Cavities In Liquids Research Articles

A Continuum Approach to Microscopic Surface Tension for the n-Alkanes

Microscopic surface tensions of cavities in liquids or of droplets with radii down to about 0.5 nm have been predicted. Surface energies of small clusters are calculated from the unretarded dispersion forces at a spherical interface. The resulting expression for surface tension is a function of basic intermolecular properties and cluster size, with predictions for macroscopic surface tensions being in good agreement with experimental data (flat surface). The surface tension is found to decrease with decreasing radius, and for n-alkanes, such size effects occur below 2 nm; above this size, the predicted results closely approximate the planar values.

Dependence of computer model structure of an amorphous solid on hardness of the repulsive potential

In models of an amorphous solid with a potential U = ar−n(n = 3–20), the main structural elements were found to be tetrahedron and quartoctahedron. At lower n there are more tetrahedra and less quartoctahedra. In addition to the fom and size of separate Delaunay simplices, their mutual arrangement has been studied by percolafion analysis. For that we used the coloring of the Voronoi network: according to tetrahedricity of simplices to identify dense atomic configurations, and according to the radii of mouths of cavities (passages between simplices) to identify the cavities. We have found percolative cavities in liquids and percolating dense configurations in all amorphous solid models.

A general theory for the formation of a new phase. Static cavitation in a nonvolatile liquid

The rate of formation of cavities in a nonvolatile liquid subjected to negative pressure is calculated. The pressure is assumed to be sufficiently moderate, so that the critical bubble (hole) can be treated macroscopically. If this condition is satisfied one may apply the Zel'dovich saddle-point method. However, in distinction from that method, the present paper makes use of a construction of Gibbs grand canonical ensemble, which allows one to avoid the ambiguities that appear in the calculation of the microscopic initial stage of formation of the hole and yields a more accurate value of the kinetic (preexponential) factor. A more accurate value of the work required to form a critical hole, the value which occurs in the exponent, is obtained by taking into account the dependence of the surface tension of the hole on the curvature of the surface. For this purpose we use an expansion of the surface tension in powers of the curvature of the surface of the hole. Since the surface tension occurs in the exponent of the expression for the probability or rate of cavitation, it is necessary to retain the expansion terms which are linear or quadratic in the curvature, whereas the correction factors to the cavitation rate, due to higher-order terms tend to unity as the expansion of the liquid decreases, in contradistinction from the first terms. It is important that for large expansions, and hence for small curvatures of the surface of the critical hole, the series for the surface tension diverges.

Shock-induced collapse of single cavities in liquids

A two-dimensional method was used to observe the interactions of plane shock waves with single cavities. This allowed study of processes occurring within the cavity during collapse. Results were obtained from high-speed framing photography. A variety of collapse shock pressures were launched into thin liquid sheets either by firing a rectangular projectile or by using an explosive plane-wave generator. The range of these shock pressures was from 0.3 to 3.5 GPa. Cavities were found to collapse asymmetrically to produce a high-speed liquid jet which was of approximately constant velocity at low shock pressures. At high pressures, the jet was found to accelerate and crossed the cavity faster than the collapse-shock traversed the same distance in the liquid. In the final moments of collapse, high temperatures were concentrated in two lobes of trapped gas and light emission was observed from these regions. Other cavity shapes were studied and in the case of cavities with flat rear walls, multiple jets were observed to form during the collapse.

Calculations of temperature within and without a pulsating gas-filled cavity

The temperature of the gas within a spherical cavity driven by a sinusoidal pressure field is calculated using an existing model [H. G. Flynn, J. Acoust. Soc. Am. 57, 1379–1396 (1975)] for cavitation dynamics. The temperature field in the liquid surrounding the bubble also is calculated with this model. For this work it is assumed that temperature variations are due to heat conduction only, although corrections for evaporation, condensation, etc., may be included if desired. Because the temperature T in the liquid at the cavity interface is allowed to vary (which reduces heat conduction by reducing the thermal gradient at the interface) the effect of holding T fixed is investigated. Results are presented for argon-filled and air-filled cavities in water or various organic liquids. [Work supported by ONR and NIH.]

Cavities in molecular liquids and the theory of hydrophobic solubilities.

Thermal configurational data on neat liquids are used to obtain the work of formation of hard spherical cavities of atomic size in six molecular solvents: n-hexane, n-dodecane, n-undecyl alcohol, chloroform, carbon tetrachloride, and water. These results are used to test a recent suggestion that the differences between nonaqueous solvents and liquid water in solvation of inert gases are not principally due to the hydrogen-bonded structure of liquid water but rather to the comparatively small size of the water molecule. The frequencies of occurrence of cavities in liquid water can be meaningfully distinguished from those in the organic solvents. Liquid water has a larger fractional free volume, but that free volume is distributed in smaller packets. With respect to cavity work, water is compared to a solvent of the same molecular density and composed of hard spheres of the same size as the water molecule. That comparison indicates that the hard-sphere liquid finds more ways to configure its free volume in order to accommodate an atomic solute of substantial size and thus, would be more favorable solvent for inert gases. The scaled particle model of inert gas solubility in liquid water predicts cavity works 20% below the numerical data for TIP4P water at 300 K and 1.0 g/cm3 for cavity radii near 2.0 angstroms. It is argued that the sign of this difference is just the sign that ought to be expected and that the magnitude of this difference measures structural differences between water and the directly comparable hard-sphere liquid. In conjunction with previous data, these results indicate that atomic sized cavities should be considered submacroscopic.

Nonlinear acoustics of micro-inhomogeneous media

Acoustic waves can interact in micro-inhomogeneous media much more intensively than in homogeneous media. This has been repeatedly observed in experiments with ground species, marine sediments, porous materials and metals. This paper considers two models of such media which seem to be applicable to the description of these results. One of them is based on the consideration of nonlinear sound scattering by separate spherical cavities in liquids and solids. The second model is based on the phenomenological stress-deformation relation in solids with microplasticity which often has hysteresis (heritage) properties associated with the micro-inhomogeneities. In metals, for example, it is caused by the movement of dislocations. Different nonlinear effects in such media (harmonic and combination frequency generation, nonlinear, variations of resonance frequency amplitude-dependent losses) are considered. Some results of experiments with metallic resonators supporting the theory developed here are also presented. These mechanisms may determine the nonlinear properties of real soils and rocks summarized in a table given in the paper.

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.

Microscopic surface tension down to molecular dimensions and microthermodynamic surface areas of molecules or clusters

Surface tension, surface energy, and entropy of small droplets, n clusters, and of cavities in liquids for sizes down to a single molecule are obtained. Rigourous relations are derived that relate microsurface properties to the usual handbook properties of bulk liquids. The microvalues and their dependence on the ratio of the cluster, droplet, or cavity size to the average liquid molecular size are given for common solvents, polar and nonpolar, including alcohols, water, hydrocarbons, rare gas liquids, and liquid (or solid) metals. Microscopic values are less than bulk-planar values by around 40% for nonpolar liquids, and greater for polar liquids by around 60%. The n-cluster (or cavity) sizes ? at which the microsurface properties approach the bulk values within a desired percentage, e.g., 5%, are given. The ordinary, bulk thermodynamic properties of liquids are also related to new useful quantities: ’’microthermodynamic surface areas’’ of molecules from which, using the equations given, ’’experimental’’ geometric (van der Waals) surface areas of molecules are calculated. The molecular surface properties introduced in the theory of ’’solvophobic forces’’ by this author earlier are finding applications presently in areas like HPLC (’’high pressure liquid chromatogrphy’’), multicomponent adsorption from solution phase (e.g., purification of waters from trace carcinogens), large ion association, protein structure, and drug–biopolymer binding, as well as the earlier ones for the prediction of rates and equilibria in diverse solvents in physical organic chemistry. The microsurface properties given now apply also to the convex case, e.g., the n clusters in nucleation and in metal cluster phenomena.

Evaluation of thermodynamic functions relative to cavity formation in liquids: uses and misuses of Scaled Particle Theory

The Scaled Particle Theory (SPT) is probably the most powerful theory presently available, that enables the calculation of the thermodynamic functions relative to the formation of cavities in liquids. We give the general relationship between the enthalpy of vaporization and the enthalpy of formation of a molecular cavity in a pure normal liquid; the good agreement with the experimental data constitutes one of the strongest arguments justifying the application of SPT to real liquids. However, we show that SPT can lead to uncertain cavity terms if the molecular diameters of the studied liquids are not well-known. We compare, on the other hand, the cavity terms (G and H) calculated from Sinanoglu's theory, since this theory has been used to that end recently, with those obtained from SPT.

Explanation of bubble creation in high electric fields by a new consideration on the structure of a liquid

This paper is the first summarizing report on a new approach. It is intended that some of the considerations will be expounded at a later date in more detail. The fundamental idea is that the physical behaviour — and therefore the breakdown property — of liquids is determined by their structure. This paper tries to substantiate this new concept. Theoretical considerations confirm the experimental fact that high electric fields cause the formation of bubbles in dielectric liquids. These considerations show that a crystal defect leads to the generation of unattached i.e. gas-like, molecules. The assumption is made, and is substantiated physically, that liquids have a crystalline structure: they consist of elementary crystals, ‘liquid grains’. Therefore gassing occurs in liquids, and, to a smaller extent, in solids too. The formation of cavities in liquids is primarily due to the thermal motion of the grains, but their growth into bubbles is due to the presence of an external electric field.

Motion and filling of cavities in a boundless liquid and close to a plane

The motion of bubbles in liquids has been studied in many earlier papers [1–8]. In this paper methods of the projection type are applied to the problem of a cavity in an ideal, incompressible liquid in the absence of vortices. The collapse of a bubble having a finite initial velocity in a boundless liquid is considered; also considered is the collapse of a stationary bubble close to a solid wall. Using the small-parameter method the generation of a jet is examined analytically. A numerical computing method not involving small parameters is developed; it is based on calculating the projection by numerical computation of the corresponding integrals. The method combines economy and simplicity of application with a high accuracy in the region in which the representation of the velocity potential by a series of spherical functions remains effective.

Collapse of One-Dimensional Cavities in Compressible Liquids

The collapse of a one-dimensional cavity in a compressible, inviscid liquid is treated exactly. Results of numerical computations for some specific examples are presented.

Discussion: “The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids” (Harper, E. Y., 1971, ASME J. Appl. Mech., 38, pp. 190–196)

Discussion: “The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids” (Harper, E. Y., 1971, ASME J. Appl. Mech., 38, pp. 190–196)

Discussion: “The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids” (Harper, E. Y., 1971, ASME J. Appl. Mech., 38, pp. 190–196)

Discussion: “The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids” (Harper, E. Y., 1971, ASME J. Appl. Mech., 38, pp. 190–196)

The Scattering of Shock Waves by Cylindrical Cavities in Liquids and Solids

The scattering of a plane acoustic shock wave by a cylindrical cavity in an inviscid fluid medium is calculated numerically and compared with a recently obtained asymptotic expansion. In contrast to the scattering by a rigid cylinder, the cavity displays a distinctive shielding effect in the shadow region characterized by a peak exitation and an inverse logarithmic decay. Experimental results are presented which indicate a strong counterpart in plastic shock diffraction.

Growth, Pulsation, and Collapse of a Gas-Filled Cavitation Bubble

A mathematical formalism has been developed for studying the dynamics of small gas-filled cavities in liquids under the influence of acoustic pressure fields. The formalism takes into account the effects of compressibility and heat conduction within the cavity, of compressibility, heat conduction, and viscosity in the surrounding liquid, and of the surface tension of the interface. The formalism consists of a set of algebraic, differential, and integral equations, and computer solutions of this set of equations have been obtained. The results of these calculations will be used to discuss the growth of cavities from some equilibrium state, the free pulsations of cavities, and the collapse of cavities. The main objective will be to provide insight of the relative importance of such effects as compressibility, heat conduction, viscosity, and surface tension on the motion of cavities. [The work described was carried out in cooperation with the Acoustics Research Laboratory at Harvard University and was supported by the Acoustics Programs of the Office of Naval Research under contract with the University of Rochester and with Harvard University.]

Initiation and development of detonation as a result of the action of weak shock waves on liquid explosives

Clearly, in handling liquid explosives safely it is important to take into account, among other things, their actual physical state. Whereas for most liquid explosives the initiating pressures for simple homogeneous compression are high (60–120 kbar); in the presence of cavitation the same liquids exploded at relatively low pressures (about 0.1–10 kbar) and, in their sensitivity to waves shock, resemble (or may even be inferior to) powdered explosives (according to [16] the initiating pressure for PETN at a density of 1.0 g/cm3 is 2.5 kbar). Under favorable conditions, especially if the vessel is capable of conducting elastic disturbances, the development of explosion in liquids leads to a low-velocity detonation which may subsequently resolve into normal detonation. In this respect, the propagation of low-velocity regimes in liquids is very similar to the propagation of low-velocity detonation in powdered explosives. Our present lack of definite ideas, about the specific reaction initiation mechanism associated with the collapse of cavities in liquids places considerable diffculties in the way of any quantitative analysis of the experimental data on the excitation and propagation of explosions.

Sonochemical cavitation phenomena in small bubbles

AbstractA theoretical study has been made on collapsing cavities in liquids. When a chemical reaction is not occurring in the cavity, the departure from the Rayleigh collapse time increases with decreasing Weber number. When a chemical reaction is taking place within the cavity, the conversion first decreases and then increases with decreasing initial radius of the cavity owing to the interaction of collapse time and gas temperature within the cavity. For large cavities the viscous damping effects are almost negligible, while for small cavities the damping of the cavity motion is quite significant. When an exothermic reaction is taking place within the cavity, the velocity of the cavity wall and maximum radius achieved upon rebound increase with each successive rebound until chemical equilibrium is approached. The influence of an increase in the number of molecules formed during the reaction upon collapse is described in the text along with a discussion of how various parameter and dimensionless groups affect the collapse of the cavity.