Cavitation Theory Research Articles

Limitations of the hydrodynamical theory of cavitation induced sonoluminescence.

The extremely short duration (<50 ps) of the flashes of light emitted by a sound field raises problems for the hydrodynamical description of sonoluminescence. Solutions to the Navier–Stokes equations with such a fast but short-lived adiabatic compression develop shock fronts. Even in the linear approximation a single 20-μ bubble that accelerates at this rate would radiate so much sound that its motion would dominate the Q of a 0.1-liter resonator. The extent to which such a quickly accelerating bubble can be considered to be in local equilibrium is discussed. Nevertheless, fluid mechanics provides valuable scaling laws that can be used to analytically determine the ambient radius, phase of collapse, and maximum and minimum radii of the trapped bubble’s oscillation. [Work supported by the USDOE: Office of Basic Science (theory) and Division of Advanced Energy Projects (experiment) and R. L. is an AT&T fellow.]

Cavitation bioeffects: Spin-offs from lithotripsy.

Lithotripter fields can produce cavitation in the organs of the body at pressure amplitudes significantly lower than those required to fragment stones. Because of limits on the expansion of the gaseous nuclei imposed by the surrounding tissue structures, cavitation in tissue is qualitatively different from that described by classical cavitation theory for a spherical bubble in an infinite fluid. Thresholds for structural and functional changes in kidney, liver, lung, heart, and blood, developmental effects in the embryo/fetus, and killing of Drosophilia larvae have been determined. Studies of the biological effects of shock waves generated by lithotripters have guided us in the search for effects of diagnostically relevant pulsed ultrasound. In particular, lung hemorrhage occurs with pulsed ultrasound at acoustic pressures of the order of 1 MPa and effects on the dynamic behavior of heart tissue have been seen with single 1–10 ms pulses at pressure amplitudes of the order of 10 MPa. The effects in lung occur at temporal average intensities orders of magnitude lower than previously associated with biological effects in mammals.

Killing of drosophila larvae by the fields of an electrohydraulic lithotripter

Drosophila larvae contain small gas bodies stabilized within their respiratory system. Because these bubbles are inhibited in their capacity to expand by the surrounding tissues, it is probable that they do not respond to acoustic fields in the manner described by classical cavitation theory that assumes a spherical bubble in an infinite fluid. However, just because of this inhibited expansion, they may serve as reasonable models for the gas bodies in mammalian tissues. Approximately one half of a population of Drosophila larvae is killed by exposure to 3 to 10 double lithotripter shocks with a positive pressure of 2–3 MPa. In contrast with the predictions of classical cavitation theory, adding a negative pressure to the exposure has little influence on the killing rate or its threshold pressure. The available evidence suggests that interaction of gas bodies in tissues with pressure fields and the resultant biological effects may be qualitatively different than predicted by classical cavitation theory and that positive rather than negative pressure may be a predictor of these effects.

The Solution of the Elrod Algorithm for a Dynamically Loaded Journal Bearing Using Multigrid Techniques

Numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

ChemInform Abstract: Effect of Static Pressure on the Ultrasonic Activation of Chemical Reactions. Selective Oxidation at Benzylic Carbon in the Liquid Phase.

AbstractIn accordance with the theory of acoustic cavitation the sonocatalytic effect on the title reaction is maximized at definite values of pressure (300 and 450 torr, resp.) allowing the best coupling with the ultrasonic field (21.5 and 48 kHz).

Effect of static pressure on the ultrasonic activation of chemical reactions. Selective oxidation at benzylic carbon in the liquid phase

The effects of sonoactivation on kinetic rates and chemical yields of a model reaction, selective oxidation at the benzylic site of indane, was studied at subatmospheric static pressures ranging from 200 to 760 Torr. The reaction occurs at a rate up to five times higher when a suitable ultrasonic field activates the reagents in solution. By varying the pressure applied to the system, the total sonochemical yields were found to follow a non-monotonic trend, with a peak value related to the frequency of ultrasounds irradiated. According to the general theory of acoustic cavitation, the results obtained are accounted for in terms of distribution and dynamics of the cavitating bubbles, whose average radius of equilibrium reaches its resonant value when tuned to a definite value of pressure, so allowing the best coupling with the ultrasonic field; under these conditions, the sonocatalytic effects on reaction parameters are maximized.

Acoustic Theory Applied to the Physics of Electrical Breakdown in Dielectrics

In order to stimulate further thought and research within the science of dielectrics, this paper discusses the remarkable correlation between acoustic theory and the physics of electrical breakdown in dielectrics. Following a brief, simplified fied review of acoustic theory and the propagation and attenuation ation of soundwaves in gases, liquids and solids, three areas in dielectrics are addressed in which the breakdown mechanisms require further clarification. These are the relative electrical strengths of gases and mixtures; streamer initiation in liquid hydrocarbons; and the incubation period before treeing or breakdown own occurs within solid dielectrics. Acoustic analysis of gas breakdown clearly shows that the relative electrical strengths of gases and mixtures vary as the inverse square of sound velocity, and consequently, are closely related to both the molecular weight and specific heat ratio of the gas or mixture. For liquid hydrocarbons, an analysis of acoustic emission levels from partial discharges combined with acoustic cavitation theory, supports the hypothesis that cavitation (collapse) of microbubbles bubbles attached to dust particles may provide the conditions for streamer initiation. Finally, attention is drawn to the relationship between the velocity of sound within solid dielectrics and Young's modulus, Poisson's ratio and density, which suggests a potential application of acoustics for assessing the mechanical strength of dielectrics as they age. Thus, simple acoustic measurements performed on solid dielectrics may provide some information on the structural condition Qf these dielectrics before treeing and subsequent breakdown occurs.

An exact formulation for the internal pressure of a cavitation bubble

Recent experiments have shown that when the acoustic driving frequency is near one of the bubble's harmonic resonances, the theoretical values predicted by the Rayleigh‐Plesset equation are inconsistent with observed values. This inconsistency lead Prosperetti to consider the internal pressure term in the Rayleigh‐Plesset equation in a more general manner. In the past, the internal pressure of a bubble was assumed to be accurately predicted by a polytropic approximation. The internal pressure is computed from the conservation equations, resulting in a more accurate formulation. The new method also provides additional information about the internal thermodynamics of a bubble, which is explored in some detail. The two models are examined using some of the recent techniques in dynamical systems. “Feigenbaum trees” are shown for the two models of interest. This method for analyzing an equation is shown to be very sensitive to the internal pressure term, and thus it is an appropriate method for comparing different acoustic cavitation theories. [Work supported in part by NSF and ONR.]

Sonoluminescence and sonochemical reactions in cavitation fields. A review

Contemporary ideas on the nature of cavitation are reviewed in this paper. The general theories of sonoluminescence and sonochemical reactions, the origin, stability and splitting of cavitation bubbles, the dynamics of cavitation field evolution, the peculiarities of cavitation effects at low intensity and low-frequency acoustic oscillations, the sonoluminescence quenching effect and some questions on the energetics of cavitation fields are discussed. The electrical theory of the splitting of cavitation bubbles may, as shown in the paper, become an alternative to the thermal theories of cavitation in the future.

Characterization of Creep Damage in Metals Using Small Angle Neutron Scattering.

Creep damage in polycrystalline metallic materials can be attributed to cavitation and cracking along the grain interfaces. Theories of creep cavitation that have been developed in recent years are reviewed. Further evaluation and/or refinement of these theories has been retarded by a lack of an experimental counterpart. Small angle neutron scattering studies (SANS) provide one experimental tool which is complementary to others. SANS done at NBS and elsewhere have shown that this technique is suitable for studying nucleation and early stage of growth of creep cavities. This would provide the impetus to further progress in this area.

Influence of hydrostatic pressure and multiaxial straining on cavitation in a superplastic aluminum alloy

A commercial Al-Zn-Mg-Cu alloy was processed for superplastic forming and tested in uniaxial. equibiaxial. and plane-strain conditions. In addition, a hydrostatic pressure was used to vary the mean stress. Damage, defined as cavitation porosity, was measured as a function of the true plastic strain. ϵ e . It was found to depend on the maximum principal stress when ϵ e < 1. but correlated better with the mean stress when ϵ e > 2; this implies that in the early stages, cavitation may have been controlled by a diffusional mechanism, but that plastic flow hole growth became more important when the cavities grew large. The data could not be satisfactorily correlated with the existing theories of cavitation by diffusional or plastic flow processes; this may have been due to several reasons, e.g. cavities formed inhomogeneously (although always at inclusions and at grain boundaries), the alloy was metallurgically complex, and dynamic changes in microstructure such as grain growth occurred during deformation.

Small angle neutron scattering study of fatigue induced grain boundary cavities

Small angle neutron scattering (SANS) has been used to study grain boundary cavitation in high purity copper fatigued at elevated temperatures. SANS is an extremely sensitive method for observing cavities. Void volume fractions of less than 10 −6 can be detected. Analysis of scattering data yields values for the total void volume per unit volume and the total number of voids in a fatigued sample. The size distribution of the voids also can be calculated. From a series of specimens, each fatigued under identical conditions but for varying lengths of time, it is possible to obtain the void nucleation rate and the rate of growth of the total void volume and of the individual voids. Extrapolation of curves of void volume fraction vs time of fatigue to zero time shows that cavitation begins upon commencement of fatiguing without any measurable incubation time. Void nucleation is continuous throughout fatigue. Calculated values of the individual void growth rate agree very well, as regards time dependence, temperature dependence, and even absolute value, with growth rates derived from a theory of fatigueinduced cavitation based on transient effects in vacancy diffusion.

A study of the effects localised discharge in dielectric liquids

The sequence of events following the triggering of a trigatron gap in dielectric liquids has been studied. An initial shock wave travelling at sonic velocity is followed by an event which may be either an expanding bubble or a heat wave obeying the heat diffusion equation. This region of reduced density subsequently collapses in a manner predicted by Rayleigh's theory of cavitation. Finally a jet of bubbles is ejected from the trigger electrode. These observations are all of importance in relation to the electrical breakdown of dielectric liquids.

EFFECT OF DISPERSED AND CONTINUOUS PHASE VISCOSITY ON DROPLET SIZE OF EMULSIONS GENERATED BY HOMOGENIZATION

Abstract The average droplet diameter of an oil-in-water emulsion was measured to determine what effect the viscosities of the oil phase and water phase have on the efficiency of homogenization. The dispersed phase viscosity was adjusted by blending two oils, Castor Oil and Corn Oil, which have high and low viscosities. The continuous phase viscosity was adjusted by adding corn syrup to water. The efficiency of homogenization decreases when the oil phase viscosity increases. A mathematical expression is derived which reveals how the parameters of viscosity and homogenizing pressure affect emulsion quality. The homogenizing efficiency decreases by a small amount as continuous phase viscosity increases, but the efficiency then remains constant over a broad viscosity range. The results of the viscosity tests do not verify any one theory of homogenization, but they do correspond to the trends predicted by turbulence and cavitation theory.

Acoustic effects and bubble dynamics during the explosive boiling of droplets at the superheat limit

A droplet of volatile liquid immersed in a different heated but nonvolatile liquid can be heated to very high degrees of superheat before it boils explosively by spontaneous initiation. A series of experiments have been carried out to examine the rapid processes that occur during the early stages of the vapor explosion when departures from equilibrium are very large. The radiated acoustic field has an unexpectedly complex structure which, though not yet fully understood, appears to be related to other unexpected effects observed in the experiments. During the first few microseconds of the explosion, a previously unobserved instability develops at the liquid-vapor interface, resulting in a rather more complex flow field than that envisioned by classical cavitation theory. The nature of this instability is described and some speculations about its consequences are presented. A series of high speed photographs are presented showing the complete development of the explosion from initiation, including the processes occurring on a microsecond time scale thereafter, to the final bubble oscillations which occur on a millisecond scale.

Review of Past Work on Liquid Breakdown

The electrical breakdown of liquid dielectrics is a complicated process and there is no single theory that explains all the experimental results. Specific experimental conditions will be the determining factor as to which of the several mechanisms will be operative. Because of poor control of liquid purity prior to 1950 the large scatter of breakdown measurements had precluded a determination of factors controlling the intrinsic dielectric strength. During the fifties it became possible to measure a breakdown strength which depends upon a particular variable, other variables being held constant. This is done by giving special attention to chemical and physical purification (filtering) of the sample, close control of the electrode surface polish and geometry, and the use of pulsed voltages. Under these antiseptic laboratory conditions, the extrinsic mechanisms (which usually result in low values of breakdown) can be more or less avoided and one can measure a relatively high strength. These values can be reproduced by different investigators and serve as a basis for evaluation of theories of breakdown. More recently new techniques have been developed to investigate transient phenomena prior to, and in the early stages, of breakdown. These have supplied additional evidence concerning the mechanisms by which ionization leads to a conducting path between the electrodes. On the one hand, there are the mechanisms in which ionization occurs in the liquid phase while on the other, those in which it occurs in a gas (low density) phase produced prior to breakdown (bubble or cavitation theory).

Experimental cavitation studies in a model head-neck system

The response of two different fluid-filled head-neck models to impact was studied experimentally to provide information concerning the validity of the widely prevalent cavitation hypothesis of brain damage. The structures consisted of an acrylic spherical shell with an outside diameter of about 188 mm and a human calvarium with a clear polyester resin occiput, representing the head, each coupled to an articulated artificial viscoelastic neck. Transient phenomena were initiated by the impact of either cylindrical projectiles fired from a pneumatic gun or by the pendulum drop of an aluminum spherical shell onto a small truncated aluminum cone attached to the head models. A short strain-gaged aluminum cylinder served to measure the input force history, while the pressure in the brain-simulating fluid was ascertained by means of Z-cut tourmaline crystals located along the impact axis at the coup, center and contrecoup positions. The occipital regions of the models were photographed at framing rates of 4000–8000 s −1 to visually examine the cavitation phenomena. Coup, contrecoup and resonating cavitation were detected and found to coincide temporally with negative pressure transients in both head-neck models. These results lend some support to the cavitation theory as a possible mechanism for brain damage.

Rheology of Adhesion

Abstract This discussion has outlined a series of considerations which begin with engineering definitions of system response of adhesive joints and end with propositions involving molecular interactions at interfaces. Connecting these extreme aspects of the argument is the central subject of the micromechanics of bonding and fracture. Cavitation theory, as simply described by Equations (6a) and (7), illustrates the scale of microresponse in which both the thermodynamic and rheological aspects of adhesion phenomena achieve a parity when applied to cavities of radius r=0.1 to 10 μ. The discussion of the micromechanics of polymer fracture provides ample evidence that pure materials, polymer composites, and adhesive joints, need to be described in terms of their microdefects. The several mathematical models for crack propagation which are imposed upon fracture mechanics data tend to oversimplify the visualization of the true micromechanisms of fracture. The fuller development of micromechanics theory and experimental analysis promises to be an important area of current developments in the better understanding of macroscopic response of filled systems, fiber reinforced composites, and adhesively bonded structures. Recent developments in the several theories of intermolecular forces and the physical chemistry of bonding provide new impetus to the chemist to design optimized polymeric materials with finely adjusted balances of surface and bulk properties. The fuller visualization of adsorption-interdiffusion bonding as a process involving both the two-dimensional interface and the three-dimensional interphase defines bonding as both a thermodynamical and a rheological process. The microstages of bond formation are somewhat the reverse of the stages of microfracture listed earlier. The microdefects that commonly exist in polymeric materials and polymer composites tend to indicate that the viscoelastic constraints typical of polymer chains and networks play an important role in preventing equilibrium bonding in the simple thermodynamic sense as expressed by idealized liquid—liquid or liquid—solid interactions. The current development and application of a refined thermodynamical and rheological argument to both bonding and fracture processes stands as a central issue in directly correlating the molecular criteria of adhesion and performance of bonded systems. Any of the simple mathematical relations introduced in this discussion may be expressed with greater detail and precision by incorporating detailed statements concerning chemical composition, macromolecular structure, and free volume state of the polymeric adhesive.

Cavitation in Viscoelastic Media

A theoretical model for cavitation in viscoelastic media is developed which incorporates both interfacial and rheological arguments. The properties of interfacial and bulk cavities are correlated, and the influence of time-dependent cavity vapor pressure Pν(t) or hydrostatic tension σ̄(t) are correlated with the extension ratio λ=r/r0 of the cavity surface in a stress relaxation model. Experimental data are analysed for cavitation by peeling, tensile loading of butt joints, and superheating of swollen elastomers. For each case an agreement between theory and experiments is obtained which identifies the specific mode of cavitation and indicates for all cases the presence of prenucleated cavities with radii r0⩾1.0 microns. The direct correlation of peeling stresses with viscoelastic restraints to interfacial cavitation provides a new type of experimental confirmation for the applicability of rate-temperature superposition to peeling data. The implicit assumption that the interfacial failure stress depends upon frequency or strain rate in the same fashion as cohesive failure stress is confirmed by cavitation theory for the general case where surface tension constraints are negligible compared to viscoelastic constraints.

Singular Perturbation in Acoustic Cavitation

Approximate solution of a model ordinary differential equation problem illustrates essential ideas in a new approach to acoustic cavitation theory. Rectified diffusion bubble growth through resonance size has been analyzed for the first time. This is a singular perturbation problem. The asymptotic expansion appropriate for the thin boundary layer of concentration oscillation effects is not uniformly valid. Details of the resonance domain, which is characterized by relatively rapid growth, are discussed. This work is based on a previous paper dealing with cavitation threshold [J. Acoust. Soc. Amer. 47, 327–331 (1960)].