On the forced oscillations of a small gas bubble in a spherical liquid-filled flask

A spherically-symmetric problem is considered in which a small gas bubble at the centre of a spherical flask filled with a compressible liquid is excited by small radial displacements of the flask wall. The bubble may be compressed, expanded and made to undergo periodic radial oscillations. Two asymptotic solutions have been found for the low-Mach-number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to the linear wave equation. The second one is an asymptotic solution for the field near the bubble, which corresponds to the Rayleigh–Plesset equation for an incompressible fluid. For the analytical solution of the low-Mach-number regime, matching of these asymptotic solutions is done, yielding a generalization of the Rayleigh–Plesset equation. This generalization takes into account liquid compressibility and includes ordinary differential equations (one of which is similar to the well-known Herring equation) and a difference equation with both lagging and leading time. These asymptotic solutions are used as boundary conditions for bubble implosion using numerical codes which are based on partial differential conservation equations. Both inverse and direct problems are considered in this study. The inverse problem is when the bubble radial motion is given and the evolution of the flask wall pressure and velocity is to be calculated. The inverse solution is important if one is to achieve superhigh gas temperatures using non-periodic forcing (Nigmatulin et al. 1996). In contrast, the direct problem is when the evolution of the flask wall pressure or velocity is given, and one wants to calculate the evolution of the bubble radius. Linear and nonlinear periodic bubble oscillations are analysed analytically. Nonlinear resonant and near-resonant periodic solutions for the bubble non-harmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The applicability of this approach bubble oscillations in experiments on single-bubble sonoluminescence is discussed.

Platelet Adhesiveness to Glass

Summary1. When anticoagulated blood is placed in a rotating glass flask, the blood/air interface initiates platelet aggregation, and the aggregates are trapped on the flask wall, without adhering to it, by the thin film of blood which forms during rotation. The interface; allows CO2 loss so that the pH of the rotating blood rises markedly and this rise is associated with the release of 3H-5HT from platelet. When CO2 diffusion and consequent pH rise is prevented, platelet loss and 3H-HT release are significantly reduced.2. A simple method for assessing the adhesiveness of single platelets to glass using a Neubauer haemocytometer chamber has been developed. The results obtained are independent of platelet number which allows the test to be used in conditions in which abnormal platelet behaviour is associated with a low platelet-count.3. Adhesiveness was negligible in heparinised PRP, and was greater in EDTA PRP than in citrated PRP. Heparin abolished the increased adhesiveness observed with the other anticoagulants and adhesiveness did not seem to be directly related to residual plasma calcium concentrations. Platelets adhered more readily to siliconised glass surfaces than to untreated glass, and adhesion was markedly temperature-dependent, being maximal at 4°C in heparinised PRP, and at 20° C in EDTA PRP.4. Adhesiveness was enhanced by aggregating agents, this enhancement being prevented by inhibitors of aggregation such as the dipyridamole analogue VK 774. Adhesiveness was unaffected by acetyl-salicylic acid.5. Adhesiveness increased markedly after surgical operations and myocardial infarction. Within-person variation was considerable, and the test is of no value in individual patients.

The attainment of high potentials by the use of radium

The original aim of the work described in this note was to measure the energy and numerical importance of each of the many distinct kinds of β -particles emitted by a single radioactive substance. Calculation of the energy of a β -particle from observation of its deflection in a magnetic field involves assumptions which are as yet insufficiently supported by experiment. Theoretically both the energies and distribution of the particles could be directly measured by giving a gradually increasing positive charge to the source of radiation; for, when the potential of the source is +V, electrons possessing energy less than e V will be drawn back to the source of radiation. Unfortunately, more than a million volts would be necessary to stop the fastest β -particles, and no method is at present known of maintaining such a high potential in vacuo . It was thought that this difficulty might possibly be overcome by using the active material itself in order to produce the high potential according to the principle employed in Strutt's radium clock. If the source of radiation were perfectly insulated its potential would rise until the swiftest β -particles could no longer escape. The present note deals with experiments made to test whether this method were practicable. It was found that high potentials were readily obtained, but the attempt to attain to a million volts tailed through the difficulties of insulation encountered. But few experiments were completed, and many failed as the result of accident. This shows that, even if perseverance had been rewarded by greater success, technical difficulties, accentuated by every effort to improve the insulation, would probably have prevented the practical application of the method. It seemed, therefore, useless to pursue the matter further, until more is known of the reasons why the insulation of a vacuum breaks down. In these experiments the source of β -radiation was 20 millicuries or more of purified radium emanation contained in a thin bulb—marked B in fig. 1—of about 1 cm. diameter. The bulb, which was just thick enough to stop all α -radiation, was supported by a fine silica rod R inside an exhausted glass flask F of 1 litre capacity. The rod, of diameter about 0⋅8 mm., was freshly drawn from transparent fused silica. The surface of the bulb and the flask was coated with silver, which was found to retain a trace of conductivity when subsequently heated to 400° C., though it then became almost transparent. The potential gained by the bulb was measured by a simple form of attracted disc electrometer, a circular aluminium disc being hung from the arm of a horizontal silica spring, the other end of which was soldered with aluminium to a projection from one of the glass walls of the flask. By observing with a microscope the. displacement of the disc, the force of attraction exerted on it by the bulb was measured, and from this it was easy to calculate the charge and the potential acquired by the bulb. The force of a dyne displaced the spring by about 0⋅1 mm. The disc was hung just at the entrance to the mouth of the flask, so that the remainder of the flask wall served the purpose of a guard-ring.