Mean force on a finite-sized spherical particle due to an acoustic field in a viscous compressible medium.

An analytical expression to evaluate the second-order mean force (acoustic radiation force) on a finite-sized, rigid, spherical particle due to an acoustic wave is presented. The medium in which the particle is situated is taken to be both viscous and compressible. A far-field derivation approach has been used in determining the force, which is a function of the particle size, acoustic wavelength, and viscous boundary-layer thickness. It is assumed that the viscous length scale is negligibly small compared to the acoustic wavelength. The force expression presented here (i) reduces to the correct inviscid behavior (for both small- and finite-sized particles) and (ii) is identical to recent viscous results [M. Settnes and H. Bruus, Phys. Rev. E 85, 016327 (2012)] for small-sized particles. Further, the computed force qualitatively matches the computational fluid dynamics (finite-element) results [D. Foresti, M. Nabavi, and D. Poulikakos, J. Fluid Mech. 709, 581 (2012)] for finite-sized particles. Additionally, the mean force is interpreted in terms of a multipole expansion. Subsequently, considering the fact that the force expansion is an infinite series, the number of terms that are required or adequate to capture the force to a specified accuracy is also provided as a function of the particle size to acoustic wavelength ratio. The dependence of the force on particle density, kinematic viscosity, and bulk viscosity of the fluid is also investigated. Here, both traveling and standing waves are considered.