Bubble Compression Research Articles

Numerical investigation of the effect of properties of the liquid on cavitation at solid surfaces

Numerical calculations were carried out on a computer with Mercon's method to investigate the effect of properties of the liquid, namely, density, pressure of the saturated vapor (gas content in a bubble), surface tension, viscosity, and wave resistance, on the instantaneous radius, velocity, and shape of the surface of a compressed cavitation bubble for various distances between two parallel solid walls confining the liquid, times, and angular coordinates. The theoretical relations found agree with earlier experimental data. Recommendations are given for using the present results in practical development of technological sonication processes and in operation of ultrasonic equipment and hydrosystems.

旋回流利用による気泡除去 第二報 テーパ形による性能向上

In developing smaller hydraulic and lubrication systems, it is a major and inevitable task to reduce the size of the reservoirs. With smaller size reservoirs, some problems exist such as if bubbles can efficiently be removed during the fluid sojourn in the reservoirs or if degradation of hydraulic oil or lubrication fluid can be reduced. In hydraulic systems, there are problems caused by oil entrainment of bubbles such as a faster rate of oil deterioration caused by bubble compression, rising temperature of surrounding fluid, fluid combustion and the system dynamics deterioration. As is well known, bubble removal is not easy even using a vacuum chamber. One of the authors has developed a bubble elimination device with a straight swirling flow tube. The device has the capability of eliminating bubbles and to decrease the dissolved gases. However, it is not applicable with a small flow rate. In this study, we have proposed and developed a new type bubble elimination device, which has a tapered contracting swirling flow tube. It can allow for effective swirl flow and provide for an appropriate pressure distribution in case of a small flow rate, compared with the former device. In this paper, the pressure distribution along the swirl flow tube is measured and using a measurement device to determine the amount of bubbles in a fluid, which has been recently developed, the amount of bubbles can be accurately measured before and after the use of the new bubble elimination device. The validity of the method has been verified using experiments.

Experimental study of detonating gas bubble oscillations using a shock tube

Oscillations of bubbles containing a mixture of a detonating gas with argon in their interior are studied. The bubbles are excited for oscillations by a pressure step generated in a shock tube. A bubble wall motion is observed by a rotating mirror camera and a radiated pressure wave by a needle hydrophone. For weak pressure steps the bubble behaves as an ordinary gas bubble. However, above a certain pressure step threshold ignition of the detonating gas occurs. Due to released heat the bubble oscillation intensity is amplified. The data obtained are used to estimate pressures and temperatures in the compressed bubble.

A Discrete Particle Model for Bubble-Slug Two-Phase Flows

Most two-phase flow models are based on the fully averaged two-fluid concept. This paper describes a new discrete particle model that is intermediate between the numerically intractable local instant description and the fully averaged two-fluid model, thereby providing a more detailed but still tractable description of dynamical two-phase flow phenomena. The new model uses a Lagrangian description for a single dispersed bubble phase and a one-dimensional Eulerian description for a single continuous liquid phase. In contrast to many other particle simulation models, the present model includes compressible phases and large bubbles whose size may be comparable to the computational cell size. The discrete Lagrangian description of the dispersed phase allows the particles to have a distribution of sizes, shapes, etc., thereby capturing the important statistical aspects of dispersed two-phase flow. In contrast to the two-fluid models, the discrete particle model allows the use of more mechanistic models for dispersed phase coalescence and breakup, wakes, etc., thereby allowing the dynamic prediction of flow regime evolution and transitions without the use of flow regime maps inherent in two-fluid models. Numerical simulations for two test problems are presented. Agreement with experimental data is generally satisfactory. Extensions of the model to heat transfer and to two discrete and two continuous phases will be described elsewhere.

Approximations in the measurement of surface tension on the oscillating bubble surfactometer.

This paper examines two factors, shape deformation and surface viscosity, that affect measurements of surface tension of lung surfactants with the oscillating bubble surfactometer. At lower surface tensions, the compressed bubble in this apparatus becomes deformed to an oblate ellipsoid that cannot be analyzed rigorously using the simplified (spherical) Laplace equation to calculate surface tension from interfacial pressure drop. However, for the small air bubbles present in this apparatus, analysis with more general equations for ellipsoids of revolution shows that deformation effects are limited to extremely low surface tensions, and the absolute error from the spherical approximation is minimal in practice. In contrast, this was not the case for the effects of surface dilational viscosity in oscillating bubble calculations. Direct measurements and values from the literature indicated that the surface dilational viscosities of lung surfactant, dipalmitoyl phosphatidylcholine, and palmitic acid were sufficient to give substantial errors if their effects on interfacial pressure drop were neglected during dynamic cycling. Surface tension calculations at maximum and minimum radii on the oscillating bubble apparatus remain accurate, because the time derivative of radius becomes zero and viscous effects vanish. However, surface tensions determined at points other than these extremes of bubble size should be interpreted with caution.

To BLEVE or not to BLEVE: Anatomy of a boiling liquid expanding vapor explosion

AbstractThe loss of containment (LOC) for Pressure Liquefied Gas (PLG) vessels under accidential fire engulfment is shown to be very complex. The LOC depends upon: (i) the extent and intesity of external heating, (ii) the pressure relief device (PRD) operation and flare (if contents flammable), (iii) the fluid and fill level, (iv) the construction of the vessel, and (v) the thermohydraulic history of the commodity prior to failure.The Simple experiments described here shows that there exists a new type of more powerful failure than the BLEVE. This even we call a BLCBE, a Boiling Liquid Compressed Bubble Explosion. A hypothesis is advanced to explain this mode of failure which is supported by an initial series of small scale experiments involving Argon, water, R11, and R123.A comprehensive test program to determine the details of the BLCBE and BLEVE failure modes is indicated along with work to determine methods of protection.

Acoustic wave propagation in one-dimensional stratified gas–liquid media: The different regimes

The problem of the propagation of acoustic waves in a one-dimensional bubbly liquid, either periodic or random is considered. This example of wave–scatterers interaction is complex enough to illustrate many of its general characteristics and yet simple enough so that an exact solution of the theoretical model can be found. Indeed, it is possible to compute exactly the response of the bubbly liquid to an incident wave in any range of concentrations, bubble size polydispersity and frequency range. In the near-field or high concentration regime, these solutions are particularly interesting since the 3-D problem cannot be solved in general. This analysis exhibits three main regimes, depending on the average value of the bubble radius R, average distance d between bubbles, and wavelength λ in the liquid. (1) For R≤λ and d≤λ, this is the ‘‘phonon’’ or ‘‘mass-spring’’ regime: the compressible bubbles act as springs connecting rigid incompressible fluid slabs that play the role of the masses in between the ‘‘springs’’. (2) For R≤λ≤d, bubbles present a kind of resonance, which is the 1-D analog of the standard 3-D bubble internal resonance. Furthermore, bubbles are coupled to each other by their radiations that propagate away in the compressible fluid: This is the ‘‘bubble’’ regime, which is the 1-D counterpart of the standard 3-D problem of an acoustic wave propagating in a diluted solution of small bubbles. (3) For λ≤R and λ≤d, the compressibility of the bubbles does not lead anymore to a resonance. This is the ‘‘stratified’’ regime, where the liquid and gas layers play symmetric roles. In the periodic systems, the dispersion relations and band structures are found. In the random systems, we compute the Anderson localization length, both numerically and analytically in the limit of uncorrelated disorder, for various system realizations.

The low Reynolds number deformation of a gas bubble in shear flow: a general approach via integral equations

The time-dependent deformation of an incompressible or compressible gas bubble in an arbitrary shear flow at low Reynolds number is formulated as a second boundary-value problem for Stokes' equations. This problem is solved via a classical Fredholm's integral equation of second kind. Contrasting with the existing previous works using the integral equation approach for this problem, the integral equation method developed here yields a unique bubble surface velocity, regardless of any flow and bubble axisymmetric property. From those previous works, the uniqueness of the surface velocity has been proved only for a spherical bubble in axisymmetric flows, and it has been conjectured that the surface velocity remains unique as long as the bubble shape and the exterior flow are axisymmetric.

The sonochemical hot spot

The origin of “sonochemistry” is acoustic cavitation: the formation, expansion, and implosive collapse of bubbles in liquids irradiated with ultrasound. The compression of such bubbles generates intense local heating, which has been quantified recently from both chemical kinetic thermometry and from high-resolution sonoluminescence spectra. The temperatures reached during cavitation are ≈5000 K, but have an effective lifetime of only a few microseconds. Consistent with this, the sonoluminescence that accompanies sonochemistry closely resembles flame emission! The chemistry generated by these hot spots is different than either ordinary thermal or photochemical processes and sonochemistry represents a fundamentally unique interaction of energy and matter. [For recent reviews see K. S. Suslick, Sci. Am. 260, 80 (Feb. 1989) and Science 247, 1439 (1990).] Recently, the use of ultrasound in liquid-powder slurries to enhance dramatically their chemical reactivity has been explored. For example, heterogeneous catalysis can be induced in normally nonreactive metals and the catalytic activity of Ni has been enhanced by 105. Using a variety of surface science techniques, it was shown that ultrasound removed the passivating oxide coating normally found on Ni and other metal surfaces, thus increasing their activity. The origin of these effects comes from extremely high-speed interparticle collisions which occur during ultrasonic irradiation of liquid-solid slurries. Turbulent flow and shockwaves produced by acoustic cavitation can drive metal particles together at sufficiently high velocities to induce melting upon collision. A series of transition metal powders have been used to probe the maximum temperatures and speeds reached during such interparticle collisions. Metal particles that are irradiated in hydrocarbon liquids with ultrasound undergo collisions at roughly half the speed of sound and generate localized effective temperatures between 2600°C and 3400°C at the point of impact. [Work supported by NSF and the UIUC Materials Res. Lab.]

Stability of a compressed gas bubble in a viscous fluid

The stability of the spherical shape of the free surface of a gas bubble compressed by an incompressible fluid as it appears in the inertial confinement fusion problem is considered. (i) The equations derived by Prosperetti [Accad. Naz. Lincei 62, 196 (1977)] generalizing the Plesset equation are recovered in cases when the outer fluid is nonviscous, the flow being not potential, and it is shown that vorticity may change drastically the results of the potential case. (ii) In the case of viscous external fluid, the equations derived by Prosperetti [Q. Appl. Math. 1, 399 (1977)] and other external conditions on a sphere of finite radius are derived. (iii) Assuming that the time scale of the dynamics of the spherical bubble is large with respect to the time scale of the perturbation (frozen assumption), the linear stability of the collapsing bubble is studied numerically. The parameters are here (a) an inertia force (related with acceleration R̈ of the radius of the bubble), (b) the Reynolds number built with the decaying rate of the bubble, (c) surface tension, and (d) the aspect ratio (ratio between the gap width of the viscous fluid and the radius of the bubble). It is shown that the spherical shape is always linearly unstable in the absence of surface tension. In the presence of surface tension, there is a critical inertia parameter value and the most dangerous mode is always stationary. For the case of a large surface tension, the spherical wavenumber l of the most dangerous mode, is low. Finally, it is shown that the Rayleigh–Taylor instability might only be observed for both small aspect ratio and Reynolds number, depending on the surface tension.

Dynamics of Haines jumps for compressible bubbles in constricted capillaries

AbstractThe unsteady, impulsive motion of a compressible bubble expanding out of a constricted capillary is quantified with a macroscopic momentum balance. Numerical solution demonstrates the importance of the Ohnesorge number, the geometry of the constriction, the length of the initial gas bubble, and the surface tension, density, and unconstricted capillary radius, which combine to form a characteristic scaling time. Experimental data for the position of the bubble front as a function of time confirm the theoretical result when the time scale for the bubble jump is longer than that required to achieve fully developed parabolic flow. Theory also predicts the capillary number of the bubble jump which, in conjunction with previous theoretical results, determines the time to snap‐off of gas bubbles moving through constricted capillaries. Excellent agreement is found with existing experimental data for Ohnesorge numbers ranging from 5 × 10−3 to 0.3.

Wave amplification in chemically active bubble media

A numerical simulation is performed for shock propagation in chemically active two‐phase “liquid‐explosive gas bubbles” media. It is established experimentally that this process is accompanied by formation of a stationary disturbance of the wavetrain form. It propagates with constant velocity exceeding essentially the equilibrium velocity characteristic of the main disturbance. Its maximum amplitude is practically constant and exceeds significantly the amplitude of an incident wave. Such a wave is called a bubble detonation wave or secondary detonation. The basis of this effect is the mechanism of separation of the shock wave in a bubble medium into the main disturbance and precursor [V. K. Kedrinskii, PMTF 4, 29–34 (1968)]. The latter decays quickly. However, in chemically active media these losses are compensated for by the bubble explosion energy, thereby providing the existence of a self‐sustaining regime. The present study is concerned with two approaches. The first one considers the interaction of a strong plane shock wave with a single spherical bubble filled in with a one‐to‐one molar acetylene‐oxygen mixture. It is shown that the refracted wave can initiate this mixture's detonation [V. K. Kedrinskii and Ch. Mader, Proc. XVI Int. Symp. on Shock Tubes and Waves, July 1987, Aachen, Federal Republic of Germany]. The mixture ignition due to adiabatic bubble compression by a weak shock wave is analyzed within the framework of relatively simple kinetics. The second approach is based on a two‐phase model and considers the process of formation of the stationary disturbance in a semi‐infinite active bubble medium. The results obtained are in good agreement with the experimental data [A. I. Sychev and A. V. Pinayev, FGV 3, 22 (1986)].A numerical simulation is performed for shock propagation in chemically active two‐phase “liquid‐explosive gas bubbles” media. It is established experimentally that this process is accompanied by formation of a stationary disturbance of the wavetrain form. It propagates with constant velocity exceeding essentially the equilibrium velocity characteristic of the main disturbance. Its maximum amplitude is practically constant and exceeds significantly the amplitude of an incident wave. Such a wave is called a bubble detonation wave or secondary detonation. The basis of this effect is the mechanism of separation of the shock wave in a bubble medium into the main disturbance and precursor [V. K. Kedrinskii, PMTF 4, 29–34 (1968)]. The latter decays quickly. However, in chemically active media these losses are compensated for by the bubble explosion energy, thereby providing the existence of a self‐sustaining regime. The present study is concerned with two approaches. The first one considers the interaction of a...

Contribution of Micro Structure to Repeated Loading Effect on Compacted Allophaneous Volcanic Ash Soil

ABSTRACT The hardening effect and delay of propagation of pore water pressure were observed in repeated loading test on the specimens of compacted allophaneous volcanic ash soils under undrained condition. These phenomena occurred even in the specimen whose degree of saturation was higher than 95%. This research was carried out to investigate the mechanism of hardening effect of repeated loading on the above highly saturated specimens from the viewpoint on the relation between hardening effect and micro structure. Then, the following results were obtained. (1) The difference of micro structure influenced not only on the behavior of soil in the standard undrained triaxial compression test but also on that in the undrained repeated loading test. (2) Undrained repeated loading had both of hardening and softening effects. (3) The hardening effect was given by the gradual increase in contact area between soil particles, anisotropy and density resulted from deformation and fracture of soil peds and compression of residual micro air bubbles during repeated loading. (4) To obtain the yielding repeated load ratio, the strain ratio (recoverable strain/irrecoverable strain) method was more favorable for allophaneous volcanic ash soils than the strain rate method. The yielding repeated load ratio was 0. 4 through all kinds of specimens used in this research.

Compression of spin-polarized hydrogen bubbles to thermal explosion.

We have compressed spin-polarized atomic hydrogen gas in small, \ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}6}$-${\mathrm{cm}}^{3}$ bubbles to densities higher than ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ using a liquid${\mathrm{\ensuremath{-}}}^{4}$He piston at temperatures from 0.3 to 0.7 K and in magnetic fields from 4.5 to 7.5 T. A best fit to the compression sweeps is obtained by fixing the binding energy of the adsorbed H atom on the liquid $^{4}\mathrm{He}$ surface to 1.15 K, which then yields the third-order dipolar recombination rate constants ${K}_{\mathrm{bbb}}^{v}$=2.7(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ ${\mathrm{cm}}^{6}$/s for the gas phase and ${K}_{\mathrm{bbb}}^{s}$=8(2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}25}$ ${\mathrm{cm}}^{4}$/s for the adsorbed surface layer. Because of inadequate transfer of the recombination heat to the surrounding He bath, the compression sweeps terminate in a spontaneous thermal explosion of the H\ensuremath{\downarrow} bubble. The pressure at the onset of the explosive recombination event is investigated as a function of ambient temperature, bubble volume, and magnetic field. Qualitative agreement with a simple thermally activated explosion model is found.

A study of continuous oil film in journal bearings. 1st report Pressure distribution.

Pressure distribution has been measured and analyzed to clarify the fundamental characteristics of ""continuous oil-film"" formed in transparent journal bearings, into which oil in general use is supplied. The results are as follows : (1) Sommerfeld's distribution for perfect oil-film is approximately observed only under limited conditions : low eccentricity and low speed. Measured pressure mostly shows quasi-Sommerfeld's distribution, which is characterized by downstream shift of pressure profile and underdevelopment of pressure trough compared with Sommerfeld's distribution. (2) Calculated pressure, taking account of compression and expansion of fine bubbles in a lubricant, shows qualitative agreement with experimental data. This would suggest that the behavior of bubbles constitutes the characteristics of continuous oil-film and remain to be further studied.

Sonolysis of Carbon Dioxide, Nitrous Oxide and Methane in Aqueous Solution

Water was irradiated with ultrasonic waves under an argon atmosphere which contained small amounts of carbon dioxide, nitrous oxide or methane. The yield of the products was measured as a function of the composition of the gas atmosphere. Maximum yields were observed at a few per cent of the added polyatomic gas. No chemical effects occurred in the irradiation under an atmosphere of pure CO2 , N2O or CH4. It is concluded that the gas mixture in the tiny gas bubbles, in which the chemical effects are brought about, is not in Henry’s equilibrium with the aqueous gas solution. The main product of the sonolysis of CO2 is CO, a small amount of formic acid also being formed. The sonolysis is explained by both the attack of H atoms from the sonolysis of water and direct decomposition of CO2 due to the high temperatures existing in compressed gas bubbles. The main products of the sonolysis of N2O are nitrogen, nitrite and nitrate. N2O enhances the rate of various oxidations such as that of iodide, nitrite and propanol-2. In the methane containing solution, a lot of hydrogen is produced, the main oxidation products being ethane, ethylene, C3- and C4-hydrocarbons and carbon monoxide. A mechanism is postulated which involves both the attack on methane by radicals from the decomposition of water and thermal decomposition of methane. The local radical concentrations are so high that a methane molecule may undergo multiple radical attack. The similarity between sonolytic reactions and reactions occurring in flames is emphasized

Analysis of ancient atmospheres

In 1967 and 1968, ice samples were taken from various depths in the ice caps of Greenland and Antarctica and transported to the Stanford Research Institute laboratories in the frozen state. These samples ranged in age from 100 to 2500 years. After the ice samples had been melted in the laboratory, the air trapped as compressed bubbles in the glacial ice during the transition from firn to ice was collected and removed by a novel technique developed for this specific purpose. Carbon monoxide and methane analyses were made on a large number of samples by using gas chromatography. Major components were also measured in a few samples by mass spectrometry. The measured methane concentration appear to be about half of present-day concentrations. The measured CO concentrations were high in value by severalfold, and initially the validity of the approach was doubted. However, in the light of recent evidence suggesting that the largest global source of CO is oxidized methane, our CO and CH4 measurements can be reinterpreted. They suggest that the background CO concentration in the atmosphere has been near current concentrations of about 0.1 ppm for many centuries. It can be inferred, therefore, that no large increase in CO concentration accompanied the advent of the Industrial Revolution.

Relaxation of ice in Deep Drill Cores from Antarctica

Cores obtained to a depth of 2164 meters in the Antarctic ice sheet at Byrd station have undergone considerable relaxation since they were drilled. This relaxation, manifested as a density decrease of the ice with time, could still be detected more than 16 months after the cores had been pulled to the surface. The greatest measurable relaxation, of the order 0.6% expansion, occurred in cores from around 800 meters' depth. Ice from 400–900 meters proved to be much more brittle than deeper ice and was characterized by an abundance of highly compressed air bubbles. These bubbles had disappeared completely by 1100 meters, most probably as a result of the diffusion of gas molecules into the ice lattice, and this, together with the formation below 1200 meters of an oriented crystal fabric (characterized by a strong vertical orientation of crystallographic c axes) is believed to be responsible for the greatly increased ductility of the deeper cores. Relaxation of ice from the brittle zone occurs primarily as a result of expansion of pressurized air bubbles. In deeper, bubble-free ice, however, relaxation can be attributed to the creation of new space resulting from the formation of cleavage cracks, plate-like voids and cavities, especially the latter, which become filled with gas derived from the air originally dissolved under pressure in the ice sheet.

Bubbles and Bubble Pressures in Antarctic Glacier Ice

Application of the gas law to fourth-place density measurements of ice samples from two deep drill holes at “Byrd” station and “Little America V”, Antarctica, shows that virtually all density increase beyond the pore close-off density (0.830 g cm−3) can be attributed to compression of the entrapped bubbles of air. Data from “Byrd” station also indicate that the lag between overburden pressure and bubble pressure, initially 4–5 kg cm−2at pore close-off, diminishes to less than 1.0 kg cm−2at about 200 m depth. By substituting the overburden pressure for the bubble pressure in the pressure-density relationship based on the gas law, one can determine ice densities below 200 m more accurately than they can be measuredper seon cores, because of the relaxation that occurs in samples recovered from high confining pressures. This relaxation, resulting in a progressive increase in the bulk volume of the ice with time, is generally attributed to decompression of the entrapped air bubbles following removal of the ice from high confining pressures. However. calculations of the stress in ice due to bubble pressure, together with measurements of bubble sizes in cores from various depths at “Byrd” station, both tend to indicate that there has been negligible decompression of the inclosed bubbles. It is suggested that most of this relaxation may be due to the formation of micro-cracks in the ice. Anomalous bubble pressure–density relations at “Little America V” tend to confirm abundant petrographic evidence of the existence of considerable deformation in the upper part of the Ross Ice Shelf.Studies of crystal–bubble relations at “Byrd” station revealed that the concentration of bubbles in ice remains remarkably constant at approximately 220 bubbles/cm3. Bubbles and crystals were found to be present in approximately equal numbers at pore close-off at 64 m depth, at which level the average bubble diameter was 0·95 mm, decreasing to 0.49 mm at 116 m and to 0·33 mm at 279 m. Despite a ten-fold increase in the size of crystals between 64 and 279 m, the bubbles showed no tendency to migrate to grain boundaries during recrystallization of the ice. The observation that most of the bubbles had assumed substantially spherical shapes by 120 m depth points to essentially hydrostatic conditions in the upper layers of the ice sheet at “Byrd” station.

Bubbles and Bubble Pressures in Antarctic Glacier Ice

Application of the gas law to fourth-place density measurements of ice samples from two deep drill holes at “Byrd” station and “Little America V”, Antarctica, shows that virtually all density increase beyond the pore close-off density (0.830 g cm−3) can be attributed to compression of the entrapped bubbles of air. Data from “Byrd” station also indicate that the lag between overburden pressure and bubble pressure, initially 4–5 kg cm−2 at pore close-off, diminishes to less than 1.0 kg cm−2 at about 200 m depth. By substituting the overburden pressure for the bubble pressure in the pressure-density relationship based on the gas law, one can determine ice densities below 200 m more accurately than they can be measured per se on cores, because of the relaxation that occurs in samples recovered from high confining pressures. This relaxation, resulting in a progressive increase in the bulk volume of the ice with time, is generally attributed to decompression of the entrapped air bubbles following removal of the ice from high confining pressures. However. calculations of the stress in ice due to bubble pressure, together with measurements of bubble sizes in cores from various depths at “Byrd” station, both tend to indicate that there has been negligible decompression of the inclosed bubbles. It is suggested that most of this relaxation may be due to the formation of micro-cracks in the ice. Anomalous bubble pressure–density relations at “Little America V” tend to confirm abundant petrographic evidence of the existence of considerable deformation in the upper part of the Ross Ice Shelf.Studies of crystal–bubble relations at “Byrd” station revealed that the concentration of bubbles in ice remains remarkably constant at approximately 220 bubbles/cm3. Bubbles and crystals were found to be present in approximately equal numbers at pore close-off at 64 m depth, at which level the average bubble diameter was 0·95 mm, decreasing to 0.49 mm at 116 m and to 0·33 mm at 279 m. Despite a ten-fold increase in the size of crystals between 64 and 279 m, the bubbles showed no tendency to migrate to grain boundaries during recrystallization of the ice. The observation that most of the bubbles had assumed substantially spherical shapes by 120 m depth points to essentially hydrostatic conditions in the upper layers of the ice sheet at “Byrd” station.