Skip to main content
×
×
Home

Microswimmer-induced chaotic mixing

  • Mir Abbas Jalali (a1) (a2), Atefeh Khoshnood (a3) and Mohammad-Reza Alam (a4)
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.

Copyright
Corresponding author
Email address for correspondence: mjalali@berkeley.edu
References
Hide All
Aref, H. 1991 Stochastic particle motion in laminar flows. Phys. Fluids A 3 (5), 10091016.
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.
Couchman, I. J. & Kerrigan, E. C. 2010 Control of mixing in a Stokes’ fluid flow. J. Process Control 20, 11031115.
Eckhardt, B. & Zammert, S. 2012 Non-normal tracer diffusion from stirring by swimming microorganisms. Eur. Phys. J. E 35 (96), 12.
Elgeti, J., Winkler, R. G. & Gompper, G. 2015 Physics of microswimmers—single particle motion and collective behaviour: a review. Rep. Prog. Phys. 78, 056601.
Fehlberg, E.1968. Classical fifth-, sixth-, seventh-, and eighth-order Runge–Kutta formulas with stepsize control. Technical Report, 287. National Aeronautics and Space Administration.
Gouillart, E., Kuncio, N., Dauchot, O., Dubrulle, B., Roux, S. & Thiffeault, J. L. 2007 Walls inhibit chaotic mixing. Phys. Rev. Lett. 99, 114501.
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.
Guasto, J. S., Johnson, K. A. & Gollub, J. P. 2010 Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105, 168102.
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers.
Jalali, M. A., Alam, M.-R. & Mousavi, S. 2014 Versatile low-Reynolds-number swimmer with three dimensional maneuverability. Phys. Rev. E 90, 053006.
Katija, K. 2012 Biogenic inputs to ocean mixing. J. Expl Biol. 215, 10401049.
Klindt, G. S. & Friedrich, B. M.2015. Flagellar swimmers oscillate between pusher- and puller-type swimming. arXiv:1504.05775v1.
Lin, Z., Thiffeault, J.-L. & Childress, S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167177.
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, 190198.
Lopez, D. & Lauga, E. 2014 Dynamics of swimming bacteria at complex interfaces. Phys. Fluids 26, 071902.
Mathew, G., Mezić, I. & Petzold, L. 2005 A multiscale measure for mixing. Physica D 211, 2346.
Mathew, G., Mezić, I., Grivopoulos, S., Vaidya, U. & Petzold, L. 2007 Optimal control of mixing in Stokes fluid flows. J. Fluid Mech. 580, 261281.
Nienow, A. W., Edwards, M. F. & Harnby, N. 1997 Mixing in the Process Industries. Butterworth-Heinemann.
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. vol. 3. Cambridge University Press.
Ottino, J. M. 1990 Mixing, chaotic advection, and turbulence. Annu. Rev. Fluid Mech. 22, 207254.
Ottino, J. M. & Wiggins, S. 2004 Introduction: mixing in microfluidics. Phil. Trans. R. Soc. Lond. A 362, 923935.
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.
Pushkin, D. O. & Yeomans, J. M. 2013 Fluid mixing by curved trajectories of microswimmers. Phys. Rev. Lett. 111, 188101.
Rauwendaal, C.(Ed.) 1991 Mixing in Polymer Processing. vol. 23. CRC Press.
Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezić, I., Stone, H. A. & Whitesides, G. M. 2002 Chaotic mixer for microchannels. Science 295, 647651.
Sturman, R. & Springham, J. 2013 Rate of chaotic mixing and boundary behavior. Phys. Rev. E 87, 012906.
Thiffeault, J. L., Gouillart, E. & Dauchot, O. 2011 Moving walls accelerate mixing. Phys. Rev. E 84, 036313.
Wu, X.-L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 30173020.
Wagner, G. L., Young, W. R. & Lauga, E. 2014 Mixing by microorganisms in stratified fluids. J. Mar. Res. 72, 4772.
Wiggins, S. & Ottino, J. M. 2004 Foundations of chaotic mixing. Phil. Trans. R. Soc. Lond. A 362, 937970.
Wilhelmus, M. M. & Dabiri, J. O. 2014 Observations of large-scale fluid transport by laser-guided plankton aggregations. Phys. Fluids 26, 101302.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed