Flagellated and Ciliated Microswimmers

The propulsion mechanism and the swimming dynamics of various ciliated microorganisms are investigated. Ciliated microswimmers, ranging from a single flagellated sperm cell to multiciliated microswimmers, propel themselves by cilia attached to their cell membrane. The underlying complex biomachinery of a cilium, the axoneme, employs an evolutionary developed mechanism, which is tailored to generate an optimal beating pattern to propel the swimmer through the environment it encounters. In this work mesoscale hydrodynamics simulations are used to simulate the whip-like motion of the cilium at low Reynolds numbers. The particle-based approach of multi-particle collision dynamics enables simulations of self-propelled microswimmers in complex confinements where steric and hydrodynamic interactions strongly influence the swimming dynamics. Details of cilia arrangement and beat shape are critical in understanding propulsion and surface attraction. The axonemal beating of cilia and flagella is modeled by a semi-flexible polymer with periodically changing intrinsic curvature. In the spirit of a minimalistic modeling approach, the axoneme is only bend along one degree of freedom, creating a defined beat plane. The first part discusses surface attraction and guidance of sperm cells swimming in confinement. In particular, the motion of sperm in geometrically structured (zigzag) microchannels provides an interesting geometry for the manipulation and sorting of sperm cells. Sperm swim along the channel walls, but are deflected from the sidewall at sharp bends. The simulation results are in qualitative agreement with recent microfluidic experiments and provide a better insight into the mechanisms of sperm navigation under strong confinement. The effective adhesion of a sperm cell to a flat surface depends both on the envelope of its planar beat shape and on the orientation of its beat plane. A proposed self-propelled steric model explains the average deflection around corners. Further investigation of various beat patterns with increasing wavelength results in complex surface attraction dynamics of the sperm cell. The insight from the steric model helps to understand the surface attraction in terms of the beat-shape envelope. It is found that when the beat pattern exceeds a critical wavelength, the flagellum buckles and beats in a complex three-dimensional shape, which strongly increases surface attraction. Indeed, the analysis of three-dimensional experimental holographic data of freely swimming human sperm cells shows that on average the beat pattern is relatively planar but exhibits regular nonplanar components twice per beat. By comparing this high-resolution experimental data with simulation results, a possible explanation for the nonplanar beating is obtained. Simulated sperm with imposed planar bends and two orders of magnitude smaller twist than bending rigidity undergo a twist instability and exhibit a three-dimensional beat pattern. Simulations allow to map the phase space of the twist instability, which shows no dependence on the bending rigidity, but a sharp transition from planar to three-dimensional beating below a critical twist rigidity. A localized twist wave goes through the cilium, which twists the cilium at a very narrow segment close to the point of minimal in-plane bending. This creates essentially two beat planes, separating the cilium in two segments of planar beating before and after the twisting region. In the second part, propulsion and synchronization of multi-ciliated spherical swimmers with different cilia densities and arrangements are studied. Instead of pre-imposing the intrinsic curvature, a ratchet-like mechanism drives the ciliary beat pattern. Therefore, the beat period can be influenced by the flow generated from the motion of the other cilia. The propulsion velocity of ciliated spherical swimmers increases sub-linearly with increasing cilia density. Large differences in propulsion speed for equal numbers of cilia with different arrangements on the sphere are found. For symmetric ciliated swimmers, the emergence of a stable synchronization state is found to depend on the initial condition. In some symmetric 9-cilia swimmers, long stable phases of synchronization emerge. Swimmers whose phase difference increases due to phase slips have a slower propulsion velocity than swimmers which develop a constant phase-lag between cilia. Turning to an oscillator model for cilia synchronization, the emergence of metachronal coordination in different topologies above a surface is studied. The oscillators are modeled as hydrodynamically interacting spheres propelled along a circular trajectory. Non-dimensionalization of the model provides the radial confinement strength as the only control parameter. Boundary effects influence the synchronization as well as the confinement strength. In open chains of oscillators as well as in circular arrangements, stable large-scale patterns of synchronization emerge until a critical confinement strength. No long-term coordination emerges above a critical confinement strength in any of the studies topologies. Finally, the cilium model is used to simulate a tuft of cilia, modeled to describe the placement of cilia in brain ventricles of mice. It is found that the particle flux towards the surface is located in hot-spots where the flux is significantly enhanced compared to purely diffusive transport. This shows the important role of ciliary beating in molecular transport towards primary cilia on the surface of the ventricles

Motion at low Reynolds number

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.Includes bibliographical references (p. 181-192).The work described in this thesis centers on inertialess motion at low Reynolds numbers at the crossroad between biofluids and microfluids. Here we address questions regarding locomotion of micro-swimmers, transport of nutrient around micro-organisms as well as mixing and heat exchange inside micro-droplets of water. A general framework for the investigation of optimal locomotion strategies for slender swimmers has been developed and applied to different systems. Here we exclusively study the hydrodynamical aspects of locomotion without further consideration for the swimmers internal dynamics. The first system studied is the "three-link" swimmer, first introduced and discussed by Nobel prize laureate E.M. Purcell in his famous lecture "Life at low Reynolds number" [121]. For this simple swimmer, we find and later discuss optimal stroke kinematics and swimmer geometries. We then further investigate flagellated swimmers and verify the convergence of the optimization procedure in the case of a single flagellum, for which the optimal stroke kinematics are known analytically. Optimal stroke kinematics and geometries for unifiagellates are also computed and found to be relevant in the context of biological microorganisms.(cont.) We then turn our attention to stroke kinematics of biflagellates and demonstrate that all the different strokes, which are experimentally observed to be performed by biflagellated organisms such as green algae chlamydomonas, are found to be local hydrodynamical optima. These observations strongly suggest the central role of hydrodynamics in the internal dynamical organization of the stroke patterns. Finally, we present experimental results on convective transport and mixing inside small droplets of water sitting on superhydrophobic substrates. We demonstrate by a scaling analysis, that the regular convection pattern is due to a thermocapillary driven Marangoni flow at the surface of the droplet. We develop an analytical solution for the temperature and flow field inside the droplet, which is found to be in agreement with our experimentally recorded data.by Daniel See-Wai Tam.Ph.D