Andrew J. Szeri

Water Vapour, Sonoluminescence and Sonochemistry

Sonoluminescence is the production of light from acoustically forced bubbles; sonochemistry is a related chemical processing technique. The two phenomena share a sensitive dependence on the liquid phase. The present work is an investigation of the fate and consequences of water vapour in the interior of strongly forced argon micro–bubbles. Due to the extreme nonlinearity of the volume oscillations, excess water vapour is trapped in the bubble during a rapid inertial collapse. Water vapour is prevented from exiting by relatively slow diffusion and non–equilibrium condensation at the bubble wall. By reducing the compression heating of the mixture and through primarily endothermic chemical reactions, the water vapour reduces the temperatures within the bubble significantly. The quantity and disposition of hydroxyl radicals produced within the bubble are studied in some detail, as this is of keen interest in sonochemistry. It was recently shown by Moss and co–workers that light emission from a sonoluminescence bubble depends sensitively on the water–vapour content. The quantity of trapped water vapour determined in the present analysis is in excellent agreement with the amount found by Moss and co–workers to match photon yields and pulse widths of recent experiments.

Dissolution or growth of soluble spherical oscillating bubbles

A new theoretical formulation is presented for mass transport across the dynamic interface associated with a spherical bubble undergoing volume oscillations. As a consequence of the changing internal pressure of the bubble that accompanies volume oscillations, the concentration of the dissolved gas in the liquid at the interface undergoes large-amplitude oscillations. The convection-diffusion equations governing transport of dissolved gas in the liquid are written in Lagrangian coordinates to account for the moving domain. The Henrys law boundary condition is split into a constant and an oscillating part, yielding the smooth and the oscillatory problems respectively. The solution of the oscillatory problem is valid everywhere in the liquid but differs from zero only in a thin layer of the liquid in the neighbourhood of the bubble surface. The solution to the smooth problem is also valid everywhere in the liquid; it evolves via convection-enhanced diffusion on a slow timescale controlled by the Peclet number, assumed to be large. Both the oscillatory and smooth problems are treated by singular perturbation methods: the oscillatory problem by boundary-layer analysis, and the smooth problem by the method of multiple scales in time. Using this new formulation, expressions are developed for the concentration field outside a bubble undergoing arbitrary nonlinear periodic volume oscillations. In addition, the rate of growth or dissolution of the bubble is determined and compared with available experimental results. Finally, a new technique is described for computing periodically driven nonlinear bubble oscillations that depend on one or more physical parameters. This work extends a large body of previous work on rectified diffusion that has been restricted to the assumptions of infinitesimal bubble oscillations or of threshold conditions, or both. The new formulation represents the first self-consistent, analytical treatment of the depletion layer that accompanies nonlinear oscillating bubbles that grow via rectified diffusion.

Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the Rayleigh–Plesset equation

When a bubble collapses mildly the interior pressure field is spatially uniform; this is an assumption often made to close the Rayleigh–Plesset equation of bubble dynamics. The present work is a study of the self-consistency of this assumption, particularly in the case of violent collapses. To begin, an approximation is developed for a spatially non-uniform pressure field, which in a violent collapse is inertially driven. Comparisons of this approximation show good agreement with direct numerical solutions of the compressible Navier–Stokes equations with heat and mass transfer. With knowledge of the departures from pressure uniformity in strongly forced bubbles, one is in a position to develop criteria to assess when pressure uniformity is a physically valid assumption, as well as the significance of wave motion in the gas. An examination of the Rayleigh–Plesset equation reveals that its solutions are quite accurate even in the case of significant inertially driven spatial inhomogeneity in the pressure field, and even when wave-like motions in the gas are present. This extends the range of utility of the Rayleigh–Plesset equation well into the regime where the Mach number is no longer small; at the same time the theory sheds light on the interior of a strongly forced bubble.

Interaction of lithotripter shockwaves with single inertial cavitation bubbles

The dynamic interaction of a shockwave (modelled as a pressure pulse) with an initially spherically oscillating bubble is investigated. Upon the shockwave impact, the bubble deforms non-spherically and the flow field surrounding the bubble is determined with potential flow theory using the boundary-element method (BEM). The primary advantage of this method is its computational efficiency. The simulation process is repeated until the two opposite sides of the bubble surface collide with each other (i.e. the formation of a jet along the shockwave propagation direction). The collapse time of the bubble, its shape and the velocity of the jet are calculated. Moreover, the impact pressure is estimated based on water-hammer pressure theory. The Kelvin impulse, kinetic energy and bubble displacement (all at the moment of jet impact) are also determined. Overall, the simulated results compare favourably with experimental observations of lithotripter shockwave interaction with single bubbles (using laser-induced bubbles at various oscillation stages). The simulations confirm the experimental observation that the most intense collapse, with the highest jet velocity and impact pressure, occurs for bubbles with intermediate size during the contraction phase when the collapse time of the bubble is approximately equal to the compressive pulse duration of the shock wave. Under this condition, the maximum amount of energy of the incident shockwave is transferred to the collapsing bubble. Further, the effect of the bubble contents (ideal gas with different initial pressures) and the initial conditions of the bubble (initially oscillating vs. non-oscillating) on the dynamics of the shockwave-bubble interaction are discussed.

Coupled dynamics of translation and collapse of acoustically driven microbubbles

Pressure gradients drive the motion of microbubbles relative to liquids in which they are suspended. Examples include the hydrostatic pressure due to a gravitational field, and the pressure gradients in a sound field, useful for acoustic levitation. In this paper, the equations describing the coupled dynamics of radial oscillation and translation of a microbubble are given. The formulation is based on a recently derived expression for the hydrodynamic force on a bubble of changing size in an incompressible liquid [J. Magnaudet and D. Legendre, Phys. Fluids 10, 550-556 (1998)]. The complex interaction between radial and translation dynamics is best understood by examination of the added momentum associated with the liquid motion caused by the moving bubble. Translation is maximized when the bubble collapses violently. The new theory for coupled collapse and translation dynamics is compared to past experiments and to previous theories for decoupled translation dynamics. Special attention is paid to bubbles of relevance in biomedical applications.

Shape stability and violent collapse of microbubbles in acoustic traveling waves

Acoustically driven bubbles can develop shape instabilities and, if forced sufficiently strongly, distort greatly and break up. Perturbation theory provides some insight as to how these nonspherical shape modes grow initially but loses validity for large deformations. To validate the perturbation theory, we use a numerical model based on the boundary integral method capable of simulating nonspherical, axisymmetric bubbles subject to acoustic driving. The results show that the perturbation theory compares well with numerical simulations in predicting bubble breakup and stability. Thereafter, we compare the peak temperatures and pressures of spherical to nonspherical bubble collapses by forcing them with standing waves and traveling waves, respectively. This comparison is made in parameter ranges of relevance to both single bubble sonoluminescence and multibubble sonoluminescence and sonochemistry. At moderate forcing, spherical and nonspherical collapses achieve similar peak temperatures and pressures but,...

Pathological pattern formation and cortical propagation of epileptic seizures

The stochastic partial differential equations (SPDEs) stated by Steyn-Ross and co-workers constitute a model of mesoscopic electrical activity of the human cortex. A simplification in which spatial variation and stochastic input are neglected yields ordinary differential equations (ODEs), which are amenable to analysis by techniques of dynamical systems theory. Bifurcation diagrams are developed for the ODEs with increased subcortical excitation, showing that the model predicts oscillatory electrical activity in a large range of parameters. The full SPDEs with increased subcortical excitation produce travelling waves of electrical activity. These model results are compared with electrocortical data recorded at two subdural electrodes from a human subject undergoing a seizure. The model and observational results agree in two important respects during seizure: (i) the average frequency of maximum power, and (ii) the speed of spatial propagation of voltage peaks. This suggests that seizing activity on the human cortex may be understood as an example of pathological pattern formation. Included is a discussion of the applications and limitations of these results.

Synchronization measures of the scalp electroencephalogram can discriminate healthy from Alzheimer's subjects.

Three synchronization measures are applied to scalp electroencephalogram (EEG) data collected from 20 patients diagnosed to have either: (1) no dementia, (2) mild cognitive impairment (MCI), or (3) Alzheimers disease (AD). We apply the three synchronization measures--the phase synchronization, and two measures of nonlinear interdependency--to the data collected from awake patients resting with eyes closed. We show that the synchronization in potential between electrodes near the left and right occipital lobes provides a statistically significant discriminant between the healthy and AD subjects, and the MCI and AD subjects. None of the three measures appears able to distinguish between the healthy and MCI subjects, although MCI subjects show synchronization values intermediate between healthy subjects (with high synchronization values) and AD subjects (with low synchronization values) on average.

Sonoluminescence and diffusive transport

A new model is presented for the gas dynamics within a bubble at conditions that lead to the phenomenon of sonoluminescence. The spherically symmetric Navier–Stokes equations with variable properties are solved together with momentum and energy equations in the liquid. Calculations are presented for bubbles of argon, helium, and xenon in liquid water. The first main result is that in contrast to recent models of air bubbles in water, there are no sharp shocks focusing at the origin of the bubble. An alternative mechanism for energy focusing in noble gas bubbles is proposed that is consistent with a smooth onset of sonoluminescence with increasing acoustic forcing, as observed in experiments. The second main result concerns an observed correlation between sonoluminescence intensity and the thermal conductivity of the gas, which suggests that heat transfer plays a dominant role in the focusing of acoustic energy. It is shown instead that mechanical effects associated with the molecular mass of the gas figur...

Impact of a compound droplet on a flat surface: A model for single cell epitaxy

The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We=2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing.