Optimal feeding is optimal swimming for all Péclet numbers

Michelin, Sébastien; Lauga, Eric

doi:10.1063/1.3642645

Cited by 89 publications

(114 citation statements)

References 43 publications

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“…A measure of efficiency of a feeding strategy involving the effort needed to carry out the strategy would be useful but probably have little to do with the efficiencies discussed in this paper. However Michelin & Lauga (2011) relate optimal feeding to optimal swimming in a particular case, suggesting perhaps a closer link than we have implied above.…”

Section: Discussionmentioning

confidence: 53%

A thermodynamic efficiency for Stokesian swimming

Childress

2012

J. Fluid Mech.

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Since free Stokesian swimming does no work external to fluid and body, the classical thermodynamic efficiency of this activity is zero. This paper introduces a potential thermodynamic efficiency by partially tethering the body so that work is done externally and instantaneously. We compare the resulting efficiency with other definitions utilized in Stokes flow, extend the instantaneous definition to encompass a full swimming stroke, and compute it for propulsion of a spherical body by a helical flagellum.

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Section: Discussionmentioning

confidence: 53%

A thermodynamic efficiency for Stokesian swimming

Childress

2012

J. Fluid Mech.

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“…Lambert, F. Picano, W.-P. Breugem and L. Brandt of uptake due to swimming permits cells of radius r > 10 µm to overcome diffusion limitations and satisfy metabolic requirements. In an optimization study of the nutrient uptake and swimming mode of an individual swimming particle, Michelin & Lauga (2011) show that the optimal swimming motion coincides with the optimal nutrient uptake for all Péclet numbers. All of these results are obtained assuming constant nutrient concentration at the particle surface.…”

Section: Introductionmentioning

confidence: 94%

“…Koch & Subramanian 2011). However, only a few of the numerical studies of individual swimming particles, including biofilms, that provide insight into the behaviour of active suspensions include mass transfer and nutrient uptake (Magar, Goto & Pedley 2003;Magar & Pedley 2005;Michelin & Lauga 2011;Taherzadeh, Picioreanu & Horn 2012). In these studies, the concentration of nutrients in the fluid medium are typically treated as a passive scalar.…”

Section: Introductionmentioning

confidence: 99%

“…In these studies, the concentration of nutrients in the fluid medium are typically treated as a passive scalar. In the case of individual swimming particles, Magar et al (2003), Magar & Pedley (2005) and Michelin & Lauga (2011) use a widely adopted unsteady and steady swimming cell model first introduced by Lighthill (1952) and Blake (1971). In this model, referred to as the squirmer model, the swimming cell is assumed to be spherical in shape with an applied tangential surface velocity that represents the surface distortion of beating cilia.…”

Section: Introductionmentioning

confidence: 99%

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Active suspensions in thin films: nutrient uptake and swimmer motion

et al. 2013

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A numerical study of swimming particle motion and nutrient transport is conducted for a semidilute to dense suspension in a thin film. The steady squirmer model is used to represent the motion of living cells in suspension with the nutrient uptake by swimming particles modelled using a first-order kinetic equation representing the absorption process that occurs locally at the particle surface. An analysis of the dynamics of the neutral squirmers inside the film shows that the vertical motion is reduced significantly. The mean nutrient uptake for both isolated and populations of swimmers decreases for increasing swimming speeds when nutrient advection becomes relevant as less time is left for the nutrient to diffuse to the surface. This finding is in contrast to the case where the uptake is modelled by imposing a constant nutrient concentration at the cell surface and the mass flux results to be an increasing monotonic function of the swimming speed. In comparison to non-motile particles, the cell motion has a negligible influence on nutrient uptake at lower particle absorption rates since the process is rate limited. At higher absorption rates, the swimming motion results in a large increase in the nutrient uptake that is attributed to the movement of particles and increased mixing in the fluid. As the volume fraction of swimming particles increases, the squirmers consume slightly less nutrients and require more power for the same swimming motion. Despite this increase in energy consumption, the results clearly demonstrate that the gain in nutrient uptake make swimming a winning strategy for micro-organism survival also in relatively dense suspensions.

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“…They showed that the Sherwood number (Sh), indicating the ratio of the total rate of mass transfer to the rate of 482 T. Ishikawa, S. Kajiki, Y. Imai and T. Omori diffusive mass transfer, increases with the square root of the Péclet number (Pe), indicating the ratio of advection to diffusion, in the high-Pe regime, as opposed to with the cube root for a rigid sphere. Michelin & Lauga (2011) investigated the optimal feeding stroke of a steady squirmer. They showed that the optimal feeding stroke is independent of Pe, although the rate of feeding depends strongly on Pe.…”

Section: Introductionmentioning

confidence: 99%

Nutrient uptake in a suspension of squirmers

et al. 2016

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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.

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Optimal feeding is optimal swimming for all Péclet numbers

Cited by 89 publications

References 43 publications

A thermodynamic efficiency for Stokesian swimming

A thermodynamic efficiency for Stokesian swimming

Active suspensions in thin films: nutrient uptake and swimmer motion

Nutrient uptake in a suspension of squirmers

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