### Abstract

A highly accurate semi-analytical method was developed to predict the acoustic field generated by a real transducer in an axisymmetric sonobioreactor consisting of multiple fluid-, linear elastic solid-, and/or poroelastic-layers. The accuracy of the method is independent of the spacing of the grid-points and computational costs are not proportional to the ratio of the system's characteristic dimensions to the acoustic wavelength, both improvements over the use of full numerical methods. Contrary to similar semi-analytical approaches, the method is not limited to the prediction of freely propagating waves. Acoustic reflection and perfect absorption are readily implemented. The method was numerically validated and matched the analytical function describing the pressure amplitude along the axis of a cylindrical transducer with a root-mean-square error of less than 2%. The method was also experimentally validated, but it was shown that the method is not applicable when certain components of the system have a diameter smaller than that of the acoustic beam. The method was used to model an ultrasonic bioreactor as an example problem, where its accuracy and computational efficiency were shown to be instrumental in bioreactor design.

Original language | English (US) |
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Pages (from-to) | 122-136 |

Number of pages | 15 |

Journal | Wave Motion |

Volume | 56 |

DOIs | |

State | Published - Jul 1 2015 |

### Keywords

- Angular spectrum
- Bioacoustics
- Biot theory
- Sonochemistry
- Transfer matrix
- Ultrasound

### ASJC Scopus subject areas

- Modeling and Simulation
- Physics and Astronomy(all)
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Wave Motion*,

*56*, 122-136. https://doi.org/10.1016/j.wavemoti.2015.02.007