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