Oscillatory dynamics of a charged microbubble under ultrasound

Abstract

can show highly irregular oscillations which are chaotic and of unpredictable amplitude. For applications where damage caused on surfaces due to bubble cavitation can be disastrous, such as in medicine, it is desirous to operate the sonic device in a "safe" regime, and / or to be able to have control over the bubble's motion. Often in biological systems, it is known that bubbles in fluids can be electrostatically charged. Studies of the dynamics governing the oscillations, growth and collapse of charged bubbles are therefore of immense relevance because of their prevalence in diverse applications and situations. Experimental and theoretical work on the presence of charge on gas bubbles in fluids goes back to, for example, the work of McTaggart, Alty and Akulichev [9, 10, 16, 17], and more recently the work of Shiran and Watmough and Atchley [11, 12, 18]. None of the work, though, has addressed the issue of dynamics of a charged bubble under ultrasonic forcing. It is interesting to know what effect the presence of electric charge on the bubble would have and see if the motion of such a charged bubble forced by ultrasound would vary significantly from that of an electrically neutral bubble in a fluid. This especially becomes of practical significance when we are looking at cavitation phenomena in fluids in real-life, be it in the context of cavitation in mechanical systems or in the case of bubbles in fluids in living tissue in a medical context. Apart from the work in [15], we are not aware of any other studies in the literature of the dynamics of acoustically forced charged bubbles suspended in a fluid. Their work however used the value 4/3 for the polytropic constant which entailed cancellation of all the charged terms; thus their work does not really address the issue of charge which it sets out to do. The extremely nonlinear nature

Effect of charge on the dynamics of an acoustically forced bubble

“…Other results, including an investigation of the bifurcation structure as a function of charge, scaling relations for the maximal charge, etc. are being reported elsewhere [34].…”

“…The presence of charge Q (or surface charge density S) causes the inclusion of an electrostatic pressure term 2πS 2 /ǫ = Q 2 /(8πǫR 4 ) into the equation (see e.g., [32], also [34]):…”

The charged bubble oscillator: Dynamics and thresholds

“…When charge is present on the bubble surface, an additional electrostatic pressure term is introduced, while reducing the effective value of the surface tension . The modified equation determining the dynamics of the bubble can then be written as [12,13]…”

“…The work of Alty and others [8][9][10][11] were some of the first to discuss the presence of charge on gas bubbles in fluids. Forced oscillations of a charged bubble under ultrasonic forcing, on the other hand, were not discussed at any great detail in the literature until our recent work [12][13][14].…”

“…In our earlier papers [12,13] we had modified the Rayleigh-Plesset equation and demonstrated how the presence of electric charge could greatly influence the nonlinear oscillatory dynamics of a bubble in the presence of ultrasound forcing. In our model we assume the charge on the bubble to be uniformly distributed on its surface.…”