Propagation of acoustic pulses in some fluids with yield stress

Abstract

This study is devoted to the derivation of approximate equations governing acoustic pulses in flows with yield stress, including some time-dependent flows with a slow dependence on time of yield stress and apparent viscosity. The modeling of yield stress and apparent viscosity in the vicinity of a zero deformation rate allows us to consider a thixotropic fluid as a Bingham plastic with coefficients that are dependent on time. The ordering scheme results in equations that are valid in leading order with respect to a number of small parameters. The unusual property of the domains of a waveform with positive and negative shear stress to propagate with different velocities is discovered. The illustration concerns the initially bipolar acoustic pulse, which becomes positive after some time. The proposed theory predicts broadening of a pulse due to the yield stress, starting at some time after the beginning of its evolution.