skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections

Abstract

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g.J. Phys. Chem. B, vol. 109 (45), 2005, pp. 21406–21412;J. Fluid Mech., vol. 637, 2009, pp. 285–303) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework produces unsteady drag coefficients that depend on particle density. This is inconsistent, since the problem can be formulated mathematically without any reference to the particle’s density. We address this inconsistency in our work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short-time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature ofmore » the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation and the method of reflections. We show that our modifications to Felderhof’s framework would become significant for systems of metallic nanoparticles in liquids.« less

Authors:
ORCiD logo; ;
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1538919
DOE Contract Number:  
FG02-04ER54742
Resource Type:
Journal Article
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 841; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Mechanics; Physics

Citation Formats

Simha, A., Mo, J., and Morrison, P. J. Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections. United States: N. p., 2018. Web. doi:10.1017/jfm.2018.87.
Simha, A., Mo, J., & Morrison, P. J. Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections. United States. doi:10.1017/jfm.2018.87.
Simha, A., Mo, J., and Morrison, P. J. Thu . "Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections". United States. doi:10.1017/jfm.2018.87.
@article{osti_1538919,
title = {Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections},
author = {Simha, A. and Mo, J. and Morrison, P. J.},
abstractNote = {Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g.J. Phys. Chem. B, vol. 109 (45), 2005, pp. 21406–21412;J. Fluid Mech., vol. 637, 2009, pp. 285–303) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework produces unsteady drag coefficients that depend on particle density. This is inconsistent, since the problem can be formulated mathematically without any reference to the particle’s density. We address this inconsistency in our work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short-time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature of the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation and the method of reflections. We show that our modifications to Felderhof’s framework would become significant for systems of metallic nanoparticles in liquids.},
doi = {10.1017/jfm.2018.87},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 841,
place = {United States},
year = {2018},
month = {3}
}