Natural frequencies of two bubbles in a compliant tube: Analytical, simulation, and experimental results

Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA.
The Journal of the Acoustical Society of America (Impact Factor: 1.5). 11/2011; 130(5):3347-56. DOI: 10.1121/1.3626135
Source: PubMed


Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.

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    ABSTRACT: A numerical study was conducted to investigate the validity of using the spring-backed membrane model for compliant walls (CWs), and to explain the failure of the reference study [Duncan and Zhang, Journal of Fluid Mechanics 1991, (226) 401-423] to reproduce the bubble behavior near moderately elastic CWs. The same mathematical models used in the reference study were employed in our work. The bubble was created from its minimum-volume state, and the initial liquid pressure on the CWs was computed, rather than artificially prescribed. Our predicted bubble behavior in the vicinity of moderately elastic CWs agrees qualitatively well with experimental observations. The spring-backed membrane model was demonstrated to be capable of enabling the correct behavior of CWs and the correct bubble dynamics in their vicinity. The improper choice/specification of the initial conditions in the reference study was determined to be responsible for the failure to reproduce the bubble dynamics near moderately elastic CWs.
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