## A model of acoustic absorption in fluids based on a continuous distribution of relaxation times

Vilensky, G., ter Haar, G., Saffari, N.
(2012)
*A model of acoustic absorption in fluids based on a continuous distribution of relaxation times.*
WAVE MOTION, 49 (1).
pp. 93-108.
ISSN 0165-2125

Full text not available from this repository.

## Abstract

This work extends the quasi-equilibrium relaxation theory of sound absorption in liquids to the case of continuous distribution of relaxation times. Such extension is needed when absorption mechanisms are not confined to the action of viscosity and heat conduction, but are mainly due to the excitation of a large number of internal molecular degrees of freedom. In this case the conventional Navier-Stokes equations are not sufficient to describe the fluid motion, and additional equations are required to model normal relaxation stresses. When relaxation frequencies form a sufficiently dense distribution, as is the case for many biological fluids, it makes sense to consider the limit of continuously distributed relaxation frequencies, in order to obtain the required equation for normal relaxation stresses. In contrast to its discrete counterparts, the proposed method avoids the use of a potentially infinite number of relaxation equations for a given set of distinct relaxation frequencies. Instead, these are replaced by a single evolution equation of Boltzmann type whose right-hand side is a linear combination of the time derivatives of density and entropy. The theological functions appearing before these derivatives are expressed in terms of the absorption coefficient. Since the dependence of absorption coefficient on sound frequency is measurable experimentally, these rheological coefficients can be recovered from experimental data. The key feature of the present study is that a closed system of equations of motion can be formulated directly from absorption measurement data on the basis of the theory proposed for the very wide range of absorption laws that can occur in practice. As an illustration of the generality of the present method, a number of absorption laws documented in the experimental literature are considered in detail, in order to derive the coefficients of the related systems of equations of motion for these liquids. For example, the methodology based on modelling of acoustic absorption in biologically soft tissue by the employment of fractional derivatives, which has been recently developed in the literature, is shown to be a special case of the proposed theory. (C) 2011 Elsevier B.V. All rights reserved.

Item Type: | Article |
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Authors (ICR Faculty only): | terHaar, Gail |

All Authors: | Vilensky, G., ter Haar, G., Saffari, N. |

Additional Information: | ISI Document Delivery No.: 868MO Times Cited: 0 Cited Reference Count: 38 Vilensky, G. ter Haar, G. Saffari, N. Engineering & Physical Sciences Research Council (EPSRC)[EP/F0257501/1] The authors gratefully wish to acknowledge the support of the Engineering & Physical Sciences Research Council (EPSRC) via grant number EP/F0257501/1. Elsevier science bv Amsterdam |

Uncontrolled Keywords: | Sound absorption High intensity focused ultrasound Relaxation losses Biological fluids Soft tissue frequency power-law fractional dynamics wave-equation media attenuation ultrasound propagation |

Research teams: | ICR divisions > Radiotherapy and Imaging > Therapeutic Ultrasound |

Depositing User: | Barry Jenkins |

Date Deposited: | 23 Jan 2012 12:46 |

Last Modified: | 23 Jan 2012 12:46 |

URI: | http://publications.icr.ac.uk/id/eprint/11333 |

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