The size of individual micro-organisms is often much smaller than that of the flow field of interest, in an oceanic plankton bloom for instance. In such cases, the suspension of micro-organisms is modelled as a continuum in which the variables are volume-averaged quantities. Continuum models for suspensions of swimming micro-organisms have been proposed for the analysis of phenomena such as bioconvection. However, the continuum models proposed so far are restricted to dilute suspensions, in which cell-cell interactions are negligible. If one wishes to analyze larger cell concentrations, it will be necessary to consider the interactions between micro-organisms. Then the particle stress tensor, the velocities of the micro-organisms and the diffusion tensor in the continuum model will need to be replaced by improved expressions. In this study, we compute the motion of interacting swimming model micro-organisms in periodic suspensions in a fluid otherwise at rest, and discuss the microstructure constructed by micro-organisms.
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