Abstract
Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. Recent advances in artificial magnetic cilia carpets offer the potentiality to use a similar wall-generated background flow to steer bio-hybrid microrobots. In this paper, we provide some ground theoretical and numerical work assessing the viability of this novel means of swimmer guidance by setting up a simple model of a spherical swimmer in an oscillatory flow and analysing it from the control theory viewpoint. We show a property of local controllability around the reference free trajectories and investigate the bang–bang structure of the control for time-optimal trajectories, with an estimation of the minimal time for suitable objectives. By direct simulation, we have demonstrated that the wall actuation can improve the wall-following transport by nearly 50%, which can be interpreted by synchronous flow structure. Although an open-loop control with a periodic bang–bang actuation loses some robustness and effectiveness, a feedback control is found to improve its robustness and effective transport, even with hydrodynamic wall-swimmer interactions. The results shed light on the potentialities of flow control and open the way to future experiments on swimmer guidance.
Highlights
Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby
We have described a model of a simple spherical swimmer moving within a plane in the presence of a wall, which itself generates an oscillatory flow with a variable amplitude that we control in order to influence the positional and rotational dynamics of the swimmer and steer its trajectory
Using classical tools of control theory, we have examined the local controllability of the system around reference trajectories, partially validating its viability as a practical means of control
Summary
Active walls such as cilia and bacteria carpets generate background flows that can influence the trajectories of microswimmers moving nearby. The motion of biological and artificial bodies in a fluid at microscopic scale, or microswimmers, has been a subject of growing interest in the last decades, with increasing understanding of the mechanisms at stake in order to efficiently swim at this scale and the rise of promising applications in the biomedical field, such as targeted drug delivery or non-invasive surgery performed by swimming microrobots. To serve these purposes, the need for propulsion and guidance of microdevices and biological particles is becoming increasingly prevalent. The general interactions of swimmers with background flows have been extensively considered, both experimentally and theoretically [1,2]
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