Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T22:49:33.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Artificial chemotaxis of phoretic swimmers: instantaneous and long-time behaviour

Published online by Cambridge University Press:  12 October 2018

Maria Tătulea-Codrean Open the ORCID record for Maria Tătulea-Codrean [Opens in a new window]  and
Eric Lauga
Maria Tătulea-Codrean
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Eric Lauga*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Phoretic swimmers are a class of artificial active particles that has received significant attention in recent years. By making use of self-generated gradients (e.g. in temperature, electric potential or some chemical product) phoretic swimmers are capable of self-propulsion without the complications of mobile body parts or a controlled external field. Focusing on diffusiophoresis, we quantify in this paper the mechanisms through which phoretic particles may achieve chemotaxis, both at the individual and the non-interacting population level. We first derive a fully analytical law for the instantaneous propulsion and orientation of a phoretic swimmer with general axisymmetric surface properties, in the limit of zero Péclet number and small Damköhler number. We then apply our results to the case of a Janus sphere, one of the most common designs of phoretic swimmers used in experimental studies. We next put forward a novel application of generalised Taylor dispersion theory in order to characterise the long-time behaviour of a population of non-interacting phoretic swimmers. We compare our theoretical results with numerical simulations for the mean drift and anisotropic diffusion of phoretic swimmers in chemical gradients. Our results will help inform the design of phoretic swimmers in future experimental applications.

JFM classification

Complex Fluids: Colloids Biological Fluid Dynamics: Propulsion
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 921 - 957
Check for updates
Copyright
© 2018 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

Agudo-Canalejo, J., Illien, P. & Golestanian, R. 2018 Phoresis and enhanced diffusion compete in enzyme chemotaxis. Nano Lett. 18, 2711–2717.Google Scholar
Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21, 61–99.Google Scholar
Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interaction. J. Fluid Mech. 74, 1–29.Google Scholar
Bearon, R. N., Bees, M. A. & Croze, O. A. 2012 Biased swimming cells do not disperse in pipes as tracers: a population model based on microscale behaviour. Phys. Fluids 24, 121902.Google Scholar
Berg, H. C. 1975 Chemotaxis in bacteria. Annu. Rev. Biophys. Bioengng 4, 119–136.Google Scholar
Bickel, T., Majee, A. & Würger, A. 2013 Flow pattern in the vicinity of self-propelling hot Janus particles. Phys. Rev. E 88, 012301.Google Scholar
Bickel, T., Zecua, G. & Würger, A. 2014 Polarization of active Janus particles. Phys. Rev. E 89, 050303(R).Google Scholar
Brady, J. 2011 Particle motion driven by solute gradients with application to autonomous motion: continuum and colloidal perspectives. J. Fluid Mech. 667, 216–259.Google Scholar
Brown, A. & Poon, W. 2014 Ionic effects in self-propelled Pt-coated Janus swimmers. Soft Matt. 10, 4016–4027.Google Scholar
Córdova-Figueroa, U. M. & Brady, J. F. 2008 Osmotic propulsion: the osmotic motor. Phys. Rev. Lett. 100, 158303.Google Scholar
Córdova-Figueroa, U. M., Brady, J. F. & Shklyaev, S. 2013 Osmotic propulsion of colloidal particles via constant surface flux. Soft Matt. 9, 6382–6390.Google Scholar
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.Google Scholar
Ebbens, S., Tu, M.-H., Howse, J. R. & Golestanian, R. 2012 Size dependence of the propulsion velocity for catalytic Janus-sphere swimmers. Phys. Rev. E 85, 020401.Google Scholar
Ebbens, S. J. & Howse, J. R. 2011 Direct observation of the direction of motion for spherical catalytic swimmers. Langmuir 27, 12293–12296.Google Scholar
Einstein, A. 1905 Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322, 549–560.Google Scholar
Frankel, I. & Brenner, H. 1991 Generalized Taylor dispersion phenomena in unbounded homogeneous shear flows. J. Fluid Mech. 230, 147–181.Google Scholar
Frankel, I. & Brenner, H. 1993 Taylor dispersion of orientable Brownian particles in unbounded homogeneous shear flows. J. Fluid Mech. 255, 129–156.Google Scholar
Geiseler, A., Hanggi, P., Marchesoni, F., Mulhern, C. & Savel’ev, S. 2016 Chemotaxis of artificial microswimmers in active density waves. Phys. Rev. E 94, 012613.Google Scholar
Golestanian, R. 2012 Collective behavior of thermally active colloids. Phys. Rev. Lett. 108, 3.Google Scholar
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2005 Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 94, 220801.Google Scholar
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nanoswimmers. New J. Phys. 9, 126.Google Scholar
Hill, N. A. & Bees, M. A. 2002 Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Phys. Fluids. 14, 2598–2605.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.Google Scholar
Izri, Z., van der Linden, M. N., Michelin, S. & Dauchot, O. 2014 Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion. Phys. Rev. Lett. 113, 248302.Google Scholar
Jiang, H.-R., Yoshinaga, N. & Sano, M. 2010 Active motion of a Janus particle by self-thermophoresis in a defocused laser beam. Phys. Rev. Lett. 105, 268302.Google Scholar
Jülicher, F. & Prost, J. 2009 Generic theory of colloidal transport. Eur. Phys. J. E 29, 27–36.Google Scholar
Khair, A. S. 2013 Diffusiophoresis of colloidal particles in neutral solute gradients at finite Péclet number. J. Fluid Mech. 731, 64–94.Google Scholar
Lauga, E. 2016 Bacterial hydrodynamics. Annu. Rev. Fluid Mech. 48, 105–130.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming micro-organisms. Rep. Prog. Phys. 72, 096601.Google Scholar
Manela, A. & Frankel, I. 2003 Generalized Taylor dispersion in suspensions of gyrotactic swimming micro-organisms. J. Fluid Mech. 490, 99–127.Google Scholar
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Péclet numbers. J. Fluid Mech. 747, 572–604.Google Scholar
Michelin, S. & Lauga, E. 2015 Autophoretic locomotion from geometric asymmetry. Eur. Phys. J. E 38, 7.Google Scholar
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25, 061701.Google Scholar
Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. 2010 Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Engng 12, 55–85.Google Scholar
Nelson, P. C. 2008 Biological Physics: Energy, Information, Life. W. H. Freeman.Google Scholar
Palacci, J., Sacanna, S., Kim, S.-H., Yi, G.-R., Pine, D. J. & Chaikin, P. M. 2014 Light-activated self-propelled colloids. Phil. Trans. R. Soc. A 372, 20130372.Google Scholar
Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. 2013 Living crystals of light-activated colloidal surfers. Science 339, 936–940.Google 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, 13424–13431.Google Scholar
Pedley, T. J. & Kessler, J. O. 1990 A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155–182.Google Scholar
Pohl, O. & Stark, H. 2014 Dynamic clustering and chemotactic collapse of self-phoretic active particles. Phys. Rev. Lett. 112, 238303.Google Scholar
Popescu, M. N., Dietrich, S., Tasinkevych, M. & Ralston, J. 2010 Phoretic motion of spheroidal particles due to self-generated solute gradients. Eur. Phys J. E 31, 351–367.Google Scholar
Popescu, M. N., Tasinkevych, M. & Dietrich, S. 2011 Pulling and pushing a cargo with a catalytically active carrier. Eur. Phys. Lett. 95, 28004.Google Scholar
Sabass, B. & Seifert, U. 2012 Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer. J. Chem. Phys. 136, 064508.Google Scholar
Saha, S., Golestanian, R. & Ramaswamy, S. 2014 Clusters, asters, and collective oscillations in chemotactic colloids. Phys. Rev. E 89, 062316.Google Scholar
Saragosti, J., Silberzan, P. & Buguin, A. 2012 Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis. PLoS One 7, 1–6.Google Scholar
Schmitt, M. & Stark, H. 2013 Swimming active droplet: a theoretical analysis. Eur. Phys. Lett. 101, 44008.Google Scholar
Shklyaev, S., Brady, J. F. & Córdova-Figueroa, U. M. 2014 Non-spherical osmotic motor: chemical sailing. J. Fluid Mech. 748, 488–520.Google Scholar
von Smoluchowski, M. 1906 Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 326, 756–780.Google Scholar
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 4102–4104.Google Scholar
Thutupalli, S., Seemann, R. & Herminghaus, S. 2011 Swarming behavior of simple model squirmers. New J. Phys. 13, 073021.Google Scholar
Wang, W., Duan, W., Sen, A. & Mallouk, T. E. 2013 Catalytically powered dynamic assembly of rod-shaped nanomotors and passive tracer particles. Proc. Natl. Acad. Sci. USA 110, 17744–17749.Google Scholar