Properties of a Semi-dilute Suspension of Swimming l\/licro-organisms

 In this paper, we review our recent researches on a suspension of swimming micro-organisms. Firstly, interactions between two swim-ming micro-organisms are discussed. We introduce our experimental works using Paramecium caudatum, and numerical works using a squirmer model. The results show that changes in direction between two swimming cells are induced mainly by hydrodynamic forces and that bio-logical interaction is a minor factor. Secondly, the rheological and diffusive properties of a semi-dilute suspension of squirmers are discussed. We in-troduce our numerical works and show that a suspension of bottom-heavy squirmers has strong non-Newtonian properties. We also show that the spreading of squirmers is correctly described as a diffiisive process after a sufficiently long time, even though all the movements of the squirmers are deterministically calculated. Key words. Micro-organism, Suspension, Hydrodynamic Interaction, Stokesian dynamics. Viscosity, Diffusivity

 Introduction

 A suspension of micro-organisms appears, for instance, in a massive plank-ton bloom in the ocean, which is an integral part of the oceanic ecosystem. The phytoplankton absorb CO2 from the water, and thus they play an im-portant role in the global carbon cycle and hence in phenomena such as global warming. Blooms sometimes cause harmful red tides in coastal re-gions, which lead to economic damage to fish farms. In the engineering field, micro-organism suspensions are used for bioreactors to make chemi-cals and biomass. Therefore, the study of micro-organism behaviour is a proper subject for scientific investigation

 The size of individual micro-organisms is often much smaller than that of the flow field of interest, so the suspension is modelled as a continuum in which the variables are volume-averaged quantities. Various continuum models for suspensions of swimming micro-organisms have also been pro-posed for the analysis of phenomena such as bioconvection, Pedley & Kessler (1990) for instance. However, the continuum models proposed so far are restricted to dilute suspensions, in which cell-cell interactions are negligible. If one wishes to consider larger cell concentrations, it will be necessary to consider the interactions between micro-organisms. Then, the translational-rotational velocity of the micro-organisms, the particle stress tensor and the diffusion tensor in the continuum model will need to be re-fined. In this background, we have investigated the properties of a suspension of micro-organisms both experimentally and numerically. In this review paper, we introduce our recent researches on this topic. Two-cell interac-tions are the basis of many cell interactions. Thus, in chapter 2, interac-tions between two swimming micro-organisms are discussed. We introduce our experimental works using Paramecium and numerical work using a squirmer model. In chapter 3, the continuum quantities, such as the rheological and diffiisive properties, of a semi-dilute suspension of squirmers are discussed. We introduce our numerical works using a Stoke-sian-dynamics method.