TY - JOUR
T1 - Nutrient uptake in a suspension of squirmers
AU - Ishikawa, Takuji
AU - Kajiki, Shunsuke
AU - Imai, Yohsuke
AU - Omori, Toshihiro
N1 - Funding Information:
This research was supported by JSPS KAKENHI grant numbers 25000008 and 26242039.
Publisher Copyright:
© 2016 Cambridge University Press.
PY - 2016/1/22
Y1 - 2016/1/22
N2 - 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.
AB - 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.
KW - biological fluid dynamics
KW - micro-organism dynamics
KW - swimming/flying
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U2 - 10.1017/jfm.2015.741
DO - 10.1017/jfm.2015.741
M3 - Article
AN - SCOPUS:84955472143
VL - 789
SP - 481
EP - 499
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -