End Of Collapse Phase Research Articles

Multi-oscillations of a bubble in a compressible liquid near a rigid boundary

AbstractBubble dynamics near a rigid boundary are associated with wide and important applications in cavitation erosion in many industrial systems and medical ultrasonics. This classical problem is revisited with the following two developments. Firstly, computational studies on the problem have commonly been based on an incompressible fluid model, but the compressible effects are essential in this phenomenon. Consequently, a bubble usually undergoes significantly damped oscillation in practice. In this paper this phenomenon will be modelled using weakly compressible theory and a modified boundary integral method for an axisymmetric configuration, which predicts the damped oscillation. Secondly, the computational studies so far have largely been concerned with the first cycle of oscillation. However, a bubble usually oscillates for a few cycles before it breaks into much smaller ones. Cavitation erosion may be associated with the recollapse phase when the bubble is initiated more than the maximum bubble radius away from the boundary. Both the first and second cycles of oscillation will be modelled. The toroidal bubble formed towards the end of the collapse phase is modelled using a vortex ring model. The repeated topological changes of the bubble are traced from a singly connected to a doubly connected form, and vice versa. This model considers the energy loss due to shock waves emitted at minimum bubble volumes during the beginning of the expansion phase and around the end of the collapse phase. It predicts damped oscillations, where both the maximum bubble radius and the oscillation period reduce significantly from the first to second cycles of oscillation. The damping of the bubble oscillation is alleviated by the existence of the rigid boundary and reduces with the standoff distance between them. Our computations correlate well with the experimental data (Philipp & Lauterborn,J. Fluid Mech., vol. 361, 1998, pp. 75–116) for both the first and second cycles of oscillation. We have successively reproduced the bubble ring in direct contact with the rigid boundary at the end of the second collapse phase, a phenomenon that was suggested to be one of the major causes of cavitation erosion by experimental studies.

Modelling of sonochemical oxidation of the water-KI-CCl 4 system

The sonolysis of KI solution containing CCl 4 as a separate phase results in the formation of I 2, but shows characteristics which are different from those observed when KI solution alone is sonicated. By the addition of CCl 4, the rate goes up by two orders of magnitude, the rate becomes independent of KI concentration, the effect of gas atmosphere becomes less pronounced, and the rate becomes time-dependent. Further the average rate passes through a maximum as the dispersed phase hold-up is increased. These results are explained on the basis of a model which treats cavitation bubbles as microreactors which generate fragmented products from their contents and release them into the liquid phase at the end of collapse phase. The composition of the products of the microreactors is calculated assuming attainment of reaction equilibria. The significant increase in the oxidation rate has been found to be due to release of Cl 2, Cl, and HOCL which act as separate source of reactants to yield I 2. As all these quantitatively react in the reactor with KI, the rate becomes independent of KI concentration. The gas atmosphere here is found to continuously change because of formation of CO 2 and O 2. This results in the change in the composition of gas bubble with time, resulting in reduced effect of initial gas atmosphere used. The presence of a dispersed phase reduces the number of bubbles because of attenuation and scattering but increases them due to interfacial cavitation, thus yielding a maximum at a specific hold-up. The model takes these factors into account and is able to not only explain the different observed trends but also predict them quantitatively.

The formation of close binary systems

A viable solution to the origin of close binary systems, unaccounted for in recent theories, is presented. Fragmentation, occurring at the end of the secondary collapse phase (during which molecular hydrogen is dissociating), can form binary systems with separations less than 1 au. Two fragmentation modes are found to occur after the collapse is halted. The first consists of the fragmentation of a protostellar disc due to rotational instabilities in a protostellar core, involving both an $m=1$ and an $m=2$ mode. This fragmentation mechanism is found to be insensitive to the initial density distribution: it can occur in both centrally condensed and uniform initial conditions. The second fragmentation mode involves the formation of a rapidly rotating core at the end of the collapse phase which is unstable to the axisymmetric perturbations. This core bounces into a ring which quickly fragments into several components. The binary systems thus formed contain less than 1 per cent of a solar mass and therefore will need to accrete most of their final mass if they are to form a binary star system. Their orbital properties will thus be determined by the properties of the accreted matter.

Modelling of a batch sonochemical reactor

Ultrasonication of aqueous KI solution is known to yield I 2 due to reaction of iodide ions with hydroxyl radicals, which in turn are generated due to cavitation. Based on this conceptual framework, a model has been developed to predict the rate of iodine formation for KI solutions of various concentrations under different gas atmospheres. The model follows the growth and collapse of a gas—vapour cavity using the Rayleigh—Plesset bubble dynamics equation. The bubble is assumed to behave isothermally during its growth phase and a part of the collapse phase. Thereafter it is assumed to collapse adiabatically, yielding high temperatures and pressures. Thermodynamic equilibrium is assumed in the bubble at the end of collapse phase. The contents of the bubble are assumed to mix with the liquid, and the reactor contents are assumed to be well stirred. The model has been verified by conducting experiments with KI solutions of different concentrations and using different gas atmospheres. The model not only explains these results but also the existence of a maximum when ArO 2 mixtures of different compositions are employed.

Detailed Study of Dynamic Behaviour of a Focused Plasma by N2 Laser Interferometry

The behaviour and the structure of plasma during the collapse and the focus phase in a plasma focus discharge are studied using subnanosecond Mach-Zehnder interferometry, and time dependent X-ray and neutron measurements. The obtained electron density and the electron temperature are 8×1018/cm3 and 8 keV, respectively. The most highly compressed region of the pinched plasma suffers a “break-up” through a MHD instability, and then the plasma is lost by diffusion. The instance when the peak of the hard X-ray signal appears coincides with that of the break-up of the pinched column. Neutron emission begins nearly at the end of collapse phase and the peak of the neutron burst occurs in the “diffuse phase”. The rake-up ratio of the snowploughing by the collapse is about 30–40%. The electrons in the pinched column are lost at a rate of 3×1025/sec in the radial and/or the axial direction.