Ultrasonic Scattering by a Spheroidal Suspension Including Dissipative Effects

This study treats the axisymmetric interaction of a plane compressional sound wave with a viscoelastic (viscous) prolate spheroidal particle (droplet) suspended in a boundless viscous fluid medium. The method of eigen‐function expansion along with the novel features of Havriliak‐Negami model for viscoelastic material behavior and the linearized equations of Navier‐Stokes for wave motion in a viscous non‐heat‐conducting compressible fluid are employed to develop a closed form series solution involving Spheroidal harmonics of complex argument. The complications arising due to the non‐orthogonality of angular Spheroidal functions corresponding to different wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Spheroidal functions in terms of Lengedre functions which are themselves expanded in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of unknown scattering and transmission coefficients. The presented solution demonstrates that the acoustic characteristics of particulate suspensions are strongly influenced by spheroidicity of particle cross‐section. Limiting case involving an elastic (ideal) spheroidal particle (droplet) in an ideal fluid is considered and fair agreement with available solution is established.

Keywords:

• Acoustic scattering
• spheroidal particle
• viscous/viscoelastic dissipation effects

The authors wish to sincerely thank Dr. Peter E. Fallon for valuable consultations on computation of spheroidal functions of complex argument; they also greatly appreciate Dr. M. Alizadeh for providing exclusive access to the computing facilities of the computational mechanics laboratory.