Alexey O. Maksimov

Pattern formation on the surface of a bubble driven by an acoustic field

The final stable shape taken by a fluid–fluid interface when it experiences a growing instability can be important in determining features as diverse as weather patterns in the atmosphere and oceans, the growth of cell structures and viruses, and the dynamics of planets and stars. An example which is accessible to laboratory study is that of an air bubble driven by ultrasound when it becomes shape-unstable through a parametric instability. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the breathing mode, regular patterns of surface waves are observed on the bubble wall. The existing theoretical models, which take account only of the interaction between the breathing and distortion modes, cannot explain the selection of the regular pattern on the bubble wall. This paper proposes an explanation which is based on the consideration of a three-wave resonant interaction between the distortion modes. Using a Hamiltonian approach to nonlinear bubble oscillation, corrections to the dynamical equations governing the evolution of the amplitudes of interacting surface modes have been derived. Steady-state solutions of these equations describe the formation of a regular structure. Our predictions are confirmed by images of patterns observed on the bubble wall.

Sounds of marine seeps: A study of bubble activity near a rigid boundary

A passive acoustic method for detecting environmentally dangerous gas leaks from pipelines and methane naturally leaking from the seabed has been investigated. Gas escape involves the formation and release of bubbles of different sizes. Each bubble emits a sound at a specific frequency. Determination of the bubble radius from the frequency of its signature passive acoustic emission by use of so-called Minnaert formula has a restricted area of applicability near the seabed. The point is that the inertial mass and the damping constant of the birthing bubble are markedly different from those of a free bubble. The theoretical model for the bubble volume oscillations near the seabed has been proposed and an analytical solution has been derived. It was shown that the bispherical coordinates provide separation of variables and are more suitable for analysis of the volume oscillations of these constrained bubbles. Explicit formulas have been derived, which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary.

Time reversal technique for gas leakage detection

The acoustic remote sensing of subsea gas leakage traditionally uses sonars as active acoustic sensors and hydrophones picking up the sound generated by a leak as passive sensors. When gas leaks occur underwater, bubbles are produced and emit sound at frequencies intimately related to their sizes. The experimental implementation of an acoustic time-reversal mirror (TRM) is now well established in underwater acoustics. In the basic TRM experiment, a probe source emits a pulse that is received on an array of sensors, time reversed, and re-emitted. After time reversal, the resulting field focuses back at the probe position. In this study, a method for enhancing operation of the passive receiving system has been proposed by using it in the regime of TRM. Two factors, the local character of the acoustic emission signal caused by the leakage and a resonant nature of the bubble radiation at their birth, make particularly effective scattering with the conjugate wave (CW). Analytical calculations are performed for the scattering of CW wave on a single bubble when CW is formed by bubble birthing wail received on an array, time reversed, and re-emitted. The quality of leakage detection depends on the spatio-temporal distribution of ambient noise.

Volume oscillations of a constrained bubble

The behavior of a single acoustically driven bubble tethered to a wire ring is considered. The method of restraining the bubble against rising by attaching it to a wire is a common procedure in conducting precision acoustic measurements. The dynamics of the tethered bubble differs from those of free bubble due to variation in inertial (or added) mass. The objective of this study is to obtain a closed-form, leading order solution for the volume oscillations, assuming smallness of the bubble radius R0 in comparison with the acoustic wavelength λ. It was shown, by using the invariance of the Laplace equation to conformal transformations and the geometry of the problem, that the toroidal coordinates provide separation of variables and are most suitable for analysis of the oscillations of the tethered bubble. Thus, the dynamics of the bubble restraining by a wire loop in toroidal coordinates can be investigated by using analytical approach and by analogy to the dynamics of a free spherical bubble.

Dynamics of a Tethered Bubble

Small gas bubbles adhering to solids occur in a range of manufacturing processes, including printing, casting, coating and electroplating. The behavior of a gas bubbles tethered to a rigid plane boundary in an oscillatory pressure field is investigated by use conformal symmetry of the problem. The dynamics of the tethered bubble differ from those of the free bubble. The inertial (or added) mass depends on the contact angle and this variation is not monotonic. As a result, the natural frequency depends on the contact angle. Viscous damping of the tethered bubble is increased by more than two orders of magnitude, firstly, owing to the greater dissipation near rigid wall in comparison with free air/water bubble interface and secondly, because of a contact line dissipation effect.

Hopf Bifurcation in Acoustically Excited Faraday Ripples on a Bubble Wall

Observations of surface waves on the wall of a bubble which is subjected to an acoustical field demonstrate differences in the transient processes, as well as a marked variation in steady state amplitudes, that depend on the insonification conditions. To clarify these observations, the stability analysis of the system has been carried out and the presence of the Hopf bifurcation was established. The appearance of the limiting circle corresponds to the presence of periodic variations in the amplitudes of interacting breathing (volume) and distortion (surface) modes. Comparison between observation and modeling indicate qualitative similarities, for example in that the oscillations will be seen for sufficiently high pressure amplitudes and will be absent at the bottom of the threshold curve for the excitation of the ripples.

Acoustic radiation force on a parametrically distorted bubble

The subject of acoustic radiation pressure on a gas bubble is important in many applications because it controls how bubbles are moved by acoustic fields to target locations, and often how they act upon the target. Previous theoretical treatments assume a spherical bubble undergoing linear pulsations, but some (such as cleaning using Faraday waves on the bubble wall) require that the bubble be aspherical. Therefore, this paper derives ways to calculate the variation in the radiation pressure due to the non-spherical bubble oscillations. The magnitude and direction of the radiation force are determined by two factors: the amplitude of volume oscillations, Vm, and the phase relationship between those oscillations and the acoustic field which drives them. There are two key findings that correct for the predictions of a model accounting for only linear pulsations. First, the growth of the radiation force slows down as Vm ceases to increase linearly with increasing amplitude of the acoustic wave above the threshold. Second, although both models show that the direction of the force relative of the standing wave antinode can be attractive or repulsive depending on frequency, when distortion modes are included the frequency at which this force changes its sign is shifted.

Sounds of Undersea Gas Leaks

A passive acoustic method of detecting potentially environmentally disastrous gas leaks from pipelines, and methane naturally leaking from the seabed has been studied. Gas escape involves the formation and release of bubbles of different sizes. Each bubble of a given size emits a sound at a specific frequency. The traditional approach based on the determination of the bubble radius from the frequency of its signature passive acoustic emission by use of so-called Minnaert formula has a restricted area of applicability near the seabed. The point is that the inertial mass of the birthing bubble is markedly different from the one of a free bubble. It was shown that the bi-spherical coordinates provide separation of variables and are most suitable for analysis of volume oscillations of constrained bubble. The theoretical model for the bubble volume oscillations near the seabed has been proposed and an analytical solution has been derived.

Acoustic microstreaming induced by pattern of Faraday waves on a bubble wall

Interest to acoustic microstreaming is supported by the variety of applications: micromixing, transferring lipid vesicles and large molecules in desired direction, and selective particle trapping which are essential to the success of lab-on-a-chip- devices. It is generally assumed that the main contributions to the streaming generated by a gas bubble come from the pulsation and translation modes. This study deals with the microstreaming which is induced when a bubble is driven acoustically in the regime of parametrically generation of Faraday waves. The greater wall displacement amplitude for l > 1modes means that their effect on the flux of species near the bubble wall can be much greater than that of the breathing mode. The modes with a fixed order l have a high degree of degeneracy equal to (2l+1). The choice of which modes are chosen to grow to steady state, and which are selected out, determines the shape of the perturbation and hence the structures of the streaming flow. Basic features of pattern fo...

Scattering from a pair of closely spaced bubbles

Acoustic scattering by a single bubble is the most basic problem for bubble detection. For a two-phase flow, the subject of forced oscillations of a pair of bubbles is important because it controls how bubbles interact with each other. Attempts to incorporate interactions between bubbles have traditionally used a multiple scattering methodology. The proposed approach uses a bi-spherical coordinate system and is limited to a description of a sufficiently long-wave acoustical field, so that the bubbles are homobaric, and the medium in the vicinity of the bubbles can be considered incompressible. The choice of a specific coordinate system allows the authors to take into account the internal symmetry inherent in this problem and provides a partial summation on only the most important contributions to the multiple scattering series. A closed form solution was derived for the scattered acoustic field that determines its parametric dependence on bubbles sizes and the separation distance.