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Nutrient uptake in a suspension of squirmers

Published online by Cambridge University Press:  22 January 2016

Takuji Ishikawa ,
Shunsuke Kajiki ,
Yohsuke Imai  and
Toshihiro Omori
Takuji Ishikawa*
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai 980-8579, Japan Department of Biomedical Engineering, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai 980-8579, Japan
Shunsuke Kajiki
Affiliation:
Department of Biomedical Engineering, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai 980-8579, Japan
Yohsuke Imai
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai 980-8579, Japan
Toshihiro Omori
Affiliation:
Department of Bioengineering and Robotics, Tohoku University, 6-6-01, Aoba, Aoba-ku, Sendai 980-8579, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Nutrient uptake is one of the most important factors in cell growth. Despite the biological importance, little is known about the effect of cell–cell hydrodynamic interactions on nutrient uptake in a suspension of swimming micro-organisms. In this study, we numerically investigate the nutrient uptake in an infinite suspension of squirmers. In the dilute limit, our results are in good agreement with a previous study by Magar et al. (Q. J. Mech. Appl. Maths, vol. 56, 2003, pp. 65–91). When we increased the volume fraction of squirmers, the nutrient uptake of individual cells was enhanced by the hydrodynamic interactions. The average nutrient concentration in the suspension decayed exponentially as a function of time, and the relaxation time could be scaled using the Sherwood number, the Péclet number and the volume fraction of cells. We propose a fitting function for the Sherwood number, which is useful in predicting nutrient uptake in the non-dilute regime. Furthermore, we analyse the swimming energy consumed by individual cells. The results indicate that both the energetic cost and the nutrient uptake increased as the volume fraction of cells was increased, and that the uptake per unit energy was not significantly affected by the volume fraction. These findings are important in understanding the mass transport and metabolism of swimming micro-organisms in nature and for industrial applications.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Micro-organism dynamics Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 481 - 499
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Copyright
© 2016 Cambridge University Press 

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References

Beenakker, C. W. J. 1986 Ewald sum of the Rotne–Prager tensor. J. Chem. Phys. 85, 1581–1582.CrossRefGoogle Scholar
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199–208.Google Scholar
Brady, J. F. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129.Google Scholar
Brady, J. F., Phillips, R. J., Lester, J. C. & Bossis, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257–280.Google Scholar
Dombrowski, C., Cisneros, L., Chatkaew, S., Goldstein, R. E. & Kessler, J. O. 2004 Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93, 098103.Google Scholar
Doostmohammadi, A., Stocker, R. & Ardekani, A. M. 2012 Low-Reynolds-number swimming at pycnoclines. Proc. Natl Acad. Sci. USA 109, 3856–3861.CrossRefGoogle ScholarPubMed
Dunkel, J. et al. 2013 Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110, 228102.CrossRefGoogle ScholarPubMed
Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.Google Scholar
Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352–1360.Google Scholar
Ferracci, J., Ueno, H., Numayama-Tsuruta, K., Imai, Y., Yamaguchi, T. & Ishikawa, T. 2013 Hydrodynamical entrapment of ciliates at the air–liquid interface. PLoS ONE 8, e75238.CrossRefGoogle Scholar
Giacche, D. & Ishikawa, T. 2010 Hydrodynamic interaction of two unsteady model microorganisms. J. Theor. Biol. 267, 252–263.Google Scholar
Goldstein, R. E. 2015 Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech. 47, 343–375.Google Scholar
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.Google Scholar
Hernandez-Ortiz, J. P., Stoltz, C. G. & Graham, M. D. 2005 Transport and collective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett. 95, 204501.Google Scholar
Hill, N. A. & Pedley, T. J. 2005 Bioconvection. Fluid Dyn. Res. 37, 1–20.Google Scholar
Ishikawa, T. 2009 Suspension biomechanics of swimming microbes. J. R. Soc. Interface 6, 815–834.Google Scholar
Ishikawa, T., Yoshida, N., Ueno, H., Wiedeman, M., Imai, Y. & Yamaguchi, T. 2011 Energy transport in a concentrated suspension of bacteria. Phys. Rev. Lett. 107, 028102.Google Scholar
Ishikawa, T. & Hota, M. 2006 Interaction of two swimming paramecia. J. Expl Biol. 209, 4452–4463.Google Scholar
Ishikawa, T., Locsei, J. T. & Pedley, T. J. 2008 Development of coherent structures in concentrated suspensions of swimming model micro-organisms. J. Fluid Mech. 615, 401–431.Google Scholar
Ishikawa, T., Locsei, J. T. & Pedley, T. J. 2010 Fluid particle diffusion in a semidilute suspension of model micro-organisms. Phys. Rev. E 82, 021408.Google Scholar
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.Google Scholar
Jepson, A., Martinez, V. A., Schwarz-Linek, J., Morozov, A. & Poon, W. C. K. 2013 Enhanced diffusion of nonswimmers in a three-dimensional bath of motile bacteria. Phys. Rev. E 88, 041002.Google Scholar
Kasyap, T. V., Koch, D. L. & Wu, M. 2014 Hydrodynamic tracer diffusion in suspensions of swimming bacteria. Phys. Fluids 26, 081901.Google Scholar
Kim, S. & Karrila, S. J. 1992 Microhydrodynamics: Principles and Selected Applications. Butterworth Heinemann.Google Scholar
Koch, D. L. & Subramanian, G. 2011 Collective hydrodynamics of swimming microorganisms: living fluids. Annu. Rev. Fluid Mech. 43, 637–659.Google Scholar
Kurtuldu, H., Guasto, J. S., Johnson, K. A. & Gollub, J. P. 2011 Enhancement of biomixing by swimming algal cells in two-dimensional films. Proc. Natl Acad. Sci. USA 108, 10391–10395.Google Scholar
Lambert, R. A., Picano, F., Breugem, W.-P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528–557.Google Scholar
Lighthill, M. J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5, 109–118.Google Scholar
Magar, V., Goto, T. & Pedley, T. J. 2003 Nutrient uptake by a self-propelled steady squirmer. Q. J. Mech. Appl. Maths 56, 65–91.Google Scholar
Magar, V. & Pedley, T. J. 2005 Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech. 539, 93–112.Google Scholar
Michelin, S. & Lauga, E. 2011 Optimal feeding is optimal swimming for all Peclet numbers. Phys. Fluids 23, 101901.CrossRefGoogle Scholar
Michelin, S. & Lauga, E. 2013 Unsteady feeding and optimal strokes of model ciliates. J. Fluid Mech. 715, 1–31.CrossRefGoogle Scholar
Mino, G. L., Dunstan, J., Rousselet, A., Clément, E. & Soto, R. 2013 Induced diffusion of tracers in a bacterial suspension: theory and experiments. J. Fluid Mech. 729, 423–444.Google Scholar
Molina, J. J. & Yamamoto, R. 2014 Diffusion of colloidal particles in swimming suspensions. Mol. Phys. 112, 1389–1397.Google Scholar
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313–358.Google Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Chap. 4, Cambridge University Press.Google Scholar
Saintillan, D. & Shelley, M. J. 2007 Orientational order and instabilities in suspensions of self-locomoting rods. Phys. Rev. Lett. 99, 058102.Google Scholar
Saintillan, D. & Shelley, M. J. 2008a Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103.Google Scholar
Saintillan, D. & Shelley, M. J. 2008b Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20, 123304.Google Scholar
Saintillan, D. & Shelley, M. J. 2011 Emergence of coherent structures and large-scale flows in motile suspensions. J. R. Soc. Interface 68, 571–585.Google Scholar
Short, M. B., Solari, C. A., Ganguly, S., Powers, T. R., Kessler, J. O. & Goldstein, R. E. 2006 Flows driven by flagella of multicellular organisms enhance long-range molecular transport. Proc. Natl Acad. Sci. USA 103, 8315–8319.Google Scholar
Sokolov, A., Aranson, I. S., Kessler, J. O. & Goldstein, R. E. 2007 Concentration dependence of the collective dynamics of swimming bacteria. Phys. Rev. Lett. 98, 158102.CrossRefGoogle ScholarPubMed
Sokolov, A., Goldstein, R. E., Feldchtein, F. I. & Aranson, I. S. 2009 Enhanced mixing and spatial instability in concentrated bacterial suspensions. Phys. Rev. E 80, 031903.Google ScholarPubMed
Stocker, R. 2012 Marine microbes see a sea of gradients. Science 338, 628–633.Google Scholar
Underhill, P. T., Hernandez-Ortiz, J. P. & Graham, M. D. 2008 Diffusion and spatial correlations in suspensions of swimming particles. Phys. Rev. Lett. 100, 248101.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
Wu, X.-L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020.Google Scholar