Biomedical Applications of Vibration and Acoustics in Imaging and Characterizations
1 Dynamic Radiation Force of Acoustic Waves
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When an acoustic wave encounters an object, a static or dynamic radiation force is generated on the object. Static radiation force, also known as radiation pressure, has been widely studied in both acoustics and electromagnetism. It is caused by the non-linear nature of wave propagation. On the other hand, dynamic radiation force might be understood as any time-dependent force caused by wave pressure in linear or nonlinear approximation. The purpose of this chapter is to present a theoretical framework of dynamic radiation force exerted by acoustic waves on suspended objects in fluids. Applications of dynamic radiation include new acoustic imaging methods such as vibroacoustography and non-destructive material evaluation. The following analysis stems from first principles based on the differential conservation equations of fluid dynamics. Throughout this chapter, non-viscous fluids and plane progressive waves are considered. In general, a theory for radiation force comprises two elements, namely, beam-forming for an acoustic source and scattering by the object target. An exact solution of the boundary-value problem for acoustic radiation force is nearly impossible. An approximate solution using perturbation theory is provided as an alternative. On this basis, radiation force is addressed in two steps. The boundary-value problem for beam-forming is solved in second-order approximation. The obtained acoustic fields form the primary waves in linear and non-linear scattering problem for the object. The primary and secondary (scattered) fields are integrated over the surface of the object yielding the radiation force. Within the theoretical description, the spectrum of dynamic radiation force up to second-order approximation is examined. We apply the theory of dynamic radiation force wielded by bichromatic plane waves on spherical targets. An extension of the theory for polychromatic planes waves is described. The theory presented in this chapter can be readily adapted for objects with other geometrical symmetry like cylinders.