Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-25T20:52:04.032Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Newtonian effects on the slip and mobility of a self-propelling active particle

Published online by Cambridge University Press:  15 July 2020

Akash Choudhary ,
T. Renganathan  and
S. Pushpavanam Open the ORCID record for S. Pushpavanam [Opens in a new window]
Akash Choudhary
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Chennai, TN600036, India
T. Renganathan
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Chennai, TN600036, India
S. Pushpavanam*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Chennai, TN600036, India
*
†Email address for correspondence: spush@iitm.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Janus particles propel themselves by generating concentration gradients along their active surface. This induces a flow near the surface, known as the diffusio-osmotic slip, which propels the particle even in the absence of externally applied concentration gradients. In this work, we study the influence of viscoelasticity and shear-thinning (described by the second-order fluid and Carreau model, respectively) on the diffusio-osmotic slip on an active surface. Using matched asymptotic expansions, we provide an analytical expression for the modification of slip induced by the non-Newtonian behaviour. The results reveal that the modification in slip velocity, arising from polymer elasticity, is proportional to the second tangential derivative of the concentration field. Using the reciprocal theorem, we estimate the influence of this modification on the swimming velocity of a Janus sphere: (i)for second-order fluid, the contribution is non-negligible and its sign is dependent on the surface coverage of activity and (ii) for Carreau fluid, the contribution is more pronounced and always enhances the swimming velocity. The current study also has implications on the understanding of the transport of complex fluids in diffusio-osmotic pumps.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Low-Reynolds-number flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A4
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Anderson, J. L., Lowell, M. E. & Prieve, D. C. 1982 Motion of a particle generated by chemical gradients. Part 1. Non-electrolytes. J. Fluid Mech. 117, 107–121.CrossRefGoogle Scholar
Aragones, J. L., Yazdi, S. & Alexander-Katz, A. 2018 Diffusion of self-propelled particles in complex media. Phys. Rev. Fluids 3 (8), 083301.CrossRefGoogle Scholar
Baraban, L., Tasinkevych, M., Popescu, M. N., Sanchez, S., Dietrich, S. & Schmidt, O. G. 2012 Transport of cargo by catalytic Janus micro-motors. Soft Matter 8 (1), 48–52.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, Vol. 1: Fluid Mechanics. Wiley.Google Scholar
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46 (1), 199–208.CrossRefGoogle Scholar
Brady, J. F. 2011 Particle motion driven by solute gradients with application to autonomous motion: continuum and colloidal perspectives. J. Fluid Mech. 667, 216–259.CrossRefGoogle Scholar
Córdova-Figueroa, U. M. & Brady, J. F. 2008 Osmotic propulsion: the osmotic motor. Phys. Rev. Lett. 100 (15), 158303.CrossRefGoogle ScholarPubMed
Datt, C., Natale, G., Hatzikiriakos, S. G. & Elfring, G. J. 2017 An active particle in a complex fluid. J. Fluid Mech. 823, 675–688.CrossRefGoogle Scholar
Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2015 Squirming through shear-thinning fluids. J. Fluid Mech. 784, R1.CrossRefGoogle Scholar
De Corato, M., Greco, F. & Maffettone, P. L. 2015 Locomotion of a microorganism in weakly viscoelastic liquids. Phys. Rev. E 92 (5), 053008.CrossRefGoogle ScholarPubMed
Derjaguin, B. V., Sidorenkov, G. P., Zubashchenkov, E. A. & Kiseleva, E. V. 1947 Kinetic phenomena in boundary films of liquids. Kolloidn. zh 9, 335–347.Google Scholar
Ebbens, S. J. & Howse, J. R. 2011 Direct observation of the direction of motion for spherical catalytic swimmers. Langmuir 27 (20), 12293–12296.CrossRefGoogle ScholarPubMed
Fournier-Bidoz, S., Arsenault, A., Manners, I. & Ozin, G. A. 2005 Synthetic self-propelled nanorotors. Chem. Commun. 4, 441–443.CrossRefGoogle Scholar
Gao, W. & Wang, J. 2014 Synthetic micro/nanomotors in drug delivery. Nanoscale 6 (18), 10486–10494.CrossRefGoogle ScholarPubMed
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2005 Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 94 (22), 220801.CrossRefGoogle ScholarPubMed
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro-and nano-swimmers. New J. Phys. 9 (5), 126.CrossRefGoogle Scholar
Gomez-Solano, J. R., Blokhuis, A. & Bechinger, C. 2016 Dynamics of self-propelled janus particles in viscoelastic fluids. Phys. Rev. Lett. 116 (13), 138301.CrossRefGoogle ScholarPubMed
Ho, B. P. & Leal, L. G. 1976 Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid. J. Fluid Mech. 76 (4), 783–799.CrossRefGoogle 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 (4), 048102.CrossRefGoogle ScholarPubMed
Jülicher, F. & Prost, J. 2009 Generic theory of colloidal transport. Eur. Phys. J. E 29 (1), 27–36.CrossRefGoogle ScholarPubMed
Ke, H., Ye, S., Carroll, R. L. & Showalter, K. 2010 Motion analysis of self-propelled Pt-silica particles in hydrogen peroxide solutions. J. Phys. Chem. A 114 (17), 5462–5467.CrossRefGoogle ScholarPubMed
Khair, A. S., Posluszny, D. E. & Walker, L. M. 2012 Coupling electrokinetics and rheology: electrophoresis in non-Newtonian fluids. Phys. Rev. E 85 (1), 016320.CrossRefGoogle ScholarPubMed
Li, G. & Koch, D. L. 2020 Electrophoresis in dilute polymer solutions. J. Fluid Mech. 884, A9.CrossRefGoogle Scholar
Lisicki, M., Michelin, S. & Lauga, E. 2016 Phoretic flow induced by asymmetric confinement. J. Fluid Mech. 799, R5.CrossRefGoogle Scholar
Makuch, K., Hołyst, R., Kalwarczyk, T., Garstecki, P. & Brady, J. F. 2020 Diffusion and flow in complex liquids. Soft Matter 16 (1), 114–124.CrossRefGoogle ScholarPubMed
Maldonado-Camargo, L. & Rinaldi, C. 2016 Breakdown of the Stokes–Einstein relation for the rotational diffusivity of polymer grafted nanoparticles in polymer melts. Nano Lett. 16 (11), 6767–6773.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. 2019 Universal optimal geometry of minimal phoretic pumps. Sci. Rep. 9 (1), 10788.CrossRefGoogle ScholarPubMed
Michelin, S., Montenegro-Johnson, T. D., De Canio, G., Lobato-Dauzier, N. & Lauga, E. 2015 Geometric pumping in autophoretic channels. Soft Matter 11 (29), 5804–5811.CrossRefGoogle ScholarPubMed
Natale, G., Datt, C., Hatzikiriakos, S. G. & Elfring, G. J. 2017 Autophoretic locomotion in weakly viscoelastic fluids at finite Péclet number. Phys. Fluids 29 (12), 123102.CrossRefGoogle Scholar
O'Brien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92 (1), 204–216.CrossRefGoogle Scholar
Patteson, A. E., Gopinath, A. & Arratia, P. E. 2016 Active colloids in complex fluids. Curr. Opin. Colloid Interface Sci. 100 (21), 86–96.CrossRefGoogle Scholar
Paxton, W. F., Kistler, K. C., Olmeda, C. C., Sen, A., St. Angelo, S. K., 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
Paxton, W. F., Sundararajan, S., Mallouk, T. E. & Sen, A. 2006 Chemical locomotion. Angew. Chem. Int. Ed. Engl. 45 (33), 5420–5429.Google ScholarPubMed
Pietrzyk, K., Nganguia, H., Datt, C., Zhu, L., Elfring, G. J. & Pak, O. S. 2019 Flow around a squirmer in a shear-thinning fluid. J. Non-Newtonian Fluid Mech. 268, 101–110.CrossRefGoogle Scholar
Rallabandi, B., Yang, F. & Stone, H. A. 2019 Motion of hydrodynamically interacting active particles. arXiv:1901.04311.Google Scholar
Saad, S. & Natale, G. 2019 Diffusiophoresis of active colloids in viscoelastic media. Soft Matter 15 (48), 9909–9919.CrossRefGoogle ScholarPubMed
Sabass, B. & Seifert, U. 2012 Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer. J. Chem. Phys. 136 (6), 064508.CrossRefGoogle ScholarPubMed
Sharifi-Mood, N., Koplik, J. & Maldarelli, C. 2013 Diffusiophoretic self-propulsion of colloids driven by a surface reaction: the sub-micron particle regime for exponential and van der Waals interactions. Phys. Fluids 25 (1), 012001.CrossRefGoogle Scholar
Stark, H. 2018 Artificial chemotaxis of self-phoretic active colloids: collective behavior. Acc. Chem. Res. 51 (11), 2681–2688.CrossRefGoogle ScholarPubMed
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77 (19), 4102.CrossRefGoogle ScholarPubMed
Su, H., Price, C.-A. H., Jing, L., Tian, Q., Liu, J. & Qian, K. 2019 Janus particles: design, preparation, and biomedical applications. Mater. Today Bio 4, 100033.CrossRefGoogle ScholarPubMed
Tiefenbruck, G. F. & Leal, L. G. 1980 A note on the slow motion of a bubble in a viscoelastic liquid. J. Non-Newtonian Fluid Mech. 7 (2–3), 257–264.CrossRefGoogle Scholar
Vrentas, J. S. & Vrentas, C. M. 2003 Steady viscoelastic diffusion. J. Appl. Polym. Sci. 88 (14), 3256–3263.CrossRefGoogle Scholar
Zare, Y., Park, S. P. & Rhee, K. Y. 2019 Analysis of complex viscosity and shear thinning behavior in poly (lactic acid)/poly (ethylene oxide)/carbon nanotubes biosensor based on Carreau–Yasuda model. Res. Phys. 13, 102245.Google Scholar
Zhao, C. & Yang, C. 2013 Electrokinetics of non-Newtonian fluids: a review. Adv. Colloid Interface Sci. 201, 94–108.CrossRefGoogle ScholarPubMed
Zhu, L., Lauga, E. & Brandt, L. 2012 Self-propulsion in viscoelastic fluids: pushers vs. pullers. Phys. Fluids 24 (5), 051902.CrossRefGoogle Scholar
Supplementary material: PDF

Choudhary et al. supplementary material

Choudhary et al. supplementary material

Download Choudhary et al. supplementary material(PDF)
PDF 369.1 KB