Sound Propagation in Non-Newtonian Fluids

Abstract

A perturbation analysis is applied to the basic hydrodynamic equations and developed to determine the non-Newtonian effects of a small-signal plane wave propagating through a viscous fluid which is continuous, homogeneous, and isotropic. With the emphasis on liquids, the analysis is applied to the case of a Powell-Eyring fluid (which specializes to the case of a Prandtl-Eyring model) in order to ascertain the magnitudes of second and third-order effects occurring as a result of viscous nonlinearity. It is established that the appearance of second and third harmonics, or “harmonic distortions” of the fundamental wave, can provide a measure of the deviation from Newtonian behavior that should prove useful in laboratory practice. For the purpose of demonstrating the sonic effects of non-Newtonian fluidity, numerical results are obtained for the specially assumed case of sound propagation in compressed water acting as a Powell-Eyring fluid. The second and third-order harmonic distortions are found as functions of fundamental wave frequency, signal strength, and viscous parameters.