The forcing of a micron sized gas bubble by an acoustic traveling wave in water is considered using a model which includes axisymmetric shape mode interactions to third order. In all cases, the resultant bubble motion is predicted to consist of small scale periodic oscillations superimposed upon a longer timescale, monotonically changing profile. For driving amplitudes below those necessary to cause parametrically induced instabilities to grow on the surface of the bubble, the long timescale bubble speed increases as the amplitude of the forcing increases but the resultant bubble motion induces markedly small scale deformation of the bubble surface which is dominated by the ellipsoidal mode. For cases where parametric instabilities grow but the driving pressure is not sufficient to cause bubble splitting or fragmentation, saturation due to nonlinear shape mode interactions occurs resulting in observable, sustained, finite amplitude shape deformation dominated by the parametrically excited mode. The induced shape deformation is found in turn to modify the bubble motion. In particular the speed of the long timescale monotonic translation is reduced to a new constant value and for sufficiently large forcing, this motion is found to reverse.

The nonlinear oscillations of a micron-sized air bubble in water driven by a spatially uniform, temporally periodic, single-frequency electric field are considered. Using a model that accounts for shape mode interactions to second order, thermal damping of the interior gas, viscous damping of the liquid and weak compressibility, the resultant volume mode oscillations and shape deformation are studied in detail. For a range of driving frequencies and electric field strengths, after an initial transition phase, the bubble is shown to assume a sustained, finite amplitude, oscillating ellipsoidal shape dominated by the prolate/oblate mode ( k=2 shape mode) which oscillates at twice the driving frequency. Both the volume mode and k=2 shape mode are directly excited by the electric field while higher-order even shape modes are excited through nonlinear shape mode interactions consistent with previous work. The dynamical behaviour of the k=2 shape mode is shown to depend on the difference between the shape mode’s natural frequency and twice the driving frequency and on whether the bubble is driven below, at, or above the resonance of the k=2 shape mode. In all considered cases, the volume mode oscillations are shown to be prohibitively small, even at volume resonance, to induce parametric instability growth, leaving the directly excited k=2 shape mode to dominate the resultant bubble dynamics.

A widely cited experimental dataset (Cleve et al. , J. Fluid Mech. , 2019, vol. 875, pp. 597–621) on non-spherical acoustic cavitation dynamics provides a valuable benchmark for model validation, yet its use is hindered by large uncertainties in the two key parameters: the equilibrium bubble radius and the acoustic pressure amplitude. This study introduces a robust parameter-identification framework to resolve these discrepancies and enable meaningful comparison with models. Using an in-house graphics processing unit-accelerated solver for solving the second-order perturbation model developed by Shaw ( Phys. Fluids , 2006, vol. 18, issue 7, p. 072104), the dataset is systematically re-examined. A Fourier coefficient-based error metric is developed to quantify the pronounced mismatch between simulations and measurements. The proposed method reliably corrects the vast majority of the experimental parameters, yielding excellent agreement between numerical predictions and observations. The outcome is a validated dataset with accurately identified parameters that can serve as a reliable benchmark for validating advanced computational fluid dynamics simulations and theoretical models. In addition, the approach offers a general tool for future experiments where direct measurements of local acoustic pressure remain difficult.

The parametrically induced shape distortion of a micron sized gas bubble in water driven by a temporally sinusoidal pressure field in an axisymmetric geometry is considered using a model which accounts for nonlinear shape mode interactions. Fora fixed driving frequency and considering initial bubble radii smaller than those which give rise to the prolate/oblate dominated shape via the fundamental resonance, shape distortion due either to synchronous or higher order harmonic resonances is identified. Considering cases where the parametric instability growth saturates, the resultant finite amplitude oscillations of the synchronously excited shape mode are found to be nearly sinusoidal, but shape modes excited via higher order harmonic resonances are found to consist of a number of frequency components. In the latter case, as the initial bubble radius is reduced, the order of the harmonic resonance causing the parametric excitement is found to increase, causing a shift in the constitute frequency components of the parametrically excited shape mode.

The potential for the controlled movement of a gas bubble in a liquid through parametrically induced, finite amplitude, axisymmetric shape deformation is considered. In particular, the parametric excitation of a single odd shape mode via the fundamental resonance mechanism is studied using a model that accounts for viscous, thermal, and compressible damping together with shape mode interactions to the third order. Under a single frequency time-dependent acoustic forcing, the finite amplitude, parametrically excited shape mode gives rise to small, oscillatory translation only as a consequence of nonlinear shape mode interactions. Instead, if a dual-frequency forcing is used and provided that a second shape mode is not excited parametrically, then for a number of combinations of the driving frequencies, the small amplitude oscillations are superimposed on a longer timescale, sustained linear motion. The source of the linear motion is attributed to how the frequency component not causing the parametric excitation modifies the volume mode and, in turn, the shape mode interactions. In such cases, the resultant speed of the bubble is dependent on both the driving strengths and the ratio of the driving frequencies. The results are confirmed by considering a range of driving frequencies and strengths.

The self-propulsion (translational instability) of a gas bubble in a liquid undergoing parametrically induced axisymmetric shape distortion due to being forced by a temporally sinusoidal, spatially constant acoustic field is investigated. Employing a model which accounts for the nonlinear coupling between the spherical oscillations, the axial translation and shape deformation of the bubble, the parametric excitement of two neighboring shape modes by the fundamental resonance, at the same driving frequency is studied. It is shown that provided pertinent driving pressure threshold values are exceeded, the respective shape modes are excited on different timescales. The growth of the shape mode on the faster timescale saturates giving rise to sustained constant amplitude oscillations, while the growth of the shape mode on the slower timescale is both modulated and unbounded. During the growth of the second shape mode, growing, oscillatory bubble translation is also observed.

The existence of finite amplitude shape distortion caused by parametrically excited surface instabilities for a gas bubble in water driven by a temporally periodic, spatially uniform pressure field in an axisymmetric geometry is investigated. Employing a nonlinear coupled system of equations which includes shape mode interactions to third order, the resultant spherical oscillations, translation, and shape distortion of the bubble are modelled, placing no restriction on the size of the spherical oscillations. The model accounts for viscous and thermal damping with compressibility effects. The existence of synchronous and higher order parametrically induced sustained, finite amplitude, periodic shape deformation is demonstrated. The excitement of an odd shape mode via the synchronous mechanism is shown to give rise to linear bubble self-propulsion. For larger driving amplitudes, it is shown that more than one shape mode can be parametrically excited at the same driving frequency but by different resonance mechanisms, leading to more involved shape deformation and the increased possibility of bubble self-propulsion.

Most research on sonoluminescence and sonochemistry has been conducted at acoustic frequencies above similar to 20 kHz. Consequently, mathematical models for the dynamics of acoustically-driven bubbles have hardly been examined in the audible frequency spectrum. Here, we develop a new hybrid modelling approach that combines the rigour of the advection-diffusion model whilst retaining the simplicity of a reduced-order boundary layer model to predict phase-change, mass and heat transfer in an inertially collapsing bubble excited by audible sound. Differences in these approaches are explored through a thorough validation against experimental data obtained from ultra-high speed videos of bubble dynamics at 17.8 kHz. Our results indicate that, while the boundary layer model agrees well with the advection-diffusion model at high driving frequencies, there are significant deviations at lower frequencies, where the boundary layer model overpredicts parameters such as bubble size and quantity of trapped vapour while underpredicting others such as temperature and pressure. These deviations at lower frequencies is caused by an inaccurate estimation of the boundary layer thickness originating from the time-scale competition between diffusion and fast bubble wall motion. Our work questions the suitability of existing reduced-order models developed for ultrasonic frequencies when applied to the audible range, reinforcing that further research in the audible range is needed.

A multi-relaxation time lattice-Boltzmann model is employed to investigate the dynamic evolution of two immiscible phases through an artificial, randomly generated, porous structure. The flow is driven by a constant pressure gradient, in the absence of gravitational effects. Constraining attention to two dimensions, the impact of the morphological properties of the porous structure, generated using constant radius circular solid grains, on a water-wet, oil–water two-phase flow is studied. Variations in the pore space connectivity and topology are quantified by the Euler characteristic. It is found that the wetting phase saturation and the degree of pore network homogeneity have a significant impact on the dynamic evolution of the non-wetting phase topology, which is governed by a series of coalescence and snap-off events. It is also observed that the phenomenal macro-scale steady-state based on the velocity field does not also imply a temporal topological invariance of the displaced phases. The impact of the pore space morphology on the transient dynamics of the two-phase flow is monitored and quantified through a series of hydrodynamic and topological parameters that signify the underlying flow transport processes.

We consider the resonant forcing of a gas bubble by a sinusoidal pressure wave near the second harmonic of the oblate/prolate (k = 2) shape mode in an axisymmetric geometry. Employing a model which accounts for nonlinear shape mode interactions to third order, viscous effects to the same order (in the absence of vorticity) and weak compressibility, the transition in the predicted shape deformation as the forcing strength is increased is studied in detail, together with its subsequent impact on both the spherical oscillations of the bubble and any self-propulsion that may occur. For a marked range of forcing strengths the bubble is found to undergo stable oscillatory deformation which consists of even shape modes only and is dominated by the oblate/prolate mode, the amplitude of which increases with the forcing strength. However, if the forcing strength is sufficiently large the k = 3 shape mode is also found to become resonantly excited, the growth of which occurs on a slower timescale and whose oscillation pattern consists of two dominant frequencies, the largest of which corresponds to the driving frequency. Interaction between the stable k = 2 mode and the growing k = 3 mode is found to lead to a marked non-oscillatory displacement of the bubble with the rate of displacement increasing as the amplitude of the oscillations in the k = 3 shape mode increases. Increasing the forcing strength further causes the k = 3 mode to grow faster and thus causes the bubble to translate earlier.

The nonspherical oscillations of a gas bubble being forced by a sinusoidal pressure field in an axisymmetric geometry are considered using an asymptotic model, which accounts for nonlinear shape mode interactions to third order, the effects of viscosity (in the absence of vorticity) to the same order, and weak compressibility. In particular, conditions by which a parametrically forced sub-millimeter sized bubble can achieve stable oscillatory shape deformation are studied in detail. It is found that a combination of the transfer of energy from the parametrically forced shape mode to the other modes through nonlinear shape mode coupling and viscous damping is key. Two transition regions in the spherical oscillations of the bubble are identified, the first being a consequence of the damping effects of compressibility and viscosity (with compressibility acting on a faster time scale) and the second due to nonlinear shape mode interactions. During this second transition time interval, the parametrically forced shape mode grows rapidly and nonlinearly excites other shape modes. For the moderate driving pressures considered, this growth is shown to peak and following a stabilizing transition region (only observed for the n ≥ 3 shape modes), the bubble thereafter undergoes stable, oscillatory shape deformation. Though the resultant shape deformation is dominated by the parametrically forced mode n = i, it is found to be a combination of a number of shapes modes, where the next most important mode is the second harmonic, n = 2i shape mode.

Discrete Element Method is used to simulate the impact of agglomerates consisting of autoadhesive, elastic-plastic primary particles. In order to explain the phenomenon that the elastic agglomerate fractures but the elastic-plastic agglomerate disintegrates adjacent to the impact site for the same impact velocity, we increase the impact velocity and lower the yield strength of the constituent particles of the agglomerate. We find that increasing the impact velocity can lead to the increased number of yielded contacts, and cause the elastic-plastic agglomerate to disintegrate faster. Mostly importantly, the energy dissipation process for the elastic-plastic agglomerate impact has been investigated together with the evolutions of the yielding contacts, and evolutions of velocity during impact.

In this study, the impact of agglomerates composed of autoadhesive, elastic-plastic primary particles are simulated using the discrete element method. Results obtained are compared to the impact breakage of an agglomerate of autoadhesive elastic particles. It is found that, for the same impact velocity, the elastic agglomerate fractures but the elastic-plastic agglomerate disintegrates adjacent to the impact site. For the elastic-plastic agglomerate, the impact damage increases with increase in material yield stress. It is also found that the particle size distribution of the debris is more accurately defined by a logarithmic function rather than the power law function commonly obtained for impacts of agglomerates composed of elastic particles.

AbstractWe study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr–Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio$r= 1000$, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil and gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio$r= 1000$, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally determined flow-regime map, and discuss the potential application of the present method to nonlinear analyses.

The origin and the resultant properties of the strong pulses or shocks emitted by collapsing gas bubbles into a surrounding liquid are investigated numerically. The compressible flow in both phases is resolved. Results are presented for micron- and millimetre-sized bubbles and for bubble collapse triggered either by an acoustic driving or by an initially imposed spherical shock in the liquid. The origin of the diverging shocks is investigated, and the results of a parametric study for the acoustically driven collapse reveal a predominant linear dependence of the shock strength and width on the maximum bubble radius. The results compare favourably with experimental data and agree well with acoustic theory in the limit of weak forcing.

The volume oscillations, translation, and axisymmetric deformation of a bubble in an acoustic traveling wave are considered. Assuming the bubble translation and deformation is small, but placing no restriction on the volume oscillations, a combination of the Rayleigh dissipation function and perturbation analysis is employed to account for the effects of viscosity in the absence of vorticity to third order in the small interaction terms. Contributions from the acoustic field are also determined to this order, while the free oscillation terms are drawn from a previously derived model correct to the same order of analysis. To permit the study of large amplitude acoustic forcing, appropriate compressibility terms are phenomenologically added to the volume pulsation equation. Stability maps of driving pressure versus driving frequency and driving pressure versus the equilibrium bubble radius are presented. A predominant number of results are for micron-sized bubbles driven in the ultrasonic regime, but the behavior of larger bubbles driven at frequencies in the kilohertz range is also considered. In all cases, bubbles driven above the natural frequency of their respective volume oscillations are markedly more stable with regard to the acoustic driving amplitude, consistent with previous observations. Below these respective natural frequency values, the stability/instability fronts display a much more complex structure. Accounting for shape mode viscous damping causes a general increase in bubble stability, together with a reduction in the stability/instability front complexity. In the case of micron-sized bubbles this stabilization is markedly more significant for bubbles driven above the natural frequency of the respective volume mode oscillations; for larger bubbles driven in the kilohertz range, the influence of shape mode damping is less significant.

In this work, the behaviour of a gas bubble in a low-Mach-number, weakly viscous, dielectric liquid under the action of a spatially uniform electric field is considered. Using domain perturbation analysis and assuming any shape deformation of the bubble or induced translation to be small, but placing no such restriction on the volume oscillations, appropriate equations to second order in the small-interaction terms are derived. Steady and time-dependent solutions are presented. The results indicate that only even shape modes and odd components of the interfacial charge density are excited starting from an initially stationary and uncharged spherical bubble. In order for the bubble to be set into motion it must either be initially deformed in terms of an odd shape mode or acquire an even charge density component. Situations are examined wherein all modes are excited and the presence of an instability that arises due to a coupling between an even mode of the charge density and bubble translation is demonstrated. The instability manifests itself via the sudden acceleration of the bubble and growth of its radius; this leads ultimately to conditions beyond the reach of the present theory.