Abstract: We present a theory of rising bubbles (or sharp density depletions) in the equatorial ionosphere. Both ion inertia and ion-neutral collisions are included. In the collision-dominated case the bubble velocity is independent of its size, while in the collisionless case it is proportional to the square root of the bubble size.

Abstract: Design procedures for gas sparged contractors for both low and high viscosity liquids were developed to predict overall kLa. Bubble size close to the orifice, for moderately high gas rates, was found to increase at a rate proportional to one third power of gas rate and one tenth power of liquid viscosity. Bubble breakup phenomenon was shown to be related to liquid turbulence in the vessel rather than gas turbulence in the orifice. Procedures were developed through a simple liquid circulation model to obtain a criterion for the onset of bubble breakup. Results indicate that intense liquid mixing and high interfacial area can be achieved in low viscosity liquids by gas sparging alone. In high viscosity fluids, bubble breakup was not observed. The liquid circulation model predicts laminar flow at these experimental conditions over the complete range of gas rates observed.

Abstract: The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form \begin{equation} U_s = U_c+(gD)^{\frac{1}{2}}\phi(U_c/(gD)^{\frac{1}{2}}), \end{equation} Us being the bubble velocity, Uc the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is \begin{equation} U_s = U_s + U_{s0}, \end{equation} Us0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities.

Abstract: Two different cavitation fusion reactors (CFR's) are disclosed. Each comprises a chamber containing a liquid (host) metal such as lithium or an alloy thereof. Acoustical horns in the chamber walls operate to vary the ambient pressure in the liquid metal, creating therein small bubbles which are caused to grow to maximum sizes and then collapse violently in two steps. In the first stage the bubble contents remain at the temperature of the host liquid, but in the second stage the increasing speed of collapse causes an adiabatic compression of the bubble contents, and of the thin shell of liquid surrounding the bubble. Application of a positive pressure on the bubble accelerates this adiabatic stage, and causes the bubble to contract to smaller radius, thus increasing maximum temperatures and pressures reached within the bubble. At or near its minimum radius the bubble generates a very intense shock wave, creating high pressures and temperatures in the host liquid. These extremely high pressures and temperatures occur both within the bubbles and in the host liquid, and cause hydrogen isotopes in the bubbles and liquid to undergo thermonuclear reactions. In one type of CFR the thermonuclear reaction is generated by cavitation within the liquid metal itself, and in the other type the reaction takes place primarily within the bubbles. The fusion reactions generate energy that is absorbed as heat by the liquid metal, and this heat is removed from the liquid by conduction through the acoustical horns to an external heat exchanger, without any pumping of the liquid metal.

Abstract: An experimental study was undertaken to determine how several variables affect the size of gas bubbles formed at nozzles in liquid pig iron. The frequency of bubble formation was measured by an acoustic device, which could detect the vibrations produced by the bubble release. Accurate knowledge of the gas flow rate then enabled the calculation of bubble volumes. The use of large baths (60 Kg), melted by induction heating, permitted a wide range of experimental parameters: gas flow rate (0.5 to 1000 cc/s), outside nozzle diameter (0.64 to 5.1 cm), inside diameter (0.16 to 0.64 cm), chamber volume (23 to 2200 cc), nozzle depth (7.6 to 20 cm), surface tension (700 to 1500 dynes/cm) and nozzle orientation (up, down and sideways). The resulting bubble volumes were between 0.5 and 100 cc. The bubbles were found to form at the outer diameter of the nozzles due to the nonwettability of the nozzles. Furthermore, the bubbles were of a uniform size at low flow rates, but increased in volume with the flow rate, so that a constant frequency was established. In addition, the bubble volume was strongly dependent on the chamber volume upstream from the nozzle. This is known as a “capacitance” effect and is due to compressibility of the gas. “Doublets” or “double bubbles” at small chamber volumes and bubble “pairs” at large chamber volumes were also observed. These phenomena result in smaller bubbles, which make precise predictions of bubble size difficult. The results are compared with those obtained by other investigators in aqueous and metallic systems.

Abstract: An experimental study was carried out to gain a better understanding of the dynamic behavior of gas bubbles during the structural foam injection molding operation. For the study, a rectangular mold cavity with glass windows on both sides was constructed, which permitted us to record on a movie film the dynamic behavior of gas bubbles in the mold cavity as a molten polymer containing inert gas was injected into it. The mold was designed so that either isothermal or nonisothermal injection molding could be carried out. Materials used were polystyrene, high-density polyethylene, and polycarbonate. As chemical blowing agents, sodium bicarbonate (which generates carbon dioxide), a proprietary hydrazide and 5-phenyl tetrazole, both generating nitrogen, were used. Injection pressure, injection melt temperature, and mold temperature were varied to investigate the kinetics of bubble growth (and collapse) during the foam injection molding operation. It was found that the processing variables (e.g., the mold temperature, the injection pressure, the concentration of blowing agent) have a profound influence on the nucleation and growth rates of gas bubbles during mold filling. Some specific observations made from the present study are as follows: an increase in melt temperature, blowing agent concentration, and mold temperature brings about an increase in bubble growth but more non-uniform cell size and its distribution, whereas an increase in injection pressure (and hence injection speed) brings about a decrease in bubble growth but more uniform cell size and its distribution. Whereas almost all the theoretical studies published in the literature deal with the growth (or collapse) of a stationary single spherical gas bubble under isothermal conditions, in structural foam injection molding the shape of the bubble is not spherical because the fluid is in motion during mold filling. Moreover, a temperature gradient exists in the mold cavity and the cooling subsequent to mold filling influences bubble growth significantly. It is suggested that theoretical study be carried out on bubble growth in an imposed shear field under nonisothermal conditions.

Abstract: The Sherwood number and drag coefficient for a single gas bubble moving in a power law fluid and a Bingham plastic fluid are obtained using perturbation methods The perturbation parameters for power law and Bingham plastic fluids are m (= n – 1/2) and E (= R/U), respectively It is found that in the case of power law fluid, mass transfer and drag increase with increasing pseudoplasticity These theoretical results are found to be in good agreement with the available experimental data and the data obtained in the present study In the case of Bingham plastic fluid, mass transfer and drag are found to increase with increase in the Bingham number NB (= 2e) Contours of plug flow regions, where local stresses are less than the yield stress, are obtained as a function of the Bingham number NB These results qualitatively predict the zero terminal velocity observed for bubble motion in liquids with very high yield stress They are also in good agreement with the trends of the results obtained previously for solid sphere motion in Bingham plastic fluids

Abstract: An experimental study was carried out to investigate the flow behavior of gas-charged molten polymers in foam extrusion. For the study, a rectangular slit die with glass windows was constructed to permit visual observations, from the direction perpendicular to flow, of the dynamic behavior of gas bubbles when a gas-charged molten polymer flows between two parallel planes. Pictures were taken of gas bubbles in the flow channel with the aid of a camera attached to a microscope, and these were later used to determine the position at which gas bubbles start to grow. Using three melt pressure transducers mounted on the short side of the rectangular slot, pressure distributions were measured along the longitudinal centerline of the die. The polymeric materials used were high-density polyethylene and polystyrene, and the chemical blowing agents used were a proprietary hydrazide which generates nitrogen, and sodium bicarbonate which generates carbon dioxide. It was observed that the gas-charged molten polymer shows a curved pressure profile as the melt approaches the die exit, whereas the polymer without a blowing agent shows a linear pressure profile. The visual observations of the bubble growth in the flow channel, together with the pressure measurements, permitted us to determine the bubble inflation pressure, often referred to as the critical pressure for bubble inflation. It was found that the critical pressure decreases with increasing melt extrusion temperature, and increases with increasing blowing agent concentration. It was also found that the bulk viscosity of gas-charged molten polymers decreases with increasing blowing agent concentration and with increasing melt temperature. A general remark is made concerning the precaution one should take when an Instron rheometer is used for determining the bulk viscosity of gas-charged molten polymers.

Abstract: The process of thinning of a film formed between a deformable bubble and a solid substratum is considered. The solution is obtained by matching the asymptotic coordinate expansions, valid both in the vicinity of and at a distance from the axis of symmetry. It is demonstrated that when the interfaces are at a short distance from each other, the film can be considered as being practically plane-parallel. An expression is deduced for the rate of thinning of such a film, coincident in form with the well-known law of Reynolds. With the surfaces further apart from each other, equations are obtained for the deformation of the bubble and for the rate of its approach to the solid substratum.

Abstract: Four of the problems deal with the mechanics of bubble production and bursting, and the collection and sizing of jet drops; three concern the transfer of the bacterium Serratia marcescens from bursting bubbles to jet drops. The problem of producing bubbles of a specified size from glass capillary tips is overcome by paying careful attention to tip geometry. Problems associated with bubble bursting have not been solved, but it is believed that they are caused by small differences in the position of the bubble relative to the interface at the time of bursting. The collection and sizing of jet drops can cause problems, but suggestions are given to overcome them. Of the three problems involving bacteria, only the last appears to have a satisfactory solution. Experiments show that the concentration of bacteria is always highest in the top jet drop of the jet set and decreases progressively in the lower drops, being lowest in the bottom drop. This is in qualitative agreement with the hypothesis of jet drop formation advanced by MacIntyre. Increasing interest in the biological, physical, and chemical nature of the airwater interface, and the exchange processes across the interface, has resulted in numerous papers, and, in just the past 3 years, at least four review articles (MacIntyre 1974; Blanchard 1975; Liss 1975; Duce and Hoffman 1976). These articles have stressed the complexity of interfacial problems. In our own work with bubbles and jet drops, especially that involving bacteria and dissolved organic material, we have encountered numerous problems. Some have required months to overcome, but many have yet to be solved. Since these problems, both solved and unsolved, have barely been mentioned in our papers, and will no doubt be encountered by others who pursue this area of research, we feel it worthwhile to consid’ The research was supported by the Atmospheric Science Section, National Science Foundation. er them here. The solved problems are of obvious interest, but those unsolved may be even more so, since their solution should provide key insights into the water-to-air transfer of materials. The seven problems that follow were selected from notes made in the course of our experiments of the past several years. We appreciate the criticism of M. and E. Baylor, R. Cipriano, and P. Liss on the first draft of this paper.

Abstract: This paper deals experimentally with the mechanism of an impulsive pressure generated by a collapsing bubble. In a water filled shock tube, an expansion wave and a subsequent compression wave are applied to single, twin and triadic bubbles. The growth, collapse and rebound of bubbles situated at various distances from a solid boundary are observed by means of high-speed photography and in-line Fraunhofer holography using a pulsed dye laser. The results indicate that the impulsive pressure is caused by a shock wave radiated at the instant of the rebound of a collapsing bubble, and that the subsequent jet impingement does not produce any detectable effects. The pressure pulse is found to be of the order 104 ∼ 105 atm, and its duration 2 ∼ 3 μsec.

Abstract: Crystalline properties of Ne+‐implanted garnet films with varying implantation energies and dosages have been studied by means of the double‐crystal x‐ray‐diffraction method, and it was found that when implantation‐induced damage was low, Pendellosung interference was observed which is directly related to crystal perfection, and a layer with large microscopic strain was found to become amorphous. The damage profiles were determined by measuring changes in x‐ray rocking curves after etching the implanted layers. Based on these experimental results, an implanted layer model was derived. The influences of the crystalline properties on the magnetic properties were also investigated from the viewpoints of the flux keeper and hard‐bubble‐suppression effects. For high implantation dosage the amorphous layer becomes magnetically inactive. This phenomenon is ascribed to randomly oriented micro‐magnetic‐domains with zero net magnetization caused by large microscopic strain in the amorphous layer. The effect of anne...

Abstract: The relationship between the volume of an intraocular gas bubble and the area of retina covered by the bubble was studied with the use of both a transparent model and a mathematical model of the vitreous cavity. The arc of contact of intraocular bubbles was calculated for vitreous cavities of various diameters. A 0.28 cm3 bubble will cover 90 degrees of retina and be of sufficient size to manage many of the problems for which an internal retinal tamponade would be useful. Larger retinal tears require disproportionately large increases in bubble volume to achieve modest increases in the area of retina covered. Estimating bubble size by observing the height of the bubble meniscus in the dilated pupil is subject to errors induced by small shifts in the angle of observation. A correct evaluation requires that the plane of observation be adjusted so that it coincides with the plane of the meniscus.

Abstract: The dependence of the positronium decay rate on the gas density is considered. It is known that the positronium can be localized in a dense gas with the formation of a cavity “bubble” around the positronium. It results in a significant delay of the annihilation. The paper containes the quantitative theory of this phenomenon. A comparison is made with the experimental data for He4, He3, Ne.

Abstract: An improved two-stage model is proposed to predict bubble volume and to explain the phenomena of bubble formation when bubbles are formed from a submerged single orifice accompanied by pressure fluctuations in a gas chamber. The following conclusions are reached by comparing the calculated results based on the proposed model with the experimental results: (1) The calculated bubble volumes agree well with the experimental results over a wide range of experimental conditions. (2) The change of bubble volume with bubbling time and the phenomena of pressure fluctuations in the gas chamber are well described by the model.

Abstract: Ion implantation has become an important part of magnetic bubble technology. The damage produced by implantation places the implanted layer in a state of in‐plane compression. This can change the easy axis of magnetization from perpendicular to parallel to the surface in a material having a negative magnetostriction coefficient. Several magnetic effects result from the creation of a thin layer of in‐plane magnetization at the top of the magnetic bubble supporting material. These include flux capping of the bubbles, control of the allowable magnetic bubble states, formation of bubble guiding rails at the boundaries of implanted areas, and creation of a moving magnetic pole pattern for bubble propagation in an external rotating in‐plane magnetic field. Other observed effects include increases in lattice parameter up to ∠2% and enhancement of the etching rate of the material by as much as a factor of 1000. Implantation is now widely used to suppress hard bubbles, and there is the possibility that ion implant...

Abstract: A simplified form of the stability equation appropriate for liquids of small viscosity undergoing nearly spherically symmetric flow is derived on the basis of earlier results. This equation is then applied to the analysis of the stability characteristics of the spherical shape for growing and collapsing cavitation bubbles. It is found that viscosity does not remove the well‐known instability associated wihth the collapse process, although it does delay the growth of higher order modes. This feature explains the relatively small number of microbubbles to which a cavitation bubble gives rise upon fragmentation.

Abstract: The equations of motion of a nearly spherical bubble immersed in an incompressible and viscous liquid are deduced using the Lagrangian procedure with a dissipation function. The results appear valid for only slightly viscous liquids.