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The investigation of microswimmer dynamics provides key insights in the design of active microfluidic systems and opens doors for further studies on inertial active matter. The authors establish a theoretical foundation for the dynamics of microswimmers in confined microflows with finite fluid inertia and demonstrate non-trivial impact of inertia in a microchannel flow.

In inertial microfluidics colloidal particles in a Poiseuille flow experience the Segré-Silberberg lift force, which drives them to specific positions in the channel cross section. An external force applied along the microchannel induces a cross-streamline migration to a new equilibrium position because of the Saffman effect. We apply optimal control theory to design the time protocol of the axial control force in order to steer a single particle as precisely as possible from a channel inlet to an outlet at a chosen target position. We discuss the influence of particle radius and channel length and show that optimal steering is cheaper than using a constant control force. Using a single optimized control-force protocol, we demonstrate that even a pulse of particles spread along the channel axis can be steered to a target and that particles of different radii can be separarted most efficiently.

We perform hydrodynamic simulations using the method of multi-particle collision dynamics and a theoretical analysis to study a single squirmer microswimmer at high Péclet number, which moves in a low Reynolds number fluid and under gravity. The relevant parameters are the ratio α of swimming to bulk sedimentation velocity and the squirmer type β . The combination of self-propulsion, gravitational force, hydrodynamic interactions with the wall, and thermal noise leads to a surprisingly diverse behavior. At $\alpha \gt 1$ we observe cruising states, while for $\alpha \lt 1$ the squirmer resides close to the bottom wall with the motional state determined by stable fixed points in height and orientation. They strongly depend on the squirmer type β . While neutral squirmers permanently float above the wall with upright orientation, pullers float for α larger than a threshold value ${\alpha }_{\mathrm{th}}$ and are pinned to the wall below ${\alpha }_{\mathrm{th}}$ . In contrast, pushers slide along the wall at lower heights, from which thermal orientational fluctuations drive them into a recurrent floating state with upright orientation, where they remain on the timescale of orientational persistence.