Skip to main content

Gyrotactic swimmer dispersion in pipe flow: testing the theory

  • Ottavio A. Croze (a1), Rachel N. Bearon (a2) and Martin A. Bees (a3)

Suspensions of microswimmers are a rich source of fascinating new fluid mechanics. Recently we predicted the active pipe flow dispersion of gyrotactic microalgae, whose orientation is biased by gravity and flow shear. Analytical theory predicts that these active swimmers disperse in a markedly distinct manner from passive tracers (Taylor dispersion). Dispersing swimmers display non-zero drift and effective diffusivity that is non-monotonic with Péclet number. Such predictions agree with numerical simulations, but hitherto have not been tested experimentally. Here, to facilitate comparison, we obtain new solutions of the axial dispersion theory accounting both for swimmer negative buoyancy and a local nonlinear response of swimmers to shear, provided by two alternative microscopic stochastic descriptions. We obtain new predictions for suspensions of the model swimming alga Dunaliella salina, whose motility and buoyant mass we parametrise using tracking video microscopy. We then present a new experimental method to measure gyrotactic dispersion using fluorescently stained D. salina and provide a preliminary comparison with predictions of a non-zero drift above the mean flow for each microscopic stochastic description. Finally, we propose further experiments for a full experimental characterisation of gyrotactic dispersion measures and discuss the implications of our results for algal dispersion in industrial photobioreactors.

Corresponding author
Email address for correspondence:
Hide All
Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 6777.
Bearon, R. N. 2013 Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model. J. Math. Biol. 66, 13411359.
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 (12), 121902.
Bearon, R. N., Hazel, A. L. & Thorn, G. J. 2011 The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields. J. Fluid Mech. 680, 602635.
Bees, M. A. & Croze, O. A. 2010 Dispersion of biased micro-organisms in a fluid flowing through a tube. Proc. R. Soc. Lond. A 466, 10671070.
Bees, M. A. & Croze, O. A. 2014 Mathematics for streamlined biofuel production from unicellular algae. Biofuels 5, 5365.
Bees, M. A., Hill, N. A. & Pedley, T. J. 1998 Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows. J. Math. Biol. 36, 269298.
Crocker, J. C. & Grier, D. G. 1996 Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298310.
Croze, O. A., Ashraf, E. E. & Bees, M. A. 2010 Sheared bioconvection in a horizontal tube. Phys. Biol. 7, 046001.
Croze, O. A. & Peaudecerf, F. 2016 Geoffrey Ingram Taylor and the physics of swimming. CavMag 15, 45.
Croze, O. A., Sardina, G., Ahmed, M., Bees, M. A. & Brandt, L. 2013 Dispersion of swimming algae in laminar and turbulent channel flows: consequences for photobioreactors. J. R. Soc. Interface 10, 20121041.
De Lillo, F., Cencini, M., Durham, W. M., Barry, M., Stocker, R., Climent, E. & Boffetta, G. 2014 Turbulent fluid acceleration generates clusters of gyrotactic microorganisms. Phys. Rev. Lett. 112, 044502.
Dennisenko, P. & Lukaschuk, S. 2007 Velocity profiles and discontinuities propagation in a pipe flow of suspension of motile microorganisms. Phys. Lett. A 362, 298304.
Doi, M. & Edwards, S. F. 1986 The Theory of Polymer Dynamics. Oxford University Press.
Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S. & Goldstein, R. E. 2011 Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering. Proc. Natl Acad. Sci. USA 208, 10940.
Durham, W. M., Climent, E., Barry, M., Lillo, F. D., Boffetta, G., Cencini, M. & Stocker, R. 2013 Turbulence drives microscale patches of motile phytoplankton. Nat. Commun. 4, 2148.
Durham, W. M., Kessler, J. O. & Stocker, R. 2009 Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science 323, 10671070.
Durham, W. M. & Stocker, R. 2012 Thin phytoplankton layers: characteristics, mechanisms, and consequences. Annu. Rev. Marine Sci. 4 (1), 177207.
Eppley, R. W., Holmes, R. W. & Strickland, J. D. H. 1967 Sinking rates of marine phytoplankton measured with a fluorometer. J. Exp. Mar. Biol. Ecol. 1, 191208.
Frankel, I. & Brenner, M. 1991 Generalized Taylor dispersion in unbounded shear flows. J. Fluid Mech. 230, 147181.
Frankel, I. & Brenner, M. 1993 Taylor dispersion of orientable Brownian particles in unbounded homogeneous shear flows. J. Fluid Mech. 255, 129156.
Garcia, X., Rafaï, S. & Peyla, P. 2013 Light control of the flow of phototactic microswimmer suspensions. Phys. Rev. Lett. 110, 138106.
Hill, N. A. & Bees, M. A. 2002 Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Phys. Fluids 14, 25982605.
Hill, N. A. & Häder, D.-P. 1997 A biased random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol. 186, 503526.
Hill, N. A. & Pedley, T. J. 2005 Bioconvection. Fluid Dyn. Res. 37, 120.
Hope, A., Croze, O. A., Poon, W. C. K., Bees, M. A. & Haw, M. D. 2016 Resonant alignment of microswimmer trajectories in oscillatory shear flows. Phys. Rev. Fluids 1, 051201(R).
Hubbard, J. B. & Douglas, J. F. 1993 Hydrodynamic friction of arbitrarily shaped Brownian particles. Phys. Rev. E 47, R2983R2986.
Hwang, Y. & Pedley, T. J. 2014a Bioconvection under uniform shear: linear stability analysis. J. Fluid Mech. 738, 522562.
Hwang, Y. & Pedley, T. J. 2014b Stability of downflowing gyrotactic microorganism suspensions in a two-dimensional vertical channel. J. Fluid Mech. 749, 750777.
Kessler, J. O. 1985 Hydrodynamic focusing of motile algal cells. Nature 313, 218220.
Kessler, J. O. 1986 Individual and collective fluid dynamics of swimming cells. J. Fluid Mech. 173, 191205.
Lider, D. R.(Ed.) 2004 Handbook of Chemistry and Physics. CRC Press.
Manela, A. & Frankel, I. 2003 Generalized Taylor dispersion in suspensions of gyrotactic swimming micro-organisms. J. Fluid Mech. 490, 99127.
Marchetti, M. C., Joanny, J. F., Liverpool, T. B., Prost, J., Rao, M. & Simha, R. A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143.
Pedley, T. J. & Kessler, J. O. 1990 A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech. 212, 155182.
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming micro-organisms. Annu. Rev. Fluid Mech. 24, 313358.
Phillips, L., Ozbek, H., Igbene, A. & Litton, G.1980 Viscosity of NaCl and other solutions up to and 50 MPa pressures. Tech. Rep. LBL-11586. Lawrence Berkeley National Laboratory.
Pick, U., Karni, L. & Avron, M. 1986 Determination of ion content and ion fluxes in the halotolerant alga Dunaliella salina . Plant Physiol. 81, 9296.
Saintillan, D. & Shelley, M. J. 2006 Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20, 123304.
Taylor, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186203.
Taylor, G. I. 1954 The dispersion of matter in turbulent flow through a pipe. Proc. R. Soc. Lond. A 223, 446468.
Willams, C. R. & Bees, M. A. 2011a Photo-gyrotactic bioconvection. J. Fluid Mech. 678, 4186.
Williams, C. R. & Bees, M. A. 2011b A tale of three taxes: photo-gyro-gravitactic bioconvection. J. Expl. Biol. 214 (14), 23982408.
Zöttl, A. & Stark, H. 2012 Nonlinear dynamics of a microswimmer in Poiseuille flow. Phys. Rev. Lett. 108, 218104.
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? *

JFM classification


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