DOE OSTI2015
In this paper, a force formulation to compute the axial acoustic mean second-order force on finite-sized compressible and rigid particles is presented. The flow inside and outside the spherical inclusion is considered viscous and compressible. Other than for volumetric pulsations of the bubble/droplet, the sphericity of the inclusion is maintained (taken to be unity). A far-field derivation approach has been used to compute the force due to standing and traveling waves; and the force is expressed as a multipole expansion (infinite series). In case of a bubble and a rigid particle, there exist three length scales that govern the mean second-order force: mean radius of the spherical inclusion (R 0 ), wavelength of the incoming acoustics (λ), and the momentum diffusion thickness of the ambient fluid (δ o ). While R 0 and λ are arbitrary, we assume the viscous length scale is negligibly small compared to the acoustic wavelength. In case of a droplet, however, the following additional parameters (inside to outside fluid ratios) also play a role: density ratio ($\sim\atop{p}$), viscosity ratio ($\sim\atop{μ}$, and speed of sound ratio ($\sim\atop{c}$). The force expression yields the correct behavior in several limiting cases considered: (i) inviscid bubble and droplets with R 0 /λ « 1, (ii) inviscid bubbles with finite R 0 /λ, and (iii) finite size rigid immovable particles. In general, while the monopole alone is sufficient to capture the force for small bubbles, higher-order terms are found to be important when R 0 /λ ≥ 0.02. In addition to reporting similar behavior for droplets, we study the effect arising from $\sim\atop{p}$, $\sim\atop{μ}$, $\sim\atop{c}$, and δ o /R 0 on the mean second-order force.