Nonlinear dynamic behavior of microscopic bubbles near a rigid wall

Abstract

The nonlinear dynamic behavior of microscopic bubbles near a rigid wall is investigated. Oscillations are driven by the ultrasonic pressure field that arises in various biomedical applications such as ultrasound imaging or targeted drug delivery. It is known that, when bubbles approach a blood-vessel wall, their linear dynamic response is modified. This modification may be very useful for real-time detection of bubbles that have found targets; in future therapeutic technologies, it may be useful for controlled release of medical agents encapsulating microbubbles. In this paper, the nonlinear response of microbubbles near a wall is studied. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of a rigid wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium, and a bubble near a rigid wall. In the latter case, the wall influence is modeled by including a symmetrically oscillating image bubble. The bubble dynamics is traced using a numerical solution of the model equation. Subsequently, Floquet theory is used to accurately detect the bifurcation point where bubble oscillations stop following the driving ultrasound frequency and undergo period-changing bifurcations. Of particular interest is the detection of the subcritical period-tripling and -quadrupling transition. The parametric bifurcation maps are obtained as functions of nondimensional parameters representing the bubble radius, the frequency and pressure amplitude of the driving ultrasound field, and the distance from the wall. It is shown that the presence of the wall generally stabilises the bubble dynamics, so that much larger values of the pressure amplitude are needed to generate nonlinear responses. Thus, a clinical protocol in which selected nonlinear harmonics are examined under varying insonation amplitudes may be useful in detecting microbubble proximity to walls.

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures

“…Dynamics of the acoustically excited bubbles are nonlinear and chaotic. These dynamics have been the subject of numerous experimental [1,15,[17][18][19][20] and numerical [21][22][23][24][25][26][27][28][29][30] studies . Achieving the full potential of bubbles in applications and understanding their role in the associated phenomena not only requires a detailed knowledge over their complex behavior but also on the effect of bubble oscillations on the propagation of acoustic waves.…”

Mathematical models for the acoustic response of a solids-loaded encapsulated bubble

“…The experimental minimum in acoustic response has been explained as due to a p phase shift in the bubble response at the fundamental resonance frequency (Leighton et al, 1996;Leighton et al, 1997;Zhang et al, 2012). The same phase shift has been noted in a theoretical analysis of sinusoidally forced small amplitude bubble oscillations (Suslov et al, 2012). The frequencies of these acoustic features are shown in this paper to provide unique estimators of bubble properties.…”

“…The regular perturbation linearization results in analytical expressions for steady fundamental and second harmonic induced oscillations of the bubble wall. It is well known that subharmonic and higher order harmonic resonance solutions of nonlinear forced oscillator models for bubble active acoustic response can also be found (Prosperetti, 1974;Francescutto and Nabergoj, 1983;Parlitz et al, 1990;Suslov et al, 2012). Indeed, it has been numerically shown that subharmonic oscillations are generated at lower forcing amplitudes than a second harmonic (Parlitz et al, 1990).…”

Pulsatory rise of microbubble swarm along a vertical wall

“…Currently, researchers are studying the effects of bubbles with diameters of less than 100 m (i.e., microbubbles, Johnson and Cooke, 1981;Makuta et al, 2006;Dressaire et al, 2008;Suslov et al, 2012) on heat transfer, and expect a different effect from that of large bubbles (i.e., millimeter bubbles). The main questions over the use of such fine bubbles are the role of the high local number density of buoyant sources, and the effect of the interfacial tension that defines the rheological properties of the microbubble mixture (Llewellina and Manga, 2005).…”