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 di¬usion 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 signi cantly. 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.

When the Debye length is on the order of or larger than the height of a nanofluidic channel containing surface charge, a unipolar solution of counterions is generated to maintain electrical neutrality. A pressure-gradient-driven flow under such conditions can be used for ion separation, which forms the basis for electrochemomechanical energy conversion. The current−potential (I−O) characteristics of such a battery were calculated using continuum dynamics. When the bulk concentration is large and the channel does not become a unipolar solution of counterions, both the current and potential become small. On the other hand, when bulk concentration is so much smaller, the mass diffusion becomes the rate-controlling step and the potential drops rapidly in the high current density region. When the Debye length of the solution is about half of the channel height, the efficiency is maximized.

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 Henry's 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 Péclet 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.

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.

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.

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 figure prominently in determining the peak temperatures and pressures in the bubble, when the bubble is forced strongly enough to engender wavy disturbances that focus on the bubble center.

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, as the forcing is increased, spherical collapses become much more intense. The reduced temperature of nonspherical collapses at high forcing is due to residual kinetic energy of a liquid jet that pierces the bubble near the time of minimum volume. This is clarified by a calculation of the ͑gas͒ thermal equivalent of this liquid kinetic energy.

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.