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A note on forces exerted by a Stokeslet on confining boundaries

Published online by Cambridge University Press:  31 October 2019

Viktor Škultéty
Affiliation:
SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
Alexander Morozov*
Affiliation:
SUPA, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
*
Email address for correspondence: alexander.morozov@ed.ac.uk

Abstract

We consider a Stokeslet applied to a viscous fluid next to an infinite, flat wall, or in between two parallel walls. We calculate the forces exerted by the resulting flow on the confining boundaries, and use the results obtained to estimate the hydrodynamic contribution to the pressure exerted on boundaries by force-free self-propelled particles.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Bhattacharya, S. & Bławzdziewicz, J. 2002 Image system for Stokes-flow singularity between two parallel planar walls. J. Math. Phys. 43 (11), 57205731.Google Scholar
Bhattacharya, S. & Blawzdziewicz, J. 2008 Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution. J. Chem. Phys. 128 (21), 214704.Google Scholar
Bickel, T. 2007 Hindered mobility of a particle near a soft interface. Phys. Rev. E 75, 041403.Google Scholar
Blake, J. R. 1971 A note on the image system for a Stokeslet in a no-slip boundary. Math. Proc. Camb. Phil. Soc. 70, 303310.Google Scholar
Chwang, A. T. & Wu, T. Y.-T. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for stokes flows. J. Fluid Mech. 67, 787815.Google Scholar
Cichocki, B. & Jones, R. B. 1998 Image representation of a spherical particle near a hard wall. Physica A 258 (3), 273302.Google Scholar
Daddi-Moussa-Ider, A. & Gekle, S. 2018 Brownian motion near an elastic cell membrane: A theoretical study. Eur. Phys. J. E 41, 19.Google Scholar
Daddi-Moussa-Ider, A., Lisicki, M., Mathijssen, A. J. T. M., Hoell, C., Goh, S., Bławzdziewicz, J., Menzel, A. M. & Löwen, H. 2018 State diagram of a three-sphere microswimmer in a channel. J. Phys.: Condens. Matter 30, 254004.Google Scholar
Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S. & Goldstein, R. E. 2011 Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl Acad. Sci. USA 108, 1094010945.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics, 2nd edn. Kluwer.Google Scholar
Jepson, A., Martinez, V. A., Schwarz-Linek, J., Morozov, A. & Poon, W. C. K. 2013 Enhanced diffusion of nonswimmers in a three-dimensional bath of motile bacteria. Phys. Rev. E 88, 041002.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics, 2nd edn. Butterworth-Heinemann.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.Google Scholar
Liron, N. & Mochon, S. 1976 Stokes flow for a stokeslet between two parallel flat plates. J. Engng Maths 10, 287303.Google Scholar
López, H. M., Gachelin, J., Douarche, C., Auradou, H. & Clément, E. 2015 Turning bacteria suspensions into superfluids. Phys. Rev. Lett. 115, 028301.Google Scholar
Navardi, S. & Bhattacharya, S. 2010 A new lubrication theory to derive far-field axial pressure difference due to force singularities in cylindrical or annular vessels. J. Math. Phys. 51 (4), 043102.Google Scholar
Saintillan, D. 2018 Rheology of active fluids. Annu. Rev. Fluid Mech. 50 (1), 563592.Google Scholar
Solon, A. P., Fily, Y., Baskaran, A., Cates, M. E., Kafri, Y., Kardar, M. & Tailleur, J. 2015 Pressure is not a state function for generic active fluids. Nat. Phys. 11, 673678.Google Scholar
Spagnolie, S. E. & Lauga, E. 2012 Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105147.Google Scholar
Stenhammar, J., Nardini, C., Nash, R. W., Marenduzzo, D. & Morozov, A. 2017 Role of correlations in the collective behavior of microswimmer suspensions. Phys. Rev. Lett. 119, 028005.Google Scholar
Takatori, S. C., Yan, W. & Brady, J. F. 2014 Swim pressure: stress generation in active matter. Phys. Rev. Lett. 113, 028103.Google Scholar
Yang, X., Manning, M. L. & Marchetti, M. C. 2014 Aggregation and segregation of confined active particles. Soft Matt. 10, 64776484.Google Scholar