In analytical and numerical studies on bubbles in liquids, often the Rayleigh initial condition of a spherical bubble at maximum radius is used: the Rayleigh case. This condition cannot be realized in practice, instead the bubbles need first to be generated and expanded. The energy-deposit case with its initial condition of a small, spherical bubble of high internal pressure that expands into water at atmospheric pressure is studied for comparison with the Rayleigh case. From the many possible configurations, a single bubble near a flat solid boundary is chosen as this is a basic configuration to study erosion and cleaning phenomena. The bubble contains a small amount of non-condensable gas obeying an adiabatic law. The water is compressible according to the Tait equation. The Euler equations in axial symmetry are solved with the help of the open source software package OpenFOAM, based on the finite volume method. The volume of fluid method is used for interface capturing. Rayleigh bubbles of |$R_\mathrm{max} = 500\,\mu $|m and energy-deposit bubbles that reach |$R_\mathrm{max} = 500\,\mu $|m after expansion in an unbounded liquid are compared with respect to microjet velocity, microjet impact pressure and microjet impact times, when placed or being generated near a flat solid boundary. Velocity and pressure fields from the impact zone are given to demonstrate the sequence of phenomena from axial liquid microjet impact via annular gas-jet and annular liquid-nanojet formation to the Blake splash and the first torus-bubble splitting. Normalized distances |$D^{\ast } = D/R_\mathrm{max}$| (D = initial distance of the bubble centre from the boundary) between 1.02 and 1.5 are studied. Rayleigh bubbles show a stronger collapse with about 50% higher microjet impact velocities and also significantly higher microjet impact pressures.

A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller–Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. During the simulations, the control parameters are the two amplitudes of the acoustic driving at fixed, commensurate frequency pairs. The high-resolution bi-parametric scans in the control parameter plane show that a period-2 attractor can be continuously transformed into a period-3 one (and vice versa) by proper selection of the frequency combination and by proper tuning of the driving amplitudes. This phenomenon has opened a new way to drive the system to a desired, pre-selected attractor directly via a non-feedback control technique without the need of the annihilation of other attractors. Moreover, the residence in transient chaotic regimes can also be avoided. The results are supplemented with simulations obtained by the boundary-value problem solver AUTO, which is capable to compute periodic orbits directly regardless of their stability, and trace them as a function of a control parameter with the pseudo-arclength continuation technique.

The dynamics of a laser-induced bubble on top of a solid cylinder is studied both experimentally and numerically. When the bubble is generated close to the flat top along the axis of the cylinder and its maximum radius exceeds the one of the flat top surface, it collapses in the form of a mushroom with a footing on the cylinder, a long stem and a hat-like cap typical for a mushroom head. The head may collapse forming a thin, fast liquid jet into the stem, depending on bubble size and bubble distance to the top of the cylinder. Several experimental and numerical examples are given. The results represent a contribution to understand the behavior of bubbles collapsing close to structured surfaces and in particular, how thin, fast jets are generated.

A detailed experimental study on acoustically induced bubble jets produced far from any solid wall is presented. This particular type of bubble jet is observed when a laser-induced gas cavity is seeded in a liquid by an optical dielectric breakdown while applying a strong ultrasonic field. This generation method allows a high degree of control over jet dynamics, achievable by changing critical experimental parameters such as the laser pulse energy (i.e., the size of the bubbles), the driving signal frequency, the seeding phase (relative to the sound field), the acoustic pressure amplitude, and, in particular, the pressure gradient at the bubble inception location. The temporal evolution of the characteristic dimensions of the bubble jets is analyzed by means of numerical simulations of spherical bubble dynamics and their dependence on the local acoustic field. The jet strength is presented in terms of the jet elongation ratio, defined as the axial length over the maximum width. The most relevant parameters related to the jet strength are the maximum radius reached by the bubble prior to the jet formation and the pressure gradient during the bubble collapse phase. The existence of optimum driving parameters and the bubble seeding position to obtain the strongest jets achievable in a given acoustic pressure distribution is discussed. This study is a first step to shed some light on the jet formation process due to known time-variable pressure gradients. The work can be extended to further understanding the role of bubble jets in sonochemical reactions and biological or medical applications.

We present phase diagrams of the Toda oscillator x¨+dẋ+$e^x$-1=f cos(ωt) showing the loci of local bifurcations of periodic orbits in the (ω,f) parameter plane at d=0.05. They indicate a specific recurrent structure in the bifurcation set which is typical for nonlinear oscillators and closely connected to the nonlinear resonances of the system.

The active cavitation threshold of a dual-frequency driven single spherical gas bubble is studied numerically. This threshold is defined as the minimum intensity required to generate a given relative expansion (Rmax-RE)/RE, where RE is the equilibrium size of the bubble and Rmax is the maximum bubble radius during its oscillation. The model employed is the Keller-Miksis equation that is a second order ordinary differential equation. The parameter space investigated is composed by the pressure amplitudes, excitation frequencies, phase shift between the two harmonic components and by the equilibrium bubble radius (bubble size). Due to the large 6-dimensional parameter space, the number of the parameter combinations investigated is approximately two billion. Therefore, the high performance of graphics processing units is exploited; our in-house code is written in C++ and CUDA C software environments. The results show that for (Rmax-RE)/RE=2, the best choice of the frequency pairs depends on the bubble size. For small bubbles, below 3μm, the best option is to use just a single frequency of a low value in the giant response region. For medium sized bubbles, between 3μm and 6μm, the optimal choice is the mixture of low frequency (giant response) and main resonance frequency. For large bubbles, above 6μm, the main resonance dominates the active cavitation threshold. Increasing the prescribed relative expansion value to (Rmax-RE)/RE=3, the optimal choice is always single frequency driving with the lowest value (20kHz here). Thus, in this case, the giant response always dominates the active cavitation threshold. The phase shift between the harmonic components of the dual-frequency driving (different frequency values) has no effect on the threshold.