Fernando E. Prieto

The equation of state of solids

Abstract An equation of state for solids, in reduced variables, is obtained within the context of a system-independent formulation of the thermodynamics of high pressures. This formulation is valid for materials obeying a linear relationship between shock and particle velocities. An adequate set of scaling factors for pressure, compression, specific energy, and temperature, is first introduced. A modified Mie-Gruneisen equation, as well as many other thermodynamic relationships and coefficients, are then expressed in terms of reduced variables. Explicit expressions for the temperature along the Hugoniot, and for the equation of state, are obtained. It is also shown that when given in their reduced form, each of the two thermodynamic coefficients appearing in the equation of state can be considered as having the same constant value for many different materials. The possibility and convenience of using a “standard material” is discussed. Numerical results obtained using this reduced variables formalism are in good agreement with those computed or measured, by different authors, for various materials over a wide range of pressures. This is a good indication of the “universality” of the reduced equations obtained, and of the usefulness of the formalism.

Tandem shock wave cavitation enhancement for extracorporeal lithotripsy

Extracorporeal shock wave lithotripsy (ESWL) has been successful for more than twenty years in treating patients with kidney stones. Hundreds of underwater shock waves are generated outside the patients body and focused on the kidney stone. Stones fracture mainly due to spalling, cavitation and layer separation. Cavitation bubbles are produced in the vicinity of the stone by the tensile phase of each shock wave. Bubbles expand, stabilize and finally collapse violently, creating stone-damaging secondary shock waves and microjets. Bubble collapse can be intensified by sending a second shock wave a few hundred microseconds after the first. A novel method of generating two piezoelectrically generated shock waves with an adjustable time delay between 50 and 950 micros is described and tested. The objective is to enhance cavitation-induced damage to kidney stones during ESWL in order to reduce treatment time. In vitro kidney stone model fragmentation efficiency and pressure measurements were compared with those for a standard ESWL system. Results indicate that fragmentation efficiency was significantly enhanced at a shock wave delay of about 400 and 250 micros using rectangular and spherical stone phantoms, respectively. The system presented here could be installed in clinical devices at relatively low cost, without the need for a second shock wave generator.

Bactericidal effect of underwater shock waves on Escherichia coli ATCC 10536 suspensions

An electrohydraulic shock wave generator was used to study the bactericidal action of shock waves on Escherichia coli ATCC 10536 suspensions in 0.9% (w/v) NaCl solution (initial cell population: 8.2 log10 CFU/ml). The influence of treatment temperature, shock wave energy, number of applied shock waves, the acoustic cavitation produced by the shock wave, and the spark gap-generated light (UV and visible) were analyzed using E. coli cultures in the exponential phase. Part of the experiment was repeated in the stationary phase. Results indicate that light, number of shock waves, cavitation and interactions between them, influence bactericidal activity (P<0.05). The best viability reduction of 4.06 log10 CFU/ml was achieved at 350 shock waves, administered during approximately 14.5 min, with bacteria in the stationary phase by enhancing acoustic cavitation inside the vial, and without protecting the samples from the visible and UV radiation produced by the shock wave-generating spark.

An underwater shock wave research device

It is the purpose of this article to describe the design, construction, and operation of a highly versatile, low cost experimental facility to produce, by electrical breakdown of water, weak underwater shock waves in the 50 to 2000 bar range. The device as a whole is described and then the electrical circuit used to generate the shock waves is explained in some detail. The semi‐ellipsoidal or parabolic focusing mirrors, used to improve the efficiency in the transfer to the energy generated in an underwater shock wave, are also discussed. The measurement and control systems for operation of the device are described. Finally, a discussion of some of the experimental results is presented. As far as we know, this is the only apparatus of its kind with such a wide capability.

Evaluation of a bifocal reflector on a clinical lithotripter

PURPOSE To perform in vitro and in vivo tests using a clinical lithotripter in order to determine whether a bifocal reflector is more efficient and produces the same or less tissue damage than a conventional ellipsoidal reflector for electrohydraulic lithotripters. MATERIALS AND METHODS A standard ellipsoidal and a novel bifocal reflector were tested on a Tripter Compact lithotripter (Direx Medical Systems, Petach Tikva, Israel). The bifocal reflector was constructed by joining two sectors of two rotationally symmetrical ellipsoidal reflectors having different distances between their foci. The F1 foci of the sectors coincided, creating a separation between the F2 foci. The fragmentation efficiency of the reflectors was compared using kidney-stone models. Shockwave-induced trauma was evaluated in vivo by treating both kidneys of six healthy dogs. One kidney was exposed to shockwaves generated with the conventional reflector, and the other kidney was treated using the bifocal reflector. Pressure measurements were obtained for both reflectors using needle hydrophones. RESULTS The new design appeared to be more efficient than the conventional reflector in breaking up kidney-stone models. Tissue damage did not increase when using the bifocal reflector. CONCLUSION The use of bifocal, instead of standard ellipsoidal, reflectors should be considered as an alternative to improve extracorporeal shockwave lithotripsy.

A law of corresponding states for materials at shock pressures

Abstract By introducing an adequate set of reduced coordinates, it is shown that the analytical expression for the shock Hugoniot can be put into a form containing only pure numbers and dimensionless variables. The resulting equation is valid for those materials following a linear relationship between shock and particle velocities. A law of corresponding states for materials at shock pressures is established, and it is shown that some of the similarities already reported in the literature can be obtained as particular cases of this law. The reduction parameters are interpreted in terms of a limiting value to shock compression, and of a property that might be called shock hardness of the material. It is proved that the variables introduced in this paper not only allow the representation of all the shock wave data in one single curve, but simplify considerably all the equations involved in shock problems. To illustrate the use of these equations in the treatment of the thermodynamics of high pressure, the calculation of entropy changes is finally discussed.

Experimental facilities for impact physics research at the National University of Mexico

Abstract A gas gun for impact studies is described. The main parameters are 75.4 mm inside diameter and 13 m length. The 20-1 diaphragm breech is designed for a 40 MPa working pressure. The impact chamber is a cylinder, 62 cm in diameter and 51.5 cm in height, with a window to obtain photographic records. A 3 m 3 recuperation tank, pressure sealed to recover the helium, encloses the stopping mechanism. A building (20m×5m) was constructed so that the impact chamber and recuperation tank are inside a concrete room. The barrel and breech recoil freely, except for a couple of shock absorbers. The gun accelerates 1 kg projectiles to 1 km/s when filled with helium at design pressure. The main experimental interests are: (a) on controlled initial temperature targets, to test the previous theoretical work on the equation of state; (b) shock-induced polarization; and (c) the shock-induced phase transition of germanium.

System-independent release adiabats from shocked states∗☆

Abstract Suitable combinations of three parameters of any “linear” material: the initial density, and the coefficients of the linear relationship between shock and particle velocities, are used to define in reduced form most of the variables involved in shock pressures thermodynamic phenomena. This reduced variables formalism is applied, in conjunction with the mirror-image approximation, to obtain pressure-volume relationships for the release adiabats from any given shocked state. The resulting equations are system-independent, that is, they contain only pure numbers and reduced variables. Each adiabat is characterized by the coordinates of the point of crossing with the Hugoniot. Some of the adiabats so obtained for Al, Cu, W, Ti and Cr are in good agreement, at least down to pressures about one half that of the initial shocked state, with those computed using other procedures. A table of adiabats, valid for all “linear” materials, is also included.

Study of pressure transducers and electrodes for underwater shock wave generators

This paper describes the results obtained using different pressure transducers and electrodes to measure the pressure obtained from an experimental electrohydraulic shock wave generator.

Remarks on the Kumar isothermal equation

Abstract A comparison is made between an equation for room-temperature isotherms recently proposed by Kumar, and a universal system-independent equation of state proposed some years ago by Prieto and Renero. This comparison is made using both equations to obtain room-temperature isotherms for Cu, Pd, K and Mo. It is also shown that by the use of suitable scaling factors for the variables involved in Kumar’s equation, it can be expressed in universal system-independent form.