Thin-layer formation of spheroidal motile micro-swimmers in unsteady flow

Several meters below the ocean surface, thin layers of concentrated motile phytoplankton are ubiquitous and are responsible for high ecological activities. Gyrotactic trapping has been proposed as a potential mechanism for the layer formation of bottom-heavy swimming cells. Prior research has often simplified these active particles as small (~10 microns) spheres, thereby ignoring the influence of the size and the shape of the cell. Three open questions remain. First, how does the size of the swimmer affect the gyrotactic trapping? Second, how does the shape affect the gyrotactic trapping? Third, how does the transient trapping process interact with the time-varying background flow? In this study, we proposed a model that considers the effects of spheroidal shape on the competition between gravitational torque and viscous torque. Based on this model, we numerically investigated gyrotactic trapping in shear flow. Linear stability analysis was utilized to reveal a characteristic timescale of trapping. Subsequently, in time-varying shear flow, we identified three different regimes of thin layer formation. In sum, our findings highlight the importance of spheroidal shape for motile phytoplankton in flow and reveal that there are three mechanisms for thin layer formation in time-varying background flow.