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Dropping slender-body theory into the mud

  • S. E. Spagnolie (a1)

Abstract

The equations describing classical viscous fluid flow are notoriously challenging to solve, even approximately, when the flow is host to one or many immersed bodies. When an immersed body is slender, the smallness of its aspect ratio can sometimes be used as a basis for a ‘slender-body theory’ describing its interaction with the surrounding environment. If the fluid is complex, however, such theories are generally invalid and efforts to understand the dynamics of immersed bodies are almost entirely numerical in nature. In a valiant effort, Hewitt & Balmforth (J. Fluid Mech., vol. 856, 2018, pp. 870–897) have unearthed a theory to describe the motion of slender bodies in a viscoplastic fluid, ‘fluids’ such as mud or toothpaste which can be coaxed to flow, but only with a sufficiently large amount of forcing. Mathematical theories for some tremendously complicated physical systems may now be within reach.

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Copyright

Corresponding author

Email address for correspondence: spagnolie@math.wisc.edu

References

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Balmforth, N. J., Frigaard, I. A. & Ovarlez, G. 2014 Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu. Rev. Fluid Mech. 46, 121146.
Coussot, P. 2014 Yield stress fluid flows: A review of experimental data. J. Non-Newtonian Fluid Mech. 211, 3149.
Dabade, V., Marath, N. K. & Subramanian, G. 2015 Effects of inertia and viscoelasticity on sedimenting anisotropic particles. J. Fluid Mech. 778, 133188.
Elfring, G. J. & Lauga, E. 2015 Theory of locomotion through complex fluids. In Complex Fluids in Biological Systems, pp. 283317. Springer.
Fu, H. C., Wolgemuth, C. W. & Powers, T. R. 2009 Swimming speeds of filaments in nonlinearly viscoelastic fluids. Phys. Fluids 21, 033102.
Gray, J. & Hancock, G. 1955 The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32 (4), 802814.
Hewitt, D. R. & Balmforth, N. J. 2017 Taylor’s swimming sheet in a yield-stress fluid. J. Fluid Mech. 828, 3356.
Hewitt, D. R. & Balmforth, N. J. 2018 Viscoplastic slender-body theory. J. Fluid Mech. 856, 870897.
Hosoi, A. E. & Goldman, D. I. 2015 Beneath our feet: strategies for locomotion in granular media. Annu. Rev. Fluid Mech. 47, 431453.
Johnson, R. 1980 An improved slender-body theory for Stokes-flow. J. Fluid Mech. 99, 411431.
Keller, J. & Rubinow, S. 1976 Swimming of flagellated microorganisms. Biophys. J. 16 (2), 151170.
Koens, L. & Lauga, E. 2018 The boundary integral formulation of Stokes flows includes slender-body theory. J. Fluid Mech. 850, 112.
Lauga, E. & Powers, T. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.
Leal, L. G. 1975 The slow motion of slender rod-like particles in a second-order fluid. J. Fluid Mech. 69, 305337.
Leshansky, A. M. 2009 Enhanced low-Reynolds-number propulsion in heterogeneous viscous environments.. Phys. Rev. E 80, 051911.
Li, C., Thomases, B. & Guy, R. D.2018 Orientation dependent elastic stress concentration at tips of slender objects translating in viscoelastic fluids, arXiv:1809.03563.
Lindner, A. & Shelley, M. 2015 Elastic fibers in flows. In Fluid-Structure Interactions in Low-Reynolds-Number Flows, pp. 168192. Royal Society of Chemistry.
Liu, B., Powers, T. R. & Breuer, K. S. 2011 Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl. Acad. Sci. USA 108, 1951619520.
Martinez, V. A., Schwarz-Linek, J., Reufer, M., Wilson, L. G., Morozov, A. N. & Poon, W. C. K. 2014 Flagellated bacterial motility in polymer solutions. Proc. Natl. Acad. Sci. USA 111, 1777117776.
Mori, Y., Ohm, L. & Spirn, D.2018 Theoretical justification and error analysis for slender body theory, arXiv:1807.00178.
Pegler, S. S. & Balmforth, N. J. 2013 Locomotion over a viscoplastic film. J. Fluid Mech. 727, 129.
Spagnolie, S. E., Liu, B. & Powers, T. R. 2013 Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes. Phys. Rev. Lett. 111, 068101.
Sznitman, J. & Arratia, P. E. 2015 Locomotion through complex fluids: an experimental view. In Complex Fluids in Biological Systems, pp. 245281. Springer.
Tokpavi, D. L., Magnin, A. & Jay, P. 2008 Very slow flow of Bingham viscoplastic fluid around a circular cylinder. J. Non-Newtonian Fluid Mech. 154, 6576.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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