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Force moments of an active particle in a complex fluid

Published online by Cambridge University Press:  22 September 2017

Gwynn J. Elfring*
Affiliation:
Department of Mechanical Engineering, Institute of Applied Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
*
Email address for correspondence: gelfring@mech.ubc.ca

Abstract

A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of previous calculations of the motion of both passive and active particles in Newtonian and non-Newtonian fluids.

Type
Rapids
Copyright
© 2017 Cambridge University Press 

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References

Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545570.Google Scholar
Becker, L. E., McKinley, G. H. & Stone, H. A. 1996 Sedimentation of a sphere near a plane wall: weak non-Newtonian and inertial effects. J. Non-Newtonian Fluid Mech. 63, 201233.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111157.CrossRefGoogle Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791810.CrossRefGoogle Scholar
Datt, C., Natale, G., Hatzikiriakos, S. G. & Elfring, G. J. 2017 An active particle in a complex fluid. J. Fluid Mech. 823, 675688.Google Scholar
Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2015 Squirming through shear-thinning fluids. J. Fluid Mech. 784, R1.Google Scholar
Einarsson, J. & Mehlig, B. 2017 Spherical particle sedimenting in weakly viscoelastic shear flow. Phys. Rev. Fluids 2, 063301.Google Scholar
Einarsson, J., Yang, M. & Shaqfeh, E. S. G.2017 The Einstein viscosity with fluid elasticity. arXiv:1705.06770 [physics.flu-dyn].CrossRefGoogle Scholar
Elfring, G. J. 2015 A note on the reciprocal theorem for the swimming of simple bodies. Phys. Fluids 27, 023101.Google Scholar
Elfring, G. J. & Goyal, G. 2016 The effect of gait on swimming in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 234, 814.Google Scholar
Elfring, G. J. & Lauga, E. 2015 Theory of locomotion in complex fluids. In Complex Fluids in Biological Systems, pp. 285319. Springer.Google Scholar
Elfring, G. J., Pak, O. S. & Lauga, E. 2010 Two-dimensional flagellar synchronization in viscoelastic fluids. J. Fluid Mech. 646, 505515.Google Scholar
Gomez-Solano, J. R., Blokhuis, A. & Bechinger, C. 2016 Dynamics of self-propelled Janus particles in viscoelastic fluids. Phys. Rev. Lett. 116, 138301.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Khair, A. S. & Squires, T. M. 2010 Active microrheology: a proposed technique to measure normal stress coefficients of complex fluids. Phys. Rev. Lett. 105, 156001.Google Scholar
Koch, D. L., Lee, E. F. & Mustafa, I. 2016 Stress in a dilute suspension of spheres in a dilute polymer solution subject to simple shear flow at finite Deborah numbers. Phys. Rev. Fluids 1, 013301.Google Scholar
Koch, D. L. & Subramanian, G. 2006 The stress in a dilute suspension of spheres suspended in a second-order fluid subject to a linear velocity field. J. Non-Newtonian Fluid Mech. 138 (2), 8797.Google Scholar
Lauga, E. 2009 Life at high Deborah number. Europhys. Lett. 86, 64001.Google Scholar
Lauga, E. 2014 Locomotion in complex fluids: integral theorems. Phys. Fluids 26, 081902.CrossRefGoogle Scholar
Lauga, E. & Michelin, S. 2016 Stresslets induced by active swimmers. Phys. Rev. Lett. 117, 148001.Google Scholar
Leal, L. G. 1979 The motion of small particles in non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 5, 3378.Google Scholar
Leal, L. G. 1980 Particle motions in a viscous fluid. Annu. Rev. Fluid Mech. 12, 435476.Google Scholar
Mathijssen, A. J. T. M., Shendruk, T. N., Yeomans, J. M. & Doostmohammadi, A. 2016 Upstream swimming in microbiological flows. Phys. Rev. Lett. 116, 028104.Google Scholar
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Pèclet numbers. J. Fluid Mech. 747, 572604.Google Scholar
Oppenheimer, N., Navardi, S. & Stone, H. A. 2016 Motion of a hot particle in viscous fluids. Phys. Rev. Fluids 1, 014001.Google Scholar
Pak, O. S., Zhu, L., Brandt, L. & Lauga, E. 2012 Micropropulsion and microrheology in complex fluids via symmetry breaking. Phys. Fluids 24, 103102.Google Scholar
Papavassiliou, D. & Alexander, G. P. 2015 The many-body reciprocal theorem and swimmer hydrodynamics. Europhys. Lett. 110, 44001.CrossRefGoogle Scholar
Papavassiliou, D. & Alexander, G. P. 2017 Exact solutions for hydrodynamic interactions of two squirming spheres. J. Fluid Mech. 813, 618646.Google Scholar
Rallison, J. M. 2012 The stress in a dilute suspension of liquid spheres in a second-order fluid. J. Fluid Mech. 693, 500507.CrossRefGoogle Scholar
Riley, E. E. & Lauga, E. 2015 Small-amplitude swimmers can self-propel faster in viscoelastic fluids. J. Theor. Biol. 382, 345355.CrossRefGoogle ScholarPubMed
Sharifi-Mood, N., Mozaffari, A. & Córdova-Figueroa, U. M. 2016 Pair interaction of catalytically active colloids: from assembly to escape. J. Fluid Mech. 798, 910954.Google Scholar
Squires, T. M. & Mason, T. G. 2010 Fluid mechanics of microrheology. Annu. Rev. Fluid Mech. 42, 413438.Google Scholar
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 41024104.Google Scholar
Zia, R. N. & Brady, J. F. 2015 Theoretical microrheology. In Complex Fluids in Biological Systems, pp. 113157. Springer.Google Scholar