Acoustic wave propagation in a viscoelastic fluid undergoing a simple steady shearing motion

Abstract

The theory for the prediction of the absorption and dispersion of forced acoustic waves propagating through a viscoelastic fluid in a steady simple shearing motion is presented. The stress tensor is represented by an approximate constitutive equation for a simple fluid, obtained by a functional expansion about the basic state of a motion with a constantstretching history. The linear term is written as a sum of integrals, having kernels identified as shear and compressional relaxation functions. The absorption and dispersion depends on the direction of acoustic propagation relative to the shearing axis. Two cases are examined and the appropriate relaxation functions, or alternatively, the complex viscosity functions, obtained. These forms are compared to the shear relaxation functions obtained from shear oscillation experiments. The special case of acoustic wave propagation through a viscoelastic fluid, otherwise at rest, is considered and the results are compared to existing theories and experimental data.