Hostname: page-component-66d9dcfd78-8c77b Total loading time: 0 Render date: 2026-08-08T04:07:00.944Z Has data issue: false hasContentIssue false
  • English
  • Français

Microswimmer-induced chaotic mixing

Published online by Cambridge University Press:  19 August 2015

Mir Abbas Jalali ,
Atefeh Khoshnood  and
Mohammad-Reza Alam
Mir Abbas Jalali*
Affiliation:
Department of Astronomy, University of California, Berkeley, CA 94720, USA Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, P.O. Box 11155-9567, Tehran, Iran
Atefeh Khoshnood
Affiliation:
Reservoir Engineering Research Institute, Palo Alto, CA 94301, USA
Mohammad-Reza Alam
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
*
†Email address for correspondence: mjalali@berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Efficient mixing, typically characterised by chaotic advection, is hard to achieve in low Reynolds number conditions because of the linear nature of the Stokes equation that governs the motion. Here we show that low Reynolds number swimmers moving in quasi-periodic orbits can result in considerable stretching and folding of fluid elements. We accurately follow packets of tracers within the fluid domain and show that their trajectories become chaotic as the swimmer’s trajectory densely fills its invariant torus. The mixing process is demonstrated in two dimensions using the Quadroar swimmer that autonomously propels and tumbles along quasi-periodic orbits with multi-loop turning trajectories. We demonstrate and discuss that the streamlines of the flow induced by the Quadroar closely resemble the oscillatory flow field of the green alga Chlamydomonas reinhardtii. Our findings can thus be utilized to understand the interactions of microorganisms with their environments, and to design autonomous robotic mixers that can sweep and mix an entire volume of complex geometry containers.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Mixing: Mixing Biological Fluid Dynamics: Swimming/flying

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 669 - 683
Check for updates
Copyright
© 2015 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.)

Article purchase

Temporarily unavailable

References

Aref, H. 1991 Stochastic particle motion in laminar flows. Phys. Fluids A 3 (5), 1009–1016.Google Scholar
Chabreyrie, R., Chandre, C. & Aubry, N. 2011 Complete chaotic mixing in an electro–osmotic flow by destabilization of key periodic pathlines. Phys. Fluids 23, 072002.Google Scholar
Couchman, I. J. & Kerrigan, E. C. 2010 Control of mixing in a Stokes’ fluid flow. J. Process Control 20, 1103–1115.Google Scholar
Eckhardt, B. & Zammert, S. 2012 Non-normal tracer diffusion from stirring by swimming microorganisms. Eur. Phys. J. E 35 (96), 1–2.Google Scholar
Elgeti, J., Winkler, R. G. & Gompper, G. 2015 Physics of microswimmers—single particle motion and collective behaviour: a review. Rep. Prog. Phys. 78, 056601.CrossRefGoogle Scholar
Fehlberg, E.1968. Classical fifth-, sixth-, seventh-, and eighth-order Runge–Kutta formulas with stepsize control. Technical Report, 287. National Aeronautics and Space Administration.Google Scholar
Gouillart, E., Kuncio, N., Dauchot, O., Dubrulle, B., Roux, S. & Thiffeault, J. L. 2007 Walls inhibit chaotic mixing. Phys. Rev. Lett. 99, 114501.Google Scholar
Gouillart, E., Dauchot, O., Dubrulle, B., Roux, S. & Thiffeault, J. L. 2008 Slow decay of concentration variance due to no-slip walls in chaotic mixing. Phys. Rev. E 78, 026211.CrossRefGoogle ScholarPubMed
Guasto, J. S., Johnson, K. A. & Gollub, J. P. 2010 Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105, 168102.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers.Google Scholar
Jalali, M. A., Alam, M.-R. & Mousavi, S. 2014 Versatile low-Reynolds-number swimmer with three dimensional maneuverability. Phys. Rev. E 90, 053006.Google Scholar
Katija, K. 2012 Biogenic inputs to ocean mixing. J. Expl Biol. 215, 1040–1049.Google Scholar
Klindt, G. S. & Friedrich, B. M.2015. Flagellar swimmers oscillate between pusher- and puller-type swimming. arXiv:1504.05775v1.Google Scholar
Lin, Z., Thiffeault, J.-L. & Childress, S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167–177.Google Scholar
Liu, R. H., Sharp, K. V., Olsen, M. G., Stremler, M. A., Santiago, J. G., Adrian, R. J. & Beebe, D. J. 2000 A passive three-dimensional ‘C-shape’ helical micromixer. J. Microelectromech. Syst. 9, 190–198.Google Scholar
Lopez, D. & Lauga, E. 2014 Dynamics of swimming bacteria at complex interfaces. Phys. Fluids 26, 071902.Google Scholar
Mathew, G., Mezić, I. & Petzold, L. 2005 A multiscale measure for mixing. Physica D 211, 23–46.Google Scholar
Mathew, G., Mezić, I., Grivopoulos, S., Vaidya, U. & Petzold, L. 2007 Optimal control of mixing in Stokes fluid flows. J. Fluid Mech. 580, 261–281.Google Scholar
Nienow, A. W., Edwards, M. F. & Harnby, N. 1997 Mixing in the Process Industries. Butterworth-Heinemann.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. vol. 3. Cambridge University Press.Google Scholar
Ottino, J. M. 1990 Mixing, chaotic advection, and turbulence. Annu. Rev. Fluid Mech. 22, 207–254.Google Scholar
Ottino, J. M. & Wiggins, S. 2004 Introduction: mixing in microfluidics. Phil. Trans. R. Soc. Lond. A 362, 923–935.Google Scholar
Pak, O. S. & Lauga, E. 2015 Theoretical models in low Reynolds number locomotion. In Fluid–Structure Interactions in Low Reynolds Number Flows (ed. Duprat, C. & Stone, H. A.), RSC Publishing.Google Scholar
Pushkin, D. O. & Yeomans, J. M. 2013 Fluid mixing by curved trajectories of microswimmers. Phys. Rev. Lett. 111, 188101.Google Scholar
Rauwendaal, C.(Ed.) 1991 Mixing in Polymer Processing. vol. 23. CRC Press.Google Scholar
Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezić, I., Stone, H. A. & Whitesides, G. M. 2002 Chaotic mixer for microchannels. Science 295, 647–651.Google Scholar
Sturman, R. & Springham, J. 2013 Rate of chaotic mixing and boundary behavior. Phys. Rev. E 87, 012906.Google Scholar
Thiffeault, J. L., Gouillart, E. & Dauchot, O. 2011 Moving walls accelerate mixing. Phys. Rev. E 84, 036313.Google Scholar
Wu, X.-L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020.Google Scholar
Wagner, G. L., Young, W. R. & Lauga, E. 2014 Mixing by microorganisms in stratified fluids. J. Mar. Res. 72, 47–72.Google Scholar
Wiggins, S. & Ottino, J. M. 2004 Foundations of chaotic mixing. Phil. Trans. R. Soc. Lond. A 362, 937–970.Google Scholar
Wilhelmus, M. M. & Dabiri, J. O. 2014 Observations of large-scale fluid transport by laser-guided plankton aggregations. Phys. Fluids 26, 101302.Google Scholar