Dynamic Viscoelastic and Multiple Scattering Effects in Fiber Suspensions

Abstract

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. INTRODUCTIONSuspensions of flexible filaments or rod-like particles in either Newtonian or non-Newtonian fluids are encountered in a wide range of industrial applications in the papermaking, chemical, petroleum, mining and food industries. In particular, there is a growing interest in using ultrasound as a basis for nondestructive evaluation of concentrated suspensions of fibers in solvents and polymers such as in paper pulp suspensions and fiber-reinforced resin-matrix materials. Attanasio et al. (1969) measured the complex shear modulus of dilute suspensions of cellulose fibers as a function of frequency in the low acoustic range. Lastinger (1972) made measurements of sound speed and absorption in water-saturated stainlesssteel fibrous metals and concluded that sound absorption was qualitatively in agreement with Urick's theory for suspensions. Adams (1977) investigated the use of ultrasonic propagation measurements for the purpose of estimating the physical properties of paper fiber suspensions. McQueen (1978) developed simple acoustic theory of wave motion in two component

Effect of Inter-Fibre Distance on Energy Transfer in Unidirectional Composites Containing Ultrasonic Waves

“…In this paper, noting that the most fundamental problem of 2D multiple scattering in fibre-reinforced composites involves a cluster of two embedded fibres, we employ the classical approach of transformation of cylindrical wave functions [16,[21][22][23][24] to study scattering of Horizontally polarized shear (SH) waves in a two fibre-matrix composite system. The problem is of a scalar nature in this relatively simple case, as wave polarization is parallel to the fibres and no mode conversion occurs.…”

Multiple scattering of an acoustic wave from a network of cylindrical rods encased in a solid viscoelastic medium

“…Chen et al [15] 129 studied the multiple scattering of sound waves from circular cylin-130 ders embedded in an elastic medium. 131 Hasheminejad and Alibakhshi [16] In this paper, we first review the general case of scattering of a 142 plane obliquely incident wave from a transversely isotropic cylin-143 der embedded in a solid elastic matrix. We then, employ the Graf's 144 Addition Theorem [19] and extend this method to properly formu- …”