Hydrodynamics can determine the optimal route for microswimmer navigation

Abdallah Daddi-Moussa-Ider,Benno Liebchen,Hartmut Löwen

doi:10.1038/s42005-021-00522-6

Abdallah Daddi-Moussa-Ider, Benno Liebchen + Show 1 more

Open Access

https://doi.org/10.1038/s42005-021-00522-6

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Abstract

As compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood. Here, we systematically explore this problem and show that the characteristic microswimmer-flow-field crucially influences the navigation strategy required to reach a target in the fastest way. The resulting optimal trajectories can have remarkable and non-intuitive shapes, which qualitatively differ from those of dry active particles or motile macroagents. Our results provide insights into the role of hydrodynamics and fluctuations on optimal navigation at the microscale, and suggest that microorganisms might have survival advantages when strategically controlling their distance to remote walls.

Highlights

As compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood
Recent work has explored optimal navigation problems of dry active particles accounting for (i) and partly for (ii): the very recent works[4,5,8,9,25,26,27,28,29,30,31,32,33] have pioneered the usage of reinforcement learning[34,35,36], e.g. to determine optimal steering strategies of active particles to optimally navigate toward a target position[4,5,8,9] or to exploit external flow fields to avoid getting trapped in certain flow structures by learning smart gravitaxis[25]
Before introducing our detailed model, let us illustrate the consequences of the finding that the shortest path is not fastest for microswimmers: Consider a microswimmer which can freely control its swimming direction and aims to reach a predefined target in the presence of two obstacles (Fig. 1): While in the absence of hydrodynamics, the shortest path is optimal, an actual microswimmer takes a qualitatively different path to reach its target fastest because it produces a flow field which is reflected by the obstacles and changes its speed

Summary

Institut für Theoretische Physik II

The quest on how to navigate or steer to optimally reach a target is important, e.g., for airplanes to save fuel while facing complex wind patterns on their way to a remote destination, or for the coordination of the motion of the parts of a space-agent to safely land on the moon These classical problems are well-explored and are usually solved using optimal control theory[1]. In the presence of fluctuations, the “optimal” navigation strategy protects microswimmers from fluctutions and can drastically decrease the traveling time as compared to cases where microswimmers head straight toward the target This offers a promising perspective on the motion of microorganisms near surfaces or interfaces: it suggests that microorganisms might have a survival advantage when actively regulating their distance to remote walls in order to approach a food source via a strategic detour, rather than directly heading toward it. Besides their possible biological implications, our findings might provide a benchmark for future research on optimal navigation strategies of active particles

Results and discussion

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