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

Abstract

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.

Investigation of noninertial cavitation produced by an ultrasonic horn

“…Note that a basic feature of pattern formation, which is applicable for the interpretation of preferred patterns of parametrically unstable Faraday ripples on the sphere, is that these structures have symmetry of point subgroups including the symmetries of Platonic solids. 47,57 The maximal symmetry group for l ¼ 4 is octahedral, and Fig. 7(b) shows the pattern corresponding to this symmetry, the example showing the case where several l ¼ 4 modes are superimposed on the sphere, and the axial of symmetry no longer holds.…”

“…Consequently only the Y 4,4 , Y 4,À4 and Y 4,0 modes (i.e., l ¼ 4, and m ¼À 4, 0, 4) can form the octahedral structure. 57 The first two modes form a standing wave and have equal amplitudes (i.e., a 4,4 ¼ a 4,À4 ). The equality a 4;0 ¼ ffiffiffiffiffiffiffiffiffiffi 14=5 p a 4;4 follows from the requirement that rotation by p/2 radians about the x-and y-axes should leave the structure unchanged.…”

Quantification of undersea gas leaks from carbon capture and storage facilities, from pipelines and from methane seeps, by their acoustic emissions

“…Certainly, in the oceans natural factors give potentially wide variations in the chemical constitution of the bubble wall and the details of the bubble shape distortion, release and fragmentation (Leighton et al 1991;Maksimov & Leighton 2001, 2011Winkel et al 2004;Lee et al 2007). These will provide many potential features by which the forward model of equations (2.5) and (2.6) can be adapted as new data come in.…”

The acoustic bubble: Oceanic bubble acoustics and ultrasonic cleaning

“…The ultrasonic cleaning bath causes cavitation, whereby bubbles collapse under ultrasound to generate shock waves [27][28][29] and can also involute to form microjets [30,31], both of which can remove material from surfaces [32,33]. In contrast, the UAS system projects sound down a column of water [34] in order to excite surface waves [35][36][37] on the walls of microscopic bubbles on the surface to be cleaned. These surface waves can generate convection [38][39][40] and shear forces [1,41,42] in the liquid close to the bubble wall, and so produce a cleaning effect, and alter the way material deposits onto surfaces [43].…”