Mean force on a finite-sized rigid particle, droplet, or bubble in a viscous compressible medium

Journal Article · Fri Oct 16 00:00:00 EDT 2015 · Physics of Fluids

DOI:https://doi.org/10.1063/1.4933051· OSTI ID:1469559

Annamalai, Subramanian  ^[1]; Balachandar, S. ^[1]

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1. Univ. of Florida, Gainesville, FL (United States). Department of Mechanical and Aerospace Engineering

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 (R₀), wavelength of the incoming acoustics (λ), and the momentum diffusion thickness of the ambient fluid (δ^o). While R₀ 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 R₀/λ « 1, (ii) inviscid bubbles with finite R₀/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 R₀/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/R₀ on the mean second-order force.

• Research Organization: Univ. of Florida, Gainesville, FL (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0002378
• OSTI ID: 1469559
• Alternate ID(s): OSTI ID: 1224221
• Journal Information: Physics of Fluids, Vol. 27, Issue 10; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

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