Forces acting on a small particle in an acoustical field in a viscous fluid

Abstract

We calculate the acoustic radiation force from an ultrasound wave on a compressible, spherical particle suspended in a viscous fluid. Using Prandtl-Schlichting boundary-layer theory, we include the kinematic viscosity of the solvent and derive an analytical expression for the resulting radiation force, which is valid for any particle radius and boundary-layer thickness provided that both of these length scales are much smaller than the wavelength of the ultrasound wave (mm in water at MHz frequencies). The acoustophoretic response of suspended microparticles is predicted and analyzed using parameter values typically employed in microchannel acoustophoresis.

Performance Study of Acoustophoretic Microfluidic Silicon-Glass Devices by Characterization of Material- and Geometry-Dependent Frequency Spectra

“…It must be noted that the acoustophoretic mean orientation is based on the assumption that the dipole scattering coefficient in the Gorkov potential [2] equals zero since the definition equation (25) takes into account only the gradient of the pressure field. This is a good approximation when the acoustophoretic separation involves cells suspended in aqueous media, as the cell density is usually quite close to water density, almost canceling the contribution of the dipole scattering coefficient.…”

“…These devices exploit standing acoustic pressure waves that, through the purely mechanical parameters, such as compressibility, density, and size, induce fluid-and particle-specific forces [1][2][3] leading to acoustophoresis [4]. This phenomenon is the basis of the development of gentle [5,6] and robust methods for concentrating [7], trapping [8], washing [9], aligning [10], and separating cells [11][12][13].…”

Particle separation by phase modulated surface acoustic waves

“…This type of manipulation relies on the acoustic radiation force [12][13][14][15] to drive particles towards the pressure nodes or antinodes of a standing wave acoustic field. Numerous strategies are available to acoustically manipulate and sort microparticles and cells.…”

“…[12][13][14][15]36 The analysis of the acoustic radiation force dates to the work of King,12 where the treatment of both standing and traveling acoustic fields was carried out on incompressible spheres, much smaller in size than the wavelength of the field, at the Rayleigh scattering limit. 15 Yosioka and Kawasima 13 extended this discussion by introducing compressibility of the spheres. These results were summarized and reformulated by Gorkov 14 and a compact equation for the acoustic radiation force in standing wave fields was provided as a gradient of the acoustic potential.…”

“…These results were summarized and reformulated by Gorkov 14 and a compact equation for the acoustic radiation force in standing wave fields was provided as a gradient of the acoustic potential. Recently, Settnes and Bruus 15 included viscosity of the surrounding media in the analytical treatment and found this contributed significantly to the magnitude of forces arising from travelling waves. Particles generally have positive acoustic contrast factor and therefore, when subjected to an acoustic standing wave, they experience a force that steers them towards the pressure node.…”