Dynamic viscoelastic and multiple scattering effects in fiber suspensions

This study considers the most fundamental problem of 2-D acoustic scattering in fiber suspensions. It treats the interaction of a plane compressional sound wave with a cluster of two flexible fibers submerged in a boundless viscous fluid medium. The dynamic viscoelastic properties of the fibers and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the problem. The translational addition theorem for cylindrical wave functions, the Havriliak-Negami model for viscoelastic material behaviors and the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in the form of an infinite series. The prime objectives are to investigate the influence of dynamic viscoelastic properties of fiber material as well as multiple scattering interaction effects on acoustic scattering and its associated quantities. The analytical results are illustrated with a numerical example in which two identical viscoelastic fibers are insonified by a plane sound wave at broadside/end-on incidence. The backscattering form function amplitude and the spatial distribution of the total acoustic pressure are numerically evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, material properties, and proximity of the two fibers are examined. A limiting case involving a pair of rigid cylinders in an ideal fluid is considered, and fair agreement with a well-known solution is established.