Vertical dispersion of model microorganisms in horizontal shear flow

Microorganisms often swim upwards due to the cell's phototaxis, chemotaxis or geotaxis, in flow fields with vertical velocity gradients. In this study, the vertical dispersion of model microorganisms was investigated under horizontal shear conditions. A microorganism was modelled as a spherical squirmer with or without bottom-heaviness. First, the three-dimensional movement of 100 identical squirmers in a homogeneous suspension was computed by the Stokesian dynamics method. The results show that the dispersion of squirmers is strongly affected by the swimming velocity and bottom-heaviness of the cells and the shear rate of the background flow. The vertical diffusion is considerably smaller than the horizontal diffusion. Interestingly, the vertical diffusion decreases as the volume fraction and the stresslet of squirmers decrease, which is opposite of the tendency in diffusion with no background flow. Next, a continuum model of a suspension of squirmers was developed using the diffusion tensor and the drift velocity to simulate the spatial distribution of squirmers in macroscopic flow fields. The results of the continuum model illustrate that the gyrotactic trapping found by Durham, Kessler & Stocker (Science, vol. 323, 2009, pp. 1067-1070) also appears in the present model considering cell cell hydrodynamic interactions. In the case of horizontal Poiseuille flow, the volume fraction of bottom-heavy cells in the channel becomes considerably larger than that at the inlet. These fundamental findings are helpful for understanding the distribution of microorganisms in various water regimes in nature and industry.