Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-jpcp9 Total loading time: 0.336 Render date: 2022-12-03T09:35:48.042Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Nutrient uptake in a suspension of squirmers

Published online by Cambridge University Press:  22 January 2016

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: ishikawa@pfsl.mech.tohoku.ac.jp

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.

Type
Papers
Copyright
© 2016 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

Beenakker, C. W. J. 1986 Ewald sum of the Rotne–Prager tensor. J. Chem. Phys. 85, 15811582.CrossRefGoogle Scholar
Blake, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199208.CrossRefGoogle 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, 105129.CrossRefGoogle Scholar
Brady, J. F., Phillips, R. J., Lester, J. C. & Bossis, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257280.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Doostmohammadi, A., Stocker, R. & Ardekani, A. M. 2012 Low-Reynolds-number swimming at pycnoclines. Proc. Natl Acad. Sci. USA 109, 38563861.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, 2149.CrossRefGoogle Scholar
Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 13521360.CrossRefGoogle 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, 252263.CrossRefGoogle Scholar
Goldstein, R. E. 2015 Green algae as model organisms for biological fluid dynamics. Annu. Rev. Fluid Mech. 47, 343375.CrossRefGoogle ScholarPubMed
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373400.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Hill, N. A. & Pedley, T. J. 2005 Bioconvection. Fluid Dyn. Res. 37, 120.CrossRefGoogle Scholar
Ishikawa, T. 2009 Suspension biomechanics of swimming microbes. J. R. Soc. Interface 6, 815834.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Ishikawa, T. & Hota, M. 2006 Interaction of two swimming paramecia. J. Expl Biol. 209, 44524463.CrossRefGoogle 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, 401431.CrossRefGoogle 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, 119160.CrossRefGoogle 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.CrossRefGoogle 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, 637659.CrossRefGoogle 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, 1039110395.CrossRefGoogle ScholarPubMed
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, 528557.CrossRefGoogle 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, 109118.CrossRefGoogle Scholar
Magar, V., Goto, T. & Pedley, T. J. 2003 Nutrient uptake by a self-propelled steady squirmer. Q. J. Mech. Appl. Maths 56, 6591.CrossRefGoogle Scholar
Magar, V. & Pedley, T. J. 2005 Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech. 539, 93112.CrossRefGoogle 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, 131.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, 423444.CrossRefGoogle Scholar
Molina, J. J. & Yamamoto, R. 2014 Diffusion of colloidal particles in swimming suspensions. Mol. Phys. 112, 13891397.CrossRefGoogle Scholar
Pedley, T. J. & Kessler, J. O. 1992 Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24, 313358.CrossRefGoogle Scholar
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Chap. 4, Cambridge University Press.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M. J. 2007 Orientational order and instabilities in suspensions of self-locomoting rods. Phys. Rev. Lett. 99, 058102.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M. J. 2008a Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M. J. 2008b Instabilities, pattern formation, and mixing in active suspensions. Phys. Fluids 20, 123304.CrossRefGoogle Scholar
Saintillan, D. & Shelley, M. J. 2011 Emergence of coherent structures and large-scale flows in motile suspensions. J. R. Soc. Interface 68, 571585.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, 83158319.CrossRefGoogle ScholarPubMed
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, 628633.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Wagner, G. L., Young, W. R. & Lauga, E. 2014 Mixing by microorganisms in stratified fluids. J. Mar. Res. 72, 4772.CrossRefGoogle Scholar
Wu, X.-L. & Libchaber, A. 2000 Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 30173020.CrossRefGoogle Scholar
8
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Nutrient uptake in a suspension of squirmers
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Nutrient uptake in a suspension of squirmers
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Nutrient uptake in a suspension of squirmers
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *