Estudo do fenômeno de espalhamento acústico por meio do Método de Elementos Finitos FEM

Abstract

The propagation of acoustic waves in particles is a complex phenomenon that involves the interaction between waves and particles, resulting in the reflection, transmission, and scattering of acoustic energy. The study of acoustic scattering involves analyzing the solutions of the Helmholtz equation, considering boundary conditions and the expansion into partial waves. This analysis allows us to understand how particles interact with acoustic waves and contribute to the propagation and scattering of acoustic energy. Most theoretical analyses on scattering and acoustic radiation force Frad (the stationary force caused by the linear change of momentum flux during the scattering of an acoustic wave by a particle) in fluids assume that particles have a spherical shape, but this simplification does not represent all real-world situations. The spherical shape is considered an idealized geometric form, where the particle is symmetrical in all directions. This assumption simplifies the problem by allowing simpler mathematical equations to describe the particle’s behavior in response to acoustic radiation. However, when considering particles with non-spherical shapes, exact analytical techniques can become impractical. In such cases, more sophisticated numerical approaches are required, such as finite element methods, finite difference methods, or boundary element methods, to solve the scattering problem and obtain precise and realistic results. Here, we introduce a semi-analytical approach to deal with axially symmetric particles of sub-wavelength size (Rayleigh scattering limit) immersed in an ideal isotropic fluid. The scattering coefficients that reflect the monopole and dipole modes are determined through the numerical resolution of the scattering problem. Our method is compared with the exact result for a rigid sub-wavelength sphere in water, a fluid sphere, and a viscoelastic solid. Additionally, we extend our analysis to an spheroid, a geometry that approximates a sphere but involves analytical complications that make exact solutions more challenging. These studies are fundamental for various biomedical applications, which utilize techniques such as particle trapping, levitation, and acoustic tweezers, among others. Techniques for immobilizing particles and cells in microfluidic systems are often necessary in the concept of Lab-On-Chip technology, where particles with dimensions much smaller than the acoustic wavelength are common, known as the Rayleigh scattering regime, found in Acoustofluidic devices.