Bubble oscillations and dynamics under periodic electric fields

Oscillation of a transient bubble near an aperture made in a convex rigid plate

The electrogravitational instability of a dielectric fluid cylinder dispersed in a gravitational dielectric medium of negligible motion has been developed on using the macroscopic perturbation technique based on the normal mode analysis. The model is acting upon the pressure gradient, self-gravitating and electrodynamic (with periodic time dependent electric field) forces. For all axisymmetric and non-axisymmetric disturbances the system is governed by the Hill's second-order integro-differential equation in the disturbed surface displacement. The self-gravitating forces are destabilizing only in the axisymmetric disturbances domain 0⩽x⩽1.0668 and stabilizing in all other domains, where x is the dimensionless longitudinal wavenumber. The electric field is always stabilizing not only in the axisymmetric mode m= 0 but also in those of non-axisymmetric m≠ 0. The frequency of the time dependent periodic electric field is only destabilizing in a few axisymmetric states of perturbations while it is strongly stabilizing in the remaining axisymmetric disturbance states and also stable in all states of the non-axisymmetric perturbations. Resonance domains may arise due to the periodicity of the electric field and in some ranges of the wavenumber, the stability conditions depend solely on the frequency of the field. The self-gravitating destabilizing influence could not be suppressed whatever is the greatest value of the magnitude and frequency of the periodic electric field because the gravitational destabilizing influence will persist.

Through Euler/Euler large eddy simulation (LES) modeling, it is demonstrated that turbulent dispersion of bubbles can effectively indicate the impact of turbulent eddies on the bubble dynamics, i.e., the bubble oscillation behavior. This finding builds on previous work using the Euler/Lagrange LES modeling approach and leads to a significant improvement in predicting bubble lateral dispersion. Spatially filtered terms were proposed for the subgrid‐scale (SGS) turbulent dispersion and added mass stress force models, with a modification made to the SGS eddy viscosity to reflect bubble turbulent dispersion and oscillations. The proposed model substantially improves the prediction of bubble volume fraction distribution, bubble and liquid phase velocity profiles, the turbulent kinetic energy spectrum, and mass transfer.

The influence of the hydrodynamic interaction of spherical gas bubbles in linear, circular and ball-shaped clusters under a sudden increase in the surrounding liquid pressure is studied. The centers of the bubbles are located at the nodes of a uniform one-dimensional mesh on a segment of a straight line in the linear clusters, at the nodes of a uniform two-dimensional mesh inside a circular region of a plane in the circular clusters and at nodes of a uniform three-dimensional mesh inside a spherical region in the ball-shaped clusters. Initially, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the bubble radius is 0.25 mm, and the size of the mesh cells is 5 mm. The pressure rises by 0.8 bar. A mathematical model is applied, in which the dynamics of bubbles is described by the second-order ODEs in the radii of the bubbles and the position-vectors of their centers. It is shown that the radial oscillations of the bubbles in the clusters are significantly different from those of a single bubble. In particular, the period of their oscillations is longer, their damping is non-monotonic (with beats). The amplitudes of the oscillations and their beats are much greater in the central bubbles of the clusters than in the peripheral ones. The process of decay of the radial oscillations of the central bubbles in the circular and ball-shaped clusters begins with the phase of their amplification, during which the bubble pressure maximum becomes higher than the maximum achieved during the oscillations of a single bubble. Moreover, with growing number of bubbles in these clusters, the rate of damping of their oscillations decreases, and the oscillation beat frequency of both the central and peripheral bubbles increases.

Bubble oscillation plays a pivotal role in a multitude of medical and industrial applications. In this study, we employ a semi-analytical method to investigate the oscillation of a bubble in a viscoelastic fluid. The bubble is assumed to oscillate isothermally, and the well-known Rayleigh-Plesset equation for bubble dynamics is employed alongside the Oldroyd-B constitutive equation for the viscoelastic fluid. By applying the Leibniz integral rule, the governing integro-differential equation is converted into a system of four ordinary differential equations, which are then solved numerically. The results demonstrate that modifying each dimensionless parameter exerts a distinct influence on bubble oscillation, depending on the elasticity number and other parameters such as the amplitude of acoustic pressure. In the range of non-dimensional values under consideration, an increase in the Reynolds number, acoustic pressure, and acoustic frequency has been observed to exert a significant influence on the amplitude of bubble oscillation, relative to the influence of other parameters. As the Reynolds number approaches approximately 1.1, the bubble oscillations become chaotic. In contrast, at lower Reynolds numbers, the oscillations remain periodic. Moreover, our findings indicate that a Deborah number of 2.4 represents the most elastic fluid in which bubble oscillations were observed. When the elasticity number is approximately 10 or higher and the Reynolds number remains constant, further increases in elastic effects do not significantly impact the oscillations.

Several studies have investigated the dynamics of a single spherical bubble at rest under a nonstationary pressure forcing. However, attention has almost always been focused on periodic pressure oscillations, neglecting the case of stochastic forcing. This fact is quite surprising, as random pressure fluctuations are widespread in many applications involving bubbles (e.g., hydrodynamic cavitation in turbulent flows or bubble dynamics in acoustic cavitation), and noise, in general, is known to induce a variety of counterintuitive phenomena in nonlinear dynamical systems such as bubble oscillators. To shed light on this unexplored topic, here we study bubble dynamics as described by the Keller-Miksis equation, under a pressure forcing described by a Gaussian colored noise modeled as an Ornstein-Uhlenbeck process. Results indicate that, depending on noise intensity, bubbles display two peculiar behaviors: when intensity is low, the fluctuating pressure forcing mainly excites the free oscillations of the bubble, and the bubble's radius undergoes small amplitude oscillations with a rather regular periodicity. Differently, high noise intensity induces chaotic bubble dynamics, whereby nonlinear effects are exacerbated and the bubble behaves as an amplifier of the external random forcing.

An investigation of the multi-cycle dynamics of underwater explosion bubbles near hybrid boundaries is conducted using the experimental method. The experiments are carried out within a square steel tank. The free surface and a freely hanging steel plate comprise the hybrid boundary condition. Bubbles are initially positioned at equal distances from the two boundaries to facilitate a comparison of the relative influence exerted by each boundary. High-speed photography and pressure sensors are utilized to document the dynamics of bubbles and pressures in the flow field. An examination of the bubble behavior is conducted through the analysis of experimental imagery, elucidating the formation of a cone-shaped cavity near the free surface and the subsequent complex distortion behavior of the bubble as it interacts with the wall during the rebound phase. The investigation concentrates on the migratory properties of bubbles across various regions, revealing a spectrum of trajectories due to the varying boundary and buoyancy effects: vertical descent, “L”-shaped trajectory, “U”-shaped trajectory, and diagonal upward trajectory. Unless very close to the free surface, the direction of bubble migration changes at the end of each cycle due to local fragmentation of the bubble surface. Finally, the discussion culminated in an analysis of bubble energy conversion, revealing that the complex bubble behavior near the free surface weakens bubble collapse, resulting in minimal impact on the surrounding fluid dynamics from bubble oscillation. In the region distant from the free surface, when the bubble oscillation is weakly affected by buoyancy and boundaries, the energy emitted by bubble oscillation peaks due to the nearly spherical collapse.

Nonlinear bubble dynamics in cryogenic two-phase flow under ultrasonic excitation considering mass transfer.

This article aims to study in detail the bubble oscillation near confined free surfaces and the ensuing droplet formation using a combined boundary element-finite difference method. Three configurations are considered: (i) the bubble oscillation near a circular aperture made in a flat plate, (ii) the bubble oscillation inside and near the top opening of a vertical cylinder and (iii) the bubble oscillation between a perforated flat plate and a horizontal solid boundary. The effects of standoff distance on the bubble dynamics and on the surrounding fluid dynamics are examined. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different standoff distances could be observed in the present work. In addition, it was found that for the configurations (i) and (iii), the bubble reentrant jet is always directed away from the free surface. For the cylinder case, however, a critical standoff distance was found for which the pressure distribution in the fluid above and below the bubble are the same and the bubble takes the shape of an hourglass at the time of jet impact. For subcritical standoff distances the bubble reentrant jet is always away from the free surface. However, for supercritical standoff distances the direction of the reentrant jet is interestingly directed towards the free surface. Finally, the effect of plate and cylinder configurations on the resulting droplet dynamics was investigated. It was found that the driving force for the droplet formation is the initial velocity induced by the bubble reentrant jet rather than the pressure difference inside the liquid. Besides, in the cylinder case the droplet size is smaller and its pinch-off happens earlier than the plate case.

A three-dimensional (3D) scattered data filtering method in combination with averaging process is proposed to improve the signal-to-noise (S/N) ratio of space charge raw signal under periodic electric field. The spatial relationship between each point and its neighborhood is constructed based on the 3D information of space charge, i.e., phase, amplitude and position. Two 3D filtering methods, i.e., Gaussian kernel convolution method and moving least squares surface projection method, are used to filter the feature and non-feature areas of the space charge distribution, respectively. The effectiveness of 3D filtering is verified via analyzing the responses of space charge signal in PMMA under various periodic electric fields. In addition, the results indicate that the number of averaging times can be appropriately adjusted based on the intensity of the polarization electric field.

Cavitation is a common harmful phenomenon in hydraulic transmission systems. It not only damages flow continuity and reduces medium physical performance, but also induces vibration and noise. At the same time, the efficiency of a system is reduced due to cavitation, especially dynamic performance are deteriorated. Applying commercial CFD software FLUENT, the cavitation issuing from the orifice was numerically investigated, reducing the harm. The effect of liquid parameters (such as surface tension, gas content, and the temperature) on the oscillation of bubble is studied numerically. The modified Rayleigh-Plesset equations are presented to describe the oscillation of bubble in different liquids. Employing the finite difference calculus, the behavior of a cavitation bubble in liquids with different physics parameters are obtained. Meanwhile, the numerical results are compared with experiment results. It is observed that the viscous force decreases the growth and collapse of a bubble, making it expand or collapse less violently. And the surface-tension forces stave bubble growth progress and speed up bubble collapse process. On the other hand, both the maximum bubble radius and bubble lifetime increase with increasing temperature. These results can provide theory basis for understanding cavitation bubble dynamics in the hydraulic systems.

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluid and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elasto-visco-plastic (EVP) constitutive equation that takes into account the elastic and visco-plastic deformations of the material [P. Saramito, J. NonNewton. Fluid Mech. 158 (1-3) (2009) pp.154-161]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ODEs and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, a sot Carbopol gel and a stiffer Kaolin suspension. We find that, depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including oil industry and food processing.

To simulate the dynamics of bubbles within a ferrofluid under the action of a uniform magnetic field, an improved multicomponent multiphase pseudopotential model with a multiple-relaxation-time collision operator coupled with the lattice Boltzmann model for solving magnetic field was constructed in the current study. By comparing with basic arithmetic examples and results of previous studies, it is well demonstrated that the coupled model proposed in this study has good reliability and accuracy in simulating the dynamics of bubbles in a ferrofluid under a uniform magnetic field. Then the proposed coupled model was used to study the dynamics characteristics of two asymmetrically arranged bubbles in a ferrofluid under the action of a horizontal uniform magnetic field. The results showed that the irregular nonlinear deformation, four representative bubble motion patterns, and the bubble oscillates along and perpendicular to the magnetic field direction were found in the dynamics of the bubbles. At different magnetic Bond numbers (Bom), the variation of distances parallel to the magnetic field (d) and distances perpendicular to the magnetic field (h) makes the nonlinear deformation effect, bubble motion mode, bubble oscillation amplitude, and bubble deformation throughout the process change accordingly. However, for each Bom number, different d and h at the same Bom number have almost no effect on the time of bubble oscillation and the deformation when the bubbles are stabilized after fusion.

We have investigated the differential conductance and shot noise for the system of superconducting nanowires irradiated with a periodic electric field by nonequilibrium Green's functions. The numerical results show that the coupling between the Majorana bound states (MBSs) can be tuned by the periodic electric field. The width of barriers has huge influence on the coupling of MBSs, however, the separation between barriers affect the coupling faintly. The coupling increases with the width of barriers, the number of barriers and the strength of barriers. In addition, super-Poissonian shot noise emerges as the coupling increases.

Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μm) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows from the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh–Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh–Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.