Water Vapor Bubbles Research Articles

The effect of time dependent void density on grain boundary creep fracture—i. continuous void coalescence

When voids in a creeping solid are non-uniformly distributed over a grain boundary facet void coalescence occurs simultaneously with void growth. The effect of such coalescence on subsequent grain boundary void growth can be analysed assuming a random (i.e. Poisson) initial void distribution. A simple relationship between the fraction of voids remaining on a grain boundary facet and their area fraction is found. This relationship is independent of the mechanism by which the voids grow. When voids grow by surface diffusion or by power-law creep very little effect of coalescence on the overall rate of damage accumulation is found. However, when void growth is controlled by grain boundary diffusion, the rate of void growth is decreased dramatically during coalescence, and effectively stops. Final fracture occurs by creep controlled void growth. The model predicts a non-linear stress dependence for this process, and an activation energy different from that for boundary diffusion alone. The model is compared with creep fracture data for pure metals implanted with water vapour bubbles. Good agreement with the model is found in two cases, while in a third case void growth appears to have been controlled by surface diffusion.

Grain boundary structure and boundary segregation in AgO alloys

The significance of the atomic structure of grain boundaries in silver for the equilibrium boundary segregation of oxygen was investigated by means of the formation of water vapour bubbles at grain boundaries in AgO solid solutions annealed in H 2. Low energy boundaries exhibited numerous small water vapour bubbles, whereas in high energy boundaries a few large size voids were formed, suggesting that oxygen segregates preferentially at high energy boundaries.

The influence of tritium exposure and helium build-in on the properties of OFHC copper

Tough pitch and other high oxygen content copper alloys are known to be susceptible to hydrogen induced microstructural damage. The damage arises from the interaction of solute oxygen and oxide particles with dissolved hydrogen to form water vapor bubbles, the greatest fraction of which reside on grain boundaries. Oxygen-free high conductivity (OFHC) copper on the other hand is essentially immune to any hydrogen-induced effects. Because the oxygen content is low, no such H/sub 2/O(V) grain boundary precipitation occurs. Nor is the ductility affected to any appreciable extent even when the material is tensile tested in high pressure hydrogen. This paper summarizes the initial results of an experimental program directed towards determining the effects of the prolonged exposure of OFHC copper to a gaseous overpressure of tritium. Since this alloy is immune to any hydrogen embrittlement as described above, tritium, as a hydrogen isotope would not be expected to seriously affect its behavior. Any observed changes in microstructure or mechanical properties may therefore be ascribed to the influence of the helium born in the copper as the result of the radioactive decay of the dissolved tritium.

Effect of the ambient pressure on the explosive burning of emulsified and multicomponent fuel droplets

A simplified model to study the mechanism controlling the growth of vapor bubbles in superheated pure and multicomponent liquids is formulated. The model is used to analyze the effect of ambient pressure and of the presence of solid particles or gas pockets on the nature and character of the liquid-phase disruption which may occur during the vaporization and burnng of emulsified and multicomponent fuel droplets. The analysis is in good qualitative agreement with existing atmospheric pressure experimental results. The “micro-explosive” buring of water-in-fuel emulsion droplets is caused by the very fast growth of superheated water-vapor bubbles. It is shown that the growth rate of these bubbles is primarily governed by the pressure difference between the superheated vapor and the liquid and by the inertia imparted to the liquid by the motion of the bubble surface (“Inertia controlled growth”). For the multicomponent fuel cases the model shows that the disruption of the droplets results from a much slower vapor-bubble growth which is governed by heat diffusion from the liquid to the bubble rather than by inertial and pressure effects (“Diffusion controlled growth”). Furthermore, it is predicted that any emulsion or multicomponent fuel droplet for which liquid-phase disruption is observed at atmospheric pressure will also exhibit disruption at higher pressures. However, as the ambient-pressure is increased the bubble growth rate will decrease in both solution and emulsion cases, resulting in a less effective and slower disruption. Finally, it is shown that through a reduction in the super-heat limit temperature, the presence of solid particles or dissolved gases in the liquid may also result in a less effective and slower disruption.

Diffusive intergranular cavity growth in creep in tension and torsion

Creep experiments were performed at 500°C in tension and torsion on high conductivity copper tubes with a uniform initial coverage of implanted water vapor bubbles on all grain boundaries. No significant differences were found in the times to fracture over a wide stress range when the results were correlated according to the maximum principal tensile stress in the two fields. The results indicate that the cavities grow in a crack-like mode but at one tenth the rate predicted from the theoretical model of Pharr and Nix. This difference is attributed partly to load shedding from boundaries normal to the maximum principal tensile stress to slanted boundaries and partly to a lack of knowledge about the surface diffusion constant. The results indicate further, that the contribution to intergranular cavity growth by power-law creep in negligible in comparison to the contribution by diffusional flow. Complementary tension and torsion experiments performed in initially uncavitated samples result in shorter creep lives in torsion than in tension due to more effective cavity nucleation in the former. The times to fracture in both of these cases obey Monkman and Grant's law, indicating the presence of constraints on growth by the lagging deformations by power-law creep in the surroundings of the cavitating isolated grain facets.

The formation of water vapor bubbles in copper and their effect on intergranular creep fracture

Small, closely spaced water vapor bubbles are formed along grain boundaries in coarse grained copper by annealing first in air at 800°C and then in hydrogen at 600°C. Almost all of the cavities are formed at grain boundaries, primarily because oxygen strongly segregates to grain boundaries in copper. The average cavity diameter and planar spacing are found to be 0.8 and 3.2 μm, respectively. A study of the creep fracture properties of copper containing the above cavity microstructure indicates that intergranular cavity growth is controlled by the rate of self diffusion along the cavity surface in the manner first described by Chuang and Rice. The stress dependence of the rupture time is found to be of the form t r ~ σ −3. The temperature dependence for fracture is characterized by an activation energy of 92 kJ/mol, which is close to that for surface self diffusion. These properties, together with the absolute rupture times are in close agreement with the Chuang-Rice theory in the limit of surface diffusion control. The determination of the controlling fracture mechanism is supported by metallographic and fractographic evidence.

A numerical study of cavity growth controlled by surface diffusion

The growth of grain boundary cavities is examined using a finite difference numerical scheme. The mechanism studied is that proposed by Chuang and Rice in which atoms are driven by gradients in curvature along the surface of the cavity to the grain boundary. Atomic transport in the grain boundary is assumed to be fast compared to that along the cavity surface. In the present paper the shape evolution of an initially lenticular cavity is followed in detail and in this respect the treatment differs from the Chuang-Rice approach in which a steady-state crack-like configuration is assumed. This allows us to examine the effects of capillarity and transients on the growth process. For an isolated cavity on an infinite boundary, it is found that the Chuang-Rice treatment accurately describes cavity growth once the steady state is achieved. The effect of capillarity is manifested by an incubation period during which a ‘nose’ protrudes from the tip of the cavity. It is the nose of the cavity that behaves like the Chuang-Rice steady-state crack. An array of cavities is also studied to determine the effects of cavity interaction on the growth process. The results of this investigation compare favorably with rupture data for silver containing implanted grain boundary water vapor bubbles.

The coalescence of large grain boundary cavities in silver during tension creep

An experimental technique for implanting water vapor bubbles in silver has been used to produce a uniform distribution of very large cavities along the grain boundaries of high purity silver. By implanting these very large bubbles prior to the onset of creep, the kinetics of the final stages of creep cavity growth and coalescence can be studied. The stress and temperature dependence for the creep-rupture of silver with grain boundary cavities initially 12 μm in diameter and spaced 20 μm apart has been determined for the temperature range 200 to 400°C. It is found that the time to rupture depends on the applied stress: t r ~ σ −9. The activation energy for creep rupture of silver with this microstructure is 199 kJ/mol above 300°C and about 103 kJ/mol below that temperature. The stress and temperature dependence for the creep-rupture of the embrittled silver appears to be identical with the stress and temperature dependence for the creep of silver itself suggesting that the final stages of cavity growth consists of the plastic tearing of the ligament material between the cavities. Scanning electron microscopy of the fracture surfaces reveal brittle, intergranular grain boundary facets. These facets exhibit uniformly distributed dimples, the spacing of which corresponds to the initial gas bubble spacing, indicating that fracture occurs solely by the growth of the pre-existing gas bubbles.

The kinetics of cavity growth and creep fracture in silver containing implanted grain boundary cavities

An experimental technique has been developed for implanting water vapor bubbles (H 2O (v) of fixed size and spacing along the grain boundaries of polycrystalline silver. The effects of this microstructure on the creep fracture behavior have been studied by conducting constant stress creep tests over the temperature range 200 to 550°C. The stress and temperature dependence of creep fracture has been determined for samples containing 1 μm diameter gas bubbles spaced 10 μm apart. The time to rupture varies with the applied stress as: t r ~ σ −3.7. The activation energy for the creep fracture is found to be 85.5 kJ/mol, which is in close agreement with the activation energy for surface self diffusion. Scanning electron microscopy of the creep fracture surfaces indicates a brittle intergranular failure process. The grain boundary facets on the fracture surface exhibit a dimpled structure. The spacing of these dimples corresponds to the initial gas bubble spacing, indicating that fracture occurs solely by the growth of the pre-existing gas bubbles. It is found that the stress, temperature and microstructural dependence of the rupture time, as well as the absolute rupture time itself, can be described accurately by a model of lenticular cavity growth and creep fracture proposed by Chuang and Rice. In this treatment, self diffusion along the cavity surface is the rate limiting step and the rupture time is predicted to vary as σ −3, in close agreement with the experimental data.

Heat Transfer Controlled Collapse of a Cylindrical Vapor Bubble in a Vertical Isothermal Tube

An experimental program was conducted to determine the collapse rate of slug-type vapor bubbles rising due to buoyancy through subcooled parent liquid in a vertical isothermal tube. The experimental apparatus included a vertical glass tube with an outer glass container providing a constant temperature water bath for the inner tube. The inner tube contained distilled, deaerated water, and water vapor bubbles were generated at the bottom of this tube with a pulsed electric heater. The parent liquid was uniformly subcooled with respect to the vapor bubble resulting in heat transfer controlled bubble collapse. Collapse rates and rise velocities were recorded by high-speed motion picture photography. Over a limited range of subcooling, the bubble collapse was well behaved, and a simple, quasi-steady boundary layer heat transfer analysis adapted from slug flow over a flat plate correlated the experimental results with a high degree of accuracy. Experimental results were obtained with tubes having inside diameters of 0.0127, 0.0218, and 0.0381 m and for a range of subcooling from 0.5 to 9.0 K.

A comparison of the embrittling effects of H 2O bubbles in Ag with those of He bubbles in Ni-6% W

It is shown that water vapor bubbles can be introduced into polycrystalline silver via simple annealing procedures. These bubble microstructures are in certain respects very similar to those commonly found in irradiated metals. A comparison is made of the structure and embrittling effects of H 2O bubbles in Ag with those of He bubbles in Ni-6% W. It is shown that H 2O bubbles in Ag promote intergranular fracture, as do He bubbles in Ni-6% W. It is concluded that certain aspects of helium embrittlement induced by irradiation can be simulated by the Ag-H 2O system.

Growth rates of free vapor bubbles in liquids at uniform superheats under normal and zero gravity conditions

Extensive experimental data is presented for growth rates of vapor bubbles in water, ethanol, and isopropanol at small uniform superheats up to 4.9°C The measured phase growth occurred in the free volume of the liquid away from solid surfaces and at a nominal pressure level of 1 atm. Uniform, essentially constant superheats were obtained by a pressure release technique. Initial observation times for most bubbles occurred at about 1 ms. Final observation times as large as 450 ms were achieved Comparison of growth data taken at normal gravity to data taken at zero gravity, using a small drop tower, clearly show the point at which effects due to bubble translational motion become significant A detailed comparison is made to Scriven's exact solution for spherically symmetric, heat transfer controlled phase growth. Good agreement is obtained for the rnzero- g data over the entire observation time, while the agreement for the normal- g data is satisfactory up to times at which effects of the buoyant force become significant An interpretation that the increased growth rates observed at later times is due to bubble translational effects is supported by a semi-quantitative comparison to an approximate theory due to Aleksandrov et al. Previous experimental results for bubble growth under uniform, essentially constant superheat conditions and their relation to the present work are also discussed.

Mass-Transfer Model in Subcooled Nucleate Boiling

The mass-transfer model of subcooled boiling, conceived in 1952 by N. W. Snyder, is reviewed. Described is an experiment in which a water-vapor bubble was studied from its growth on a heated surface, through a thermal layer, and into a turbulent stream of subcooled water flowing parallel to the heated surface. The effectiveness of the turbulent subcooled stream in removing heat deposited by condensation on the surface of the bubble was determined. The results show that the thermal-energy transport associated with the mass-transfer mechanism in boiling heat transfer can be absorbed effectively at the top of the bubble. Also given are the results of a theoretical investigation in which two models of bubble dynamics were derived. The first model describes the artificial bubble produced in the experiment just noted. The second model describes the dynamics of a bubble growing on a heated surface, into a subcooled liquid, and with an evaporating thin liquid film below the bubble on the heated surface. The results show that the importance of the mass-transfer mechanism has been underestimated in the past and that this mechanism is responsible for a substantial portion, or almost all, of the heat transfer in subcooled nucleate boiling in forced convection.

Periodic precipitation (liesegang phenomenon) in solid silver—II. Modification of wagner's mathematical analysis

In the previous paper (1) an experimental study of Lieaegang precipitation in solid silver (Ag-H 2O experiment) was described. Single crystals of silver were annealed at 800°C in some partial pressure of oxygen to saturation and were then annealed in a partial pressure of hydrogen. Hydrogen diffused into the silver and reacted with the dissolved oxygen to form water vapor bubbles which under certain conditions formed in bands obeying Jablczynski's relationship. Carl Wagner's mathematical analysis of periodic precipitation has been modified, and when the spacing coefficients calculated with this theory were compared with those found experimentally, the agreement was satisfactory with one exception. It was found that the variation of the spacing coefficient with the variation of the oxygen concentration predicted by theory was opposite to the variation observed. Some suggestions have been advanced for this discrepancy, and it has been shown how some previous results in other systems can be explained by the modified Wagner analysis.

On the Mechanics of Vapor Bubble Collapse

The mechanics of vapor bubble collapse under spherically symmetrical conditions is examined to ascertain the relative importance of the effects of liquid inertia and heat transfer on the collapse rate. A dimensionless parameter, Beff, is identified to characterize the mode of collapse. Discriminating values of this parameter are suggested for the simple case where the collapse is initiated by a step change in pressure or temperature. For heat transfer controlled collapse, a model is also proposed to account for the influence of a permanent gas present in the bubble. Experimental results for bubbles with initial radii ranging from 0.3 cm to 0.9 cm collapsing in water and ethyl alcohol at atmospheric pressure levels and under free fall conditions are presented. The pressure difference ranges from 12 cm Hg to 63 cm Hg and the corresponding degrees of subcooling are 5 deg C to 45 deg C. Data are also given for water vapor bubbles containing significant amounts of nitrogen, helium, and xenon. When compared with theory, reasonable agreements are obtained. For slowly collapsing bubbles, the significance of small translational velocities is brought to attention. Photographic evidences are also given for bubble instability under suitable conditions.

Closure to “Discussions of ‘The Rate of Growth of Vapor Bubbles in Superheated Water’” (1954, ASME J. Appl. Mech., 21, pp. 199–202)

Closure to “Discussions of ‘The Rate of Growth of Vapor Bubbles in Superheated Water’” (1954, ASME J. Appl. Mech., 21, pp. 199–202)

On the Dynamics of Small Vapor Bubbles in Liquids

When a vapor bubble in a liquid changes size, evaporation or condensation of the vapor takes place at the surface of the bubble. Because of the latent heat requirement of evaporation, a change in bubble size must therefore be accompanied by a heat transfer across the bubble wall, such as to cool the surrounding liquid when the bubble grows (or heat it when the bubble becomes smaller). Since the vapor pressure at the bubble wall is determined by the temperature there, the result of a cooling of the liquid is a decrease of the vapor pressure, and this causes a decrease in the rate of bubble growth. A similar effect occurs during the collapse of a bubble which tends to slow down the collapse. In order to obtain a satisfactory theory of the behavior of a vapor bubble in a liquid, these heat transfer effects must be taken into account. In this paper, the equations of motion for a spherical vapor bubble will be derived and applied to the case of a bubble expanding in superheated liquid and a bubble collapsing in liquid below its boiling point. Because of the inclusion of the heat transfer effects, the equations are nonlinear, integro-differential equations. In the case of the collapsing bubble, large temperature variations occur; therefore, tabulated vapor pressure data were used, and the equations of motion were integrated numerically. Analytic solutions are obtainable for the case of the expanding bubble if the period of growth is subdivided into several regimes and the simplifications possible in each regime are utilized. The growth is considered here only during the time that the bubble is small. An asymptotic solution of the equations of motion, valid when the bubble becomes large (i.e. observable), has been presented previously, together with experimental verification. We shall be specifically concerned in the following discussion with the dynamics of vapor bubbles in water. This restriction was made for convenience only, since the theory is applicable without modification to many other liquids.

The Rate of Growth of Vapor Bubbles in Superheated Water

Abstract Calculations are presented for the dynamic stability of vapor and air bubbles in superheated water. These calculations indicate that the values of the bubble radii for which the equilibrium is unstable are restricted to a finite range of radii whose values are governed by the temperature of the water and the initial air content in the bubble. Two theoretical solutions for the rate of growth of these unstable bubbles are considered: (a) Solution of the equation of motion of the bubble radius with the assumption that there is no heat diffusion across the bubble wall; (b) solution which includes the effect of heat diffusion. The two solutions differ appreciably. These two solutions are then compared with the experimental data on the growth of the vapor bubbles in superheated water. This comparison shows agreement with the solution with the effect of heat diffusion included.