### Abstract

A mathematical model of a micrometer size gas bubble containing nanometer size light absorbing nanoparticles is presented. A description of such a system can be obtained in terms of a two-coupled phase model with the solid particles in suspension in a fluid phase, i.e. the gas. It is assumed that the suspension is diluted so that particle-particle interaction can be ignored. Because the heat exchange between the nanoparticles and the gas is of main interest in this calculation, it is assumed in first approximation that the gas and the particles have the same velocity and pressure. The pressure is assumed to be function of time only. In this case, only the equations of continuity and energy for both the particulate phase and the gas phase. The two-coupled model is then solved in linear approximation and a system of four differential equations with constant coefficients is obtained. The system is diagonalized and the general solution of the two coupled system is obtained. The general solution is a combination of exponential decaying oscillatory functions for the temperature of the two phases, the pressure and the microbubble radial oscillations. It was found that the oscillatory behavior takes place in the MHz range.

Original language | English (US) |
---|---|

Article number | 020002 |

Journal | Proceedings of Meetings on Acoustics |

Volume | 5 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

Event | 156th Meeting Acoustical Society of America 2008 - Miami, FL, United States Duration: Nov 10 2008 → Nov 14 2008 |

### Fingerprint

### ASJC Scopus subject areas

- Acoustics and Ultrasonics

### Cite this

*Proceedings of Meetings on Acoustics*,

*5*, [020002]. https://doi.org/10.1121/1.3046452

**Coupled two-phase model of a gas microbubble containing suspended light absorbing nonoparticles.** / Sassaroli, Elisabetta; O'Neill, Brian E.; Li, King C.

Research output: Contribution to journal › Conference article

*Proceedings of Meetings on Acoustics*, vol. 5, 020002. https://doi.org/10.1121/1.3046452

}

TY - JOUR

T1 - Coupled two-phase model of a gas microbubble containing suspended light absorbing nonoparticles

AU - Sassaroli, Elisabetta

AU - O'Neill, Brian E.

AU - Li, King C.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - A mathematical model of a micrometer size gas bubble containing nanometer size light absorbing nanoparticles is presented. A description of such a system can be obtained in terms of a two-coupled phase model with the solid particles in suspension in a fluid phase, i.e. the gas. It is assumed that the suspension is diluted so that particle-particle interaction can be ignored. Because the heat exchange between the nanoparticles and the gas is of main interest in this calculation, it is assumed in first approximation that the gas and the particles have the same velocity and pressure. The pressure is assumed to be function of time only. In this case, only the equations of continuity and energy for both the particulate phase and the gas phase. The two-coupled model is then solved in linear approximation and a system of four differential equations with constant coefficients is obtained. The system is diagonalized and the general solution of the two coupled system is obtained. The general solution is a combination of exponential decaying oscillatory functions for the temperature of the two phases, the pressure and the microbubble radial oscillations. It was found that the oscillatory behavior takes place in the MHz range.

AB - A mathematical model of a micrometer size gas bubble containing nanometer size light absorbing nanoparticles is presented. A description of such a system can be obtained in terms of a two-coupled phase model with the solid particles in suspension in a fluid phase, i.e. the gas. It is assumed that the suspension is diluted so that particle-particle interaction can be ignored. Because the heat exchange between the nanoparticles and the gas is of main interest in this calculation, it is assumed in first approximation that the gas and the particles have the same velocity and pressure. The pressure is assumed to be function of time only. In this case, only the equations of continuity and energy for both the particulate phase and the gas phase. The two-coupled model is then solved in linear approximation and a system of four differential equations with constant coefficients is obtained. The system is diagonalized and the general solution of the two coupled system is obtained. The general solution is a combination of exponential decaying oscillatory functions for the temperature of the two phases, the pressure and the microbubble radial oscillations. It was found that the oscillatory behavior takes place in the MHz range.

UR - http://www.scopus.com/inward/record.url?scp=84878955985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878955985&partnerID=8YFLogxK

U2 - 10.1121/1.3046452

DO - 10.1121/1.3046452

M3 - Conference article

AN - SCOPUS:84878955985

VL - 5

JO - Proceedings of Meetings on Acoustics

JF - Proceedings of Meetings on Acoustics

SN - 1939-800X

M1 - 020002

ER -