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

Abstract

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 (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, 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 δo/R0 on the mean second-order force.

Authors:
ORCiD logo [1];  [1]
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  1. Univ. of Florida, Gainesville, FL (United States). Department of Mechanical and Aerospace Engineering
Publication Date:
Research Org.:
Univ. of Florida, Gainesville, FL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1469559
Alternate Identifier(s):
OSTI ID: 1224221
Grant/Contract Number:  
NA0002378
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Fluids
Additional Journal Information:
Journal Volume: 27; Journal Issue: 10; Journal ID: ISSN 1070-6631
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 42 ENGINEERING

Citation Formats

Annamalai, Subramanian, and Balachandar, S. Mean force on a finite-sized rigid particle, droplet, or bubble in a viscous compressible medium. United States: N. p., 2015. Web. doi:10.1063/1.4933051.
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Annamalai, Subramanian, & Balachandar, S. Mean force on a finite-sized rigid particle, droplet, or bubble in a viscous compressible medium. United States. doi:10.1063/1.4933051.
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Annamalai, Subramanian, and Balachandar, S. Fri . "Mean force on a finite-sized rigid particle, droplet, or bubble in a viscous compressible medium". United States. doi:10.1063/1.4933051. https://www.osti.gov/servlets/purl/1469559.
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@article{osti_1469559,
title = {Mean force on a finite-sized 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 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 (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, 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 δo/R0 on the mean second-order 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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DOI:  10.1063/1.4933051
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