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Active filaments and hydrodynamic interactions in microscale propulsion



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Tanasijevic, Ivan 


Motile microogranisms are ubiquitous in nature and are therefore crucial to understand and model. Their man-made counterparts, microrobots, are also often designed based on our understanding of the motion of microorganisms with clear applications in mind, such as minimally invasive surgery or targeted drug delivery. Two important questions regarding the swimming of microorganisms and microrobots are: (i) how do they propel themselves? and, (ii) how do they interact with their environment? The work presented in this dissertation represents original research regarding both of these questions and it is accordingly split into two parts: (i) the role of active filaments in microscale propulsion and (ii) hydrodynamic interactions between model microswimmers and their environment, namely with external flows and rigid surfaces.

Active filaments. Active, slender filaments are ubiquitous in the micro-scale world, both as a part of the propulsive mechanism of microswimmers or as a flow generating mechanism in cilial carpets.

First, we consider the swimming dynamics of micro-sized thermoresponsive hydrogel ribbons (microgels) in the confined space between two planar surfaces. As the result of the stroboscopic temperature changes, the volume and, thus, the shape of the slender microgel change, which leads to repeated cycles of bending and elastic relaxation, and to net locomotion. Small devices designed for biomimetic locomotion need to exploit flows that are not symmetric in time (non-reciprocal) to escape the constraints of the scallop theorem and undergo net motion. Unlike other biological slender swimmers, the non-reciprocal bending of the gel centerline is not sufficient here to explain for the overall swimming motion. We instead suggest that the swimming of the gel results from the flux of water periodically emanating from (or entering) the gel itself due to its shrinking (or swelling). We derive a theoretical model for this hypothesis of jet-driven propulsion, which leads to excellent agreement with experimental results provided by our collaborators.

Motivated by some of the observed behaviour of the confined microgels, we next investigate the synchronisation of active filaments in strong confinement. On the biological side, cellular appendages conferring motility, such as flagella and cilia, are known to synchronise their periodic beats. The origin of synchronization is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing, both of which can lead generically to stable phase locking. In order to help uncover the physical mechanism for hydrodynamic synchronization most essential overall in biology, we theoretically investigate in this paper the effect of strong confinement on the effectiveness of hydrodynamic synchronization. Our results point to the robustness of force modulation for synchronization, an important feature for biological dynamics that therefore suggests it could be the most essential physical mechanism overall in arrays of cilia.

In the last chapter on active filaments, we report on active metasurfaces of electronically actuated artificial cilia that can create arbitrary flow patterns in fluids near a rigid surface. Our collaborators have realised this system experimentally while we developed a theoretical model for both the mechanics of actuation of a single cilium and the flows generated by a metasurface of such artificial cilia. The single cilium model confirmed that the physical mechanism of actuation originates in the oscillating natural curvature of the cilium. The results of this study illustrate a new pathway to fine scale microfluidic manipulations, with applications from microfluidic pumping to microrobotic locomotion.

Hydrodynamic interactions. In this second part of the thesis, we focus on the hydrodynamic interactions between model microswimmers and either externally imposed flows of the surrounding fluid or with rigid surfaces in their environment.

Biological and artificial microswimmers often self-propel in external flows of vortical nature; relevant examples include algae in small-scale ocean eddies, spermatozoa in uterine peristaltic flows and bacteria in microfluidic devices. A recent experiment has shown that swimming bacteria in model vortices are expelled from the vortex all the way to a well-defined depletion zone. Motivated by this work, we propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. We further discover a conserved quantity of motion that allows us to map the phase space according to the type of the orbit (bounded vs unbounded). We next introduce translational and rotational noise into the system and quantify the quality of trapping near the centre of the vortex by examining the probability of escape and mean time of escape from the region of deterministically bounded orbits. We finally show that the predictions of our model agree with past experimental measurements.

Lastly, we investigate the behaviour of microswimmers moving through complex fibrous environments whose microstructures are anisotropic. Examples include the cytoplasm of eukaryotic cells, cervical mucus, various hydrogels and polymer networks. To address the question of swimming in such media, we develop a theoretical model for the interactions between simple, model microswimmers and slender fibres. We first investigate a fundamental case of the hydrodynamic interactions between a point force and a slender filament with a combination of asymptotic analysis and numerical computations based on the boundary element method. We discover that the force distribution along the axis of the filament takes a form analogous to the standard resistive-force theory but with drag coefficients that depend logarithmically on the distance between the point force and the filament. Next, we generalise these results to address the case of a single force-free swimmer near a slender fibre. Finally, we address the stochastic dynamics of an ensemble of swimmers navigating through a lattice of slender filaments by performing agent-based simulations. We find that the ensemble statistics depend on qualitative features of the far-field hydrodynamic signature of the model swimmers, suggesting a new method to sort swimmers based on their flow characteristics.





Lauga, Eric


Microswimmers, Fluid Mechanics, Biophysics


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
European Research Council (682754)
This work was funded by Trinity College, Cambridge (IGS scholarship to I.T.). It has also received funding from the European Research Council under the European Union's Horizon 2020 research and innovation program (Grant No. 682754 to E.L.).