Analytical and numerical treatment of pulsed wave propagation into a viscous fluid

Abstract

A transient analytical expression for the propagation of pulsed ultrasound through a viscous fluid is derived by evaluating the Laplace transform in the complex domain. The numerical solution of the viscous wave equation without any restricting approximations is developed for a full space with an impulsive excitation at the origin. Different values of the viscosity coefficient for a given sound speed clearly delineate the transition from a pure parabolic, or diffusive to a pure hyperbolic or wave propagation behavior. This region is often of crucial importance from a practical point of view as ultrasonic instrumentation in medical imaging and nondestructive testing must compensate not only for phase differences due to propagation delays but also for pulse distortion due to attenuation mechanisms in the medium of interest.<>