to numerical and experimental results. For the free-running cases, simulations are conducted for a bubble of initial radius 0.3 mm located near a rigid boundary and near an aluminium layer (planar and notched surfaces). The simulations suggest that the boundary and its distance from the bubble influence the flow dynamics, inducing bubble elongation and jetting. They also indicate stress concentration in the aluminium and the likelihood of aluminium deformation associated with bubble collapse events. For the shock-induced collapse, a lithotripter shock, consisting of 56 MPa compressive and ?10 MPa tensile waves, interacts with a bubble of initial radius 0.04 mm located in a free field (case 1) and near a rigid boundary (case 2). The interaction of the shock with the bubble causes it to involute and a liquid jet is formed that achieves a velocity exceeding 1.2 km s?1 for case 1 and 2.6 km s?1 for case 2. The impact of the jet on the downstream wall of the bubble generates a blast wave with peak overpressure exceeding 1 GPa and 1.75 GPa for cases 1 and 2, respectively. The results show that the simulation technique retains sharply resolved gas/liquid interfaces regardless of the degree of geometric deformation, and reveal details of the dynamics of bubble collapse. The effects of compressibility are included for both liquid and gas phases, whereas stress distributions can be predicted within elastic–plastic solid surfaces (both planar and notched) in proximity to cavitation events. There is a movie with the online version of the paper.