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Slender phoretic theory of chemically active filaments

Published online by Cambridge University Press:  09 July 2020

Panayiota Katsamba Open the ORCID record for Panayiota Katsamba [Opens in a new window] ,
Sébastien Michelin Open the ORCID record for Sébastien Michelin [Opens in a new window]  and
Thomas D. Montenegro-Johnson Open the ORCID record for Thomas D. Montenegro-Johnson [Opens in a new window]
Panayiota Katsamba
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Sébastien Michelin
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
Thomas D. Montenegro-Johnson*
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
*
†Email address for correspondence: [email protected]
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Abstract

Artificial microswimmers, or ‘microbots’, have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their environment. Traditionally, self-phoretic particles are point like, but slender phoretic rods have become an increasingly prevalent design. While there has been substantial interest in creating efficient asymptotic theories for slender phoretic rods, hitherto such theories have been restricted to straight rods with axisymmetric patterning. However, modern manufacturing methods will soon allow fabrication of slender phoretic filaments with complex three-dimensional shapes. In this paper, we develop a slender body theory for the solute of self-diffusiophoretic filaments of arbitrary three-dimensional shape and patterning. We demonstrate analytically that, unlike other slender body theories, first-order azimuthal variations arising from curvature and confinement can make a leading-order contribution to the swimming kinematics.

JFM classification

Low-Reynolds-number flows: Slender-body theory Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A24
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Baker, R. D., Montenegro-Johnson, T. D., Sediako, A. D., Thomson, M. J., Sen, A., Lauga, E. & Aranson, I. S. 2019 Shape-programmed 3D printed swimming microtori for the transport of passive and active agents. Nat. Commun. 10 (1), 1–10.CrossRefGoogle ScholarPubMed
Bertin, N., Spelman, T. A., Stephan, O., Gredy, L., Bouriau, M., Lauga, E. & Marmottant, P. 2015 Propulsion of bubble-based acoustic microswimmers. Phys. Rev. A 4 (6), 064012.Google Scholar
Blake, J. R. 1971 Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number. Bull. Austral. Math. Soc. 5 (2), 255–264.CrossRefGoogle Scholar
Brown, A. & Poon, W. 2014 Ionic effects in self-propelled Pt-coated Janus swimmers. Soft Matt. 10, 4016–4027.CrossRefGoogle ScholarPubMed
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 (4), 787–815.CrossRefGoogle Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44 (4), 791–810.CrossRefGoogle Scholar
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437 (7060), 862–865.CrossRefGoogle ScholarPubMed
Ebbens, S., Gregory, D. A., Dunderdale, G., Howse, J. R., Ibrahim, Y., Liverpool, T. B. & Golestanian, R. 2014 Electrokinetic effects in catalytic platinum-insulator Janus swimmers. Eur. Phys. Lett. 106, 58003.CrossRefGoogle Scholar
Gaffney, E. A., Gadêlha, H., Smith, D. J., Blake, J. R. & Kirkman-Brown, J. C. 2011 Mammalian sperm motility: observation and theory. Annu. Rev. Fluid Mech. 43, 501–528.CrossRefGoogle Scholar
Gao, W., Sattayasamitsathit, S., Manesh, K. M., Weihs, D. & Wang, J. 2010 Magnetically powered flexible metal nanowire motors. J. Am. Chem. Soc. 132 (41), 14403–14405.CrossRefGoogle ScholarPubMed
Ghosh, A. & Fischer, P. 2009 Controlled propulsion of artificial magnetic nanostructured propellers. Nano Lett. 9 (6), 2243–2245.CrossRefGoogle ScholarPubMed
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9 (5), 126.CrossRefGoogle Scholar
Götz, T.2000 Interactions of fibers and flow: asymptotics, theory and numerics. PhD thesis, University of Kaiserslautern, Germany.Google Scholar
Gray, J. & Hancock, G. J. 1955 The propulsion of sea-urchin spermatozoa. J. Expl Biol. 32 (4), 802–814.Google Scholar
Hall-McNair, A. L., Montenegro-Johnson, T. D., Gadêlha, H., Smith, D. J. & Gallagher, M. T. 2019 Efficient implementation of elastohydrodynamics via integral operators. Phys. Rev. Fluids 4 (11), 113101.CrossRefGoogle Scholar
Hancock, G. J. 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. Lond. A 217 (1128), 96–121.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice Hall.Google Scholar
Howse, J. R., Jones, R. A. L., Ryan, A. J., Gough, T., Vafabakhsh, R. & Golestanian, R. 2007 Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99, 048102.CrossRefGoogle ScholarPubMed
Ibrahim, Y., Golestanian, R. & Liverpool, T. 2017 Shape dependent phoretic propulsion of slender active particles. Phys. Rev. Fluids 3 (3), 033101.Google Scholar
Johnson, R. E. 1979 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411–431.CrossRefGoogle Scholar
Koens, L. & Lauga, E. 2018 The boundary integral formulation of Stokes flows includes slender-body theory. J. Fluid Mech. 850, R1.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.CrossRefGoogle Scholar
Maggi, C., Simmchen, J., Saglimbeni, F., Katuri, J., Dipalo, M., De Angelis, F., Sanchez, S. & Di Leonardo, R. 2016 Self-assembly of micromachining systems powered by Janus micromotors. Small 12 (4), 446–451.CrossRefGoogle ScholarPubMed
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Péclet numbers. J. Fluid Mech. 747, 572–604.CrossRefGoogle Scholar
Michelin, S. & Lauga, E. 2017 Geometric tuning of self-propulsion for Janus catalytic particles. Sci. Rep. 7, 42264.CrossRefGoogle ScholarPubMed
Montenegro-Johnson, T. D., Michelin, S. & Lauga, E. 2015 A regularised singularity approach to phoretic problems. Eur. Phys. J. E 38 (12), 1–7.Google ScholarPubMed
Montenegro-Johnson, T. D. 2018 Microtransformers: controlled microscale navigation with flexible robots. Phys. Rev. Fluids 3, 062201.CrossRefGoogle Scholar
Moreau, C., Giraldi, L. & Gadêlha, H. 2018 The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella. J. R. Soc. Interface 15 (144), 20180235.CrossRefGoogle ScholarPubMed
Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. 2010 Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Engng 12, 55–85.CrossRefGoogle ScholarPubMed
Paxton, W. F., Kistler, K. C., Olmeda, C. C., Sen, A., Angelo, S. K. S., Cao, Y., Mallouk, T. E., Lammert, P. E. & Crespi, V. H. 2004 Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126 (41), 13424–13431.CrossRefGoogle ScholarPubMed
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.CrossRefGoogle Scholar
Schnitzer, O. & Yariv, E. 2015 Osmotic self-propulsion of slender particles. Phys. Fluids 27 (3), 031701.CrossRefGoogle Scholar
Schoeller, S. F., Townsend, A. K., Westwood, T. A. & Keaveny, E. E.2019 Methods for suspensions of passive and active filaments. arXiv:1903.12609.Google Scholar
Smith, D. J., Gaffney, E. A. & Blake, J. R. 2008 Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 163 (1–3), 178–188.CrossRefGoogle ScholarPubMed
Smith, D. J., Montenegro-Johnson, T. D. & Lopes, S. S. 2019 Symmetry-breaking cilia-driven flow in embryogenesis. Annu. Rev. Fluid Mech. 51, 105–128.CrossRefGoogle Scholar
Spagnolie, S. E. & Lauga, E. 2011 Comparative hydrodynamics of bacterial polymorphism. Phys. Rev. Lett. 106 (5), 058103.CrossRefGoogle ScholarPubMed
Varma, A., Montenegro-Johnson, T. D. & Michelin, S. 2018 Clustering-induced self-propulsion of isotropic autophoretic particles. Soft Matt. 14 (35), 7155–7173.CrossRefGoogle ScholarPubMed
Walker, B. J., Ishimoto, K., Gadêlha, H. & Gaffney, E. A. 2019 Filament mechanics in a half-space via regularised stokeslet segments. J. Fluid Mech. 879, 808–833.CrossRefGoogle Scholar
Williams, B. J., Anand, S. V., Rajagopalan, J. & Saif, M. T. A. 2014 A self-propelled biohybrid swimmer at low Reynolds number. Nat. Commun. 5, 3081.CrossRefGoogle ScholarPubMed
Yariv, E. 2008 Slender-body approximations for electro-phoresis and electro-rotation of polarizable particles. J. Fluid Mech. 613, 85–94.CrossRefGoogle Scholar
Yariv, E. 2019 Self-diffusiophoresis of slender catalytic colloids. Langmuir.Google ScholarPubMed
Zhang, L., Abbott, J. J., Dong, L., Kratochvil, B. E., Bell, D. & Nelson, B. J. 2009a Artificial bacterial flagella: fabrication and magnetic control. Appl. Phys. Lett. 94, 064107.Google Scholar
Zhang, L., Abbott, J. J., Dong, L., Peyer, K. E., Kratochvil, B. E., Zhang, H., Bergeles, C. & Nelson, B. J. 2009b Characterizing the swimming properties of artificial bacterial flagella. Nano Lett. 9, 3663–3667.CrossRefGoogle Scholar