Two-dimensional simulations of gas cavity responses to both weak shocks (p ≤ 30 MPa) and strong shocks (p ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s−1 are predicted by this model.

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A system for the measurement of ultrasound velocity in liquids was automated to cope with variations in temperature (293.15 K ≤ T ≤ 373.15 K) and pressure (P ≤ 100 MPa). The following problems had to be solved: supervision and monitoring of the achievement of the required pressure and temperature, creation and reception of the signal, acquisition of the measurement points, identification of the signal received on the basis of the characteristics of a reference signal, measurement of ultrasound travel times, memorization and processing of the results. The system enables substantial savings of time compared with manual methods. The system calibration procedure is also described. Measurements of octane and pentane (which had been studied previously) are used to verify the validity of the system developed and to determine its degree of accuracy (absolute average deviation from literature data 0.1% and maximum deviation from literature data 0.25%).

Semiconductor strain gauges were used to measure the internal strain along the axes of spherical and disk plaster specimens when subjected to lithotripter shock pulses. The pulses were produced by one of two lithotripters. The first source generates spherically diverging shock waves of peak pressure approximately 1 MPa at the surface of the specimen. For this source, the incident and first reflected pressure (P) waves in both sphere and disk specimens were identified. In addition, waves reflected by the disk circumference were found to contribute significantly to the strain fields along the disk axis. Experimental results compared favorably to a ray theory analysis of a spherically diverging shock wave striking either concretion. For the sphere, pressure contours for the incident P wave and caustic lines were determined theoretically for an incident spherical shock wave. These caustic lines indicate the location of the highest stresses within the sphere and therefore the areas where damage may occur. Results were also presented for a second source that uses an ellipsoidal reflector to generate a 30-MPa focused shock wave, more closely approximating the wave fields of a clinical extracorporeal lithotripter.

The Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26-4] is used to investigate the response of air bubbles to a variety of lithotripter shock waveforms. A modification of the Gilmore model is proposed to account for partial constraint of the bubble expansion that can be caused by bubble coatings (such as in echo contrast agents) and by tissues or vessels surrounding bubbles in vivo. In the modified formulation, a viscoelastic membrane is assumed to exist at the bubble interface to include the possible effects of the nonlinear elasticity and strain rate dependent viscosity on the bubble response. The stress induced in the membrane is assumed to be an exponential function of the bubble radius, which tends to restrict the bubble expansion. The viscosity is assumed to increase with the strain rate. In the absence of the membrane, the maximum bubble wall pressure induced by a negative (tensile) pulse is much larger than that induced by a positive (compressive) pulse of the same pressure waveform and amplitude. This difference increases with decreasing initial bubble radius. The addition of the viscoelastic membrane significantly decreases the predicted maximum bubble pressure and the difference in response between the positive and negative pulses. The effect of the time delay between double pulses (positive followed by negative or negative followed by positive) is also investigated for unconstrained bubbles.

The problem of shock interaction with a vortex ring is investigated within the framework of axisymmetric Euler equations solved numerically by a shock-fitted sixth-order compact difference scheme. The vortex ring, which is based on Lamb’s formula, has an upstream circulation Γ=0.01 and its aspect ratio R lies in the range 8⩽R⩽100. The shock Mach number varies in the range 1.1⩽M1⩽1.8. The vortex ring/shock interaction results in the streamwise compression of the vortex core by a factor proportional to the ratio of the upstream and downstream mean velocity U1/U2, and the generation of a toroidal acoustic wave and entropy disturbances. The toroidal acoustic wave propagates and interacts with itself on the symmetry axis of the vortex ring. This self-interaction engenders high amplitude rarefaction/compression pressure peaks upstream/downstream of the transmitted vortex core. This results in a significant increase in centerline sound pressure levels, especially near the shock (due to the upstream movement of the rarefaction peak) and in the far downstream (due to the downstream movement of the compression peak). The magnitude of the compression peak increases nonlinearly with M1. For a given M1, vortex rings with smaller aspect ratios (R<20) generate pressure disturbances whose amplitudes scale inversely with R, while vortex rings with larger aspect ratios (R>40) generate pressure disturbances whose amplitudes are roughly independent of R.

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Gruneisen's constant, y , is ideally temperature-independent on constant-volume lines; a similar constant, A, which is ideally temperature-independent on isobaric lines, has been found. The comparison between y and A shows that both expressions contain the ratio of the volumetric thermal expansion coefficient to the specific heat capacity; y has an additional temperature dependence due to the thermal part of the compressibility, whereas A has only a slight thermal component due to the volume per unit mass. A has been chosen so that A = y at the point where the temperature and pressure are both zero. For most materials it is expected that A 2 y with a different temperature dependence. It is shown empirically for a selection of ceramics that A is nearly temperature-independent and has a value between 0.7 and 1.4.