Mean force on a finitesized rigid particle, droplet, or bubble in a viscous compressible medium
In this paper, a force formulation to compute the axial acoustic mean secondorder force on finitesized 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 farfield 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 secondorder 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, higherorder 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 secondorder force.
 Authors:

^{[1]}
;
^{[1]}
 Univ. of Florida, Gainesville, FL (United States). Department of Mechanical and Aerospace Engineering
 Publication Date:
 Grant/Contract Number:
 NA0002378
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Fluids
 Additional Journal Information:
 Journal Volume: 27; Journal Issue: 10; Journal ID: ISSN 10706631
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Univ. of Florida, Gainesville, FL (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING
 OSTI Identifier:
 1469559
 Alternate Identifier(s):
 OSTI ID: 1224221
Annamalai, Subramanian, and Balachandar, S. Mean force on a finitesized rigid particle, droplet, or bubble in a viscous compressible medium. United States: N. p.,
Web. doi:10.1063/1.4933051.
Annamalai, Subramanian, & Balachandar, S. Mean force on a finitesized rigid particle, droplet, or bubble in a viscous compressible medium. United States. doi:10.1063/1.4933051.
Annamalai, Subramanian, and Balachandar, S. 2015.
"Mean force on a finitesized rigid particle, droplet, or bubble in a viscous compressible medium". United States.
doi:10.1063/1.4933051. https://www.osti.gov/servlets/purl/1469559.
@article{osti_1469559,
title = {Mean force on a finitesized rigid particle, droplet, or bubble in a viscous compressible medium},
author = {Annamalai, Subramanian and Balachandar, S.},
abstractNote = {In this paper, a force formulation to compute the axial acoustic mean secondorder force on finitesized 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 farfield 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 secondorder force: mean radius of the spherical inclusion (R0), wavelength of the incoming acoustics (λ), and the momentum diffusion thickness of the ambient fluid (δo). 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, higherorder 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 δo/R0 on the mean secondorder force.},
doi = {10.1063/1.4933051},
journal = {Physics of Fluids},
number = 10,
volume = 27,
place = {United States},
year = {2015},
month = {10}
}
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