Anomalous absorption of bulk shear acoustic waves by an ultra-thin layer of a non-Newtonian fluid

Abstract

A strong maximum of absorptivity (as much as dozens of per cent) of bulk shear acoustic waves by an ultra-thin layer of a non-Newtonian fluid between two solid surfaces is shown to be achieved at an optimal layer thickness. This optimal thickness is demonstrated to be usually much smaller than the wavelength and the wave penetration depth in the fluid. The coefficients of reflection, transmission, and absorption of shear waves polarized perpendicular to the plane of incidence are determined as functions of incidence angle, layer thickness, fluid viscosity, relaxation time(s), frequency, and parameters of solids. A frictional contact approximation, in which the layer can be considered as a contact with friction is justified for non-Newtonian fluids. The anomalous absorption of bulk shear waves in thin nonuniform fluid layers with viscosity and/or relaxation time varying across the layer is analyzed in the frictional contact approximation. It is shown that unlike the anomalous absorption in Newtonian fluids, the anomalous absorption in non-Newtonian fluid layers is frequency dependent even in the frictional contact approximation. This dependence is analyzed analytically and numerically.