Propagation of acoustic waves in steady extensional flows on non-Newtonian fluids

An analysis for the calculation of the attenuation and sound speed of a plane acoustic wave propagating through a non-Newtonian fluid that is undergoing a simple steady extensional motion is presented. The constitutive representation for the stress tensor in terms of the deformation gradient is developed for the model of a simple fluid, An explicit form is obtained for the superposed acoustic motion on the basic flow by using a functional Taylor's series having linear forms that are represented by integrals whose kernels are relaxation functions that depend on the extensional rates. An alternative representation is given as rate-dependent complex viscosities that depend on the relative orientation of the acoustic vector to the axes of extension. Several examples are described that are experimentally realizable and that can provide information on the rheological nature of the non-Newtonian fluid. [Work supported by NSF.]