Validity of the linear viscoelastic model for a polymer cylinder with ultrasonic hysteresis-type absorption in a nonviscous fluid

TL;DR

This paper investigates the conditions under which the linear viscoelastic model accurately describes ultrasonic absorption in polymer cylinders submerged in non-viscous fluids, emphasizing energy conservation and the validity domain of the model.

Contribution

It establishes mathematical constraints on absorption coefficients ensuring the model's validity and highlights the importance of the optical theorem in verifying these conditions.

Findings

Positive absorption efficiency is necessary for model validity.

Forbidden parameter values lead to unphysical negative efficiencies.

Numerical analysis confirms the validity domain depends on size, mode, and shear-wave absorption.

Abstract

A necessary condition for the validity of the linear viscoelastic model for a (passive) polymeric cylinder with an ultrasonic hysteresis-type absorption submerged in a non-viscous fluid requires that the absorption efficiency is positive (Qabs > 0) satisfying the law of the conservation of energy. This condition imposes restrictions on the values attributed to the normalized absorption coefficients for the compressional and shear-wave wavenumbers for each partial-wave mode n. The forbidden values produce negative axial radiation force, absorption and extinction efficiencies, as well as an enhancement of the scattering efficiency, not in agreement with the conservation of energy law. Numerical results for the radiation force, extinction, absorption and scattering efficiencies are performed for three viscoelastic (VE) polymer cylinders immersed in a non-viscous host liquid (i.e. water) with particular emphasis on the shear-wave absorption coefficient of the cylinder, the dimensionless size parameter and the partial-wave mode number n. Mathematical constraints are established for the non-dimensional absorption coefficients of the longitudinal and shear waves for a cylinder (i.e. 2D case) and a sphere (i.e. 3D case) in terms of the sound velocities in the VE material. The analysis suggests that the domain of validity for any viscoelastic model describing acoustic attenuation inside a lossy cylinder (or sphere) in a non-viscous fluid must be verified based upon the optical theorem.