TY - JOUR

T1 - Diffusion of swimming model micro-organisms in a semi-dilute suspension

AU - Ishikawa, Takuji

AU - Pedley, T. J.

N1 - Funding Information:
T. I. was supported by a JSPS postdoctoral fellowship for research abroad from 2003 to 2005. We are very grateful to J. T. Locsei for his contribution to the scaling arguments of § 3.2.

PY - 2007/10/10

Y1 - 2007/10/10

N2 - The diffusive behaviour of swimming micro-organisms should be clarified in order to obtain a better continuum model for cell suspensions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 or 27 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. In the case of (non-bottom-heavy) squirmers, both the translational and the orientational spreading of squirmers is correctly described as a diffusive process over a sufficiently long time scale, even though all the movements of the squirmers were deterministically calculated. Scaling of the results on the assumption that the squirmer trajectories are unbiased random walks is shown to capture some but not all of the main features of the results. In the case of (bottom-heavy) squirmers, the diffusive behaviour in squirmers' orientations can be described by a biased random walk model, but only when the effect of hydrodynamic interaction dominates that of the bottom-heaviness. The spreading of bottom-heavy squirmers in the horizontal directions show diffusive behaviour, and that in the vertical direction also does when the average upward velocity is subtracted. The rotational diffusivity in this case, at a volume fraction c = 0.1, is shown to be at least as large as that previously measured in very dilute populations of swimming algal cells (Chlamydomonas nivalis).

AB - The diffusive behaviour of swimming micro-organisms should be clarified in order to obtain a better continuum model for cell suspensions. In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 or 27 identical squirmers in a fluid otherwise at rest, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. In the case of (non-bottom-heavy) squirmers, both the translational and the orientational spreading of squirmers is correctly described as a diffusive process over a sufficiently long time scale, even though all the movements of the squirmers were deterministically calculated. Scaling of the results on the assumption that the squirmer trajectories are unbiased random walks is shown to capture some but not all of the main features of the results. In the case of (bottom-heavy) squirmers, the diffusive behaviour in squirmers' orientations can be described by a biased random walk model, but only when the effect of hydrodynamic interaction dominates that of the bottom-heaviness. The spreading of bottom-heavy squirmers in the horizontal directions show diffusive behaviour, and that in the vertical direction also does when the average upward velocity is subtracted. The rotational diffusivity in this case, at a volume fraction c = 0.1, is shown to be at least as large as that previously measured in very dilute populations of swimming algal cells (Chlamydomonas nivalis).

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U2 - 10.1017/S0022112007007847

DO - 10.1017/S0022112007007847

M3 - Article

AN - SCOPUS:34548730527

SN - 0022-1120

VL - 588

SP - 437

EP - 462

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -