Wall influence on dynamics of a microbubble

TL;DR

This study models how a wall influences the nonlinear oscillations of a microbubble under ultrasound, revealing that walls tend to stabilize bubble dynamics and affect bifurcation behavior.

Contribution

The paper introduces a modified Keller-Miksis-Parlitz model incorporating wall effects via an image bubble, providing detailed bifurcation analysis of bubble dynamics near walls.

Findings

Walls stabilize bubble oscillations, requiring higher ultrasound pressures for nonlinear responses.

Bifurcation maps show how bubble behavior depends on distance, frequency, and pressure.

Detection of subcritical period tripling and quadrupling transitions near walls.

Abstract

The nonlinear dynamic behaviour of microscopic bubbles near a wall is investigated. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of the 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 solid 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 non-dimensional 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.