Comparison of finite element and analytical modeling of scattering of an acoustic wave by particles in a fluid

Abstract

Ultrasonic wave propagation through dispersions of particles in liquids is of interest for particle characterization and process monitoring applications. Interpretation of the measurements relies on a theoretical model; we typically use a multiple scattering model which builds on models of scattering by independent particles. We report finite element modeling of an acoustic wave propagating through a liquid and interacting with a particle, using the linearized thermo-acoustic equations for propagation in a viscous liquid. We demonstrate that the interaction of the acoustic field with the particle leads to decaying thermal and shear wave fields in the region very close to the particle. Since the length scale of the thermal and shear decay is orders of magnitude smaller than the propagational mode acoustic wavelength, fine meshing is necessary in the region of the particle/fluid boundary. The simulation results are compared with analytical solutions for scattering of a plane wave by a single spherical particle, provided by Epstein and Carhart [JASA, 25, 533, (1953)] and Allegra and Hawley [(JASA, 51, 1546 (1972)].