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• W3163578627 abstract "In this thesis we use the bead-spring microswimmer design as a model system to study mechanical microswimming. The basic form of such a swimmer was introduced as the 'three-sphere swimmer' in Najafi & Golestanian, Phys. Rev. E (2004) and has found wide use in theoretical, numerical and experimental research. In our work, we have modified and extended the model in various ways, which, as explained in this thesis, allow us to gain insight into many general principles of microswimming, for instance the interplay between fluid drag force and swimmer elasticity in determining the efficiency of motion. The work presented here consists of both analytical solution of the equations of motion in the different investigated cases and corresponding numerical study.We begin this thesis with an introduction (chapter 0) to the world of low Reynolds number locomotion, and in particular to that of microswimming, explaining the current state of knowledge in the field regarding biological microswimmers and models thereof, both theoretical and experimental. We then explain in chapter 1 the details of, and the differences between, the Golestanian three-sphere swimmer and our bead-spring model. The Golestanian model consists of three spheres aligned along one line with the distances between two neighbouring spheres in each pair being changed in a controlled manner (which determines the swimming stroke), leading to propagation of the assembly. In the bead-spring model, we replace the specification of the stroke by that of the forces driving the motion, allow non-spherical and shape-varying beads in the design, and, in the last part of the thesis, investigate swimmer motion beyond the low Reynolds number (Stokes) regime. These changes result in a more comprehensive description of the motion with the influences of different factors such as the fluid viscosity, the energy input, the elasticity of the swimmer and its instantaneous and mean shapes all becoming important, unlike in the Golestanian swimmer where these influences are all subsumed in the specification of the swimming stroke. We use our model to calculate the velocity of our swimmer both with rigid and deformable spheres, and to different orders in the relative magnitude of bead size and bead separation.In chapter 2, we explain the two simulation methods used by us, the Walberla system and the LB3D code. Both of these are based on the lattice Boltzmann method (LBM), and their main difference lies in their being coupled respectively to a rigid body physics engine, which allows us to simulate any combinations of rigid objects in fluids, and an immersed boundary method (IBM) solver with which we can simulate deformable membranes.In chapter 3, we compare the swimmer velocities as obtained from theory and the two simulation systems for swimmers with rigid beads. We find good agreement which expectedly becomes better as the simulation systems become more idealised, such as by an increased simulation domain size and smaller Reynolds numbers of motion. We also explain how and why some microswimmers swim faster in more viscous fluids. We show that this puzzling phenomenon, observed experimentally for many species of bacteria, can occur in fully Newtonian fluids--a result which runs counter to the prevailing wisdom in the field--and arises from the dichotomous effects that the drag force has on motion at low Reynolds number. In particular, the so-called `aberrant' regime of motion, wherein the swimmer gets quicker as the fluid viscosity increases, is expected to show up for all mechanical microswimmers swimming due to the influence of sufficiently weak driving forces. The simulations fully support the theoretical prediction for the onset of the aberrant regime.In chapter 4, we use the LB3D code to simulate swimmers with deformable beads, to answer the question of whether passive shape changes--which are the changes in shape of a deformable swimmer in response to the fluid, not as a driving mechanism for motion--can be beneficial for swimming. This relates to the as yet unexplained phenomenon of metaboly, wherein spirochetes, which otherwse swim by flagellar propulsion, regularly change their shapes during their motion, without its being clear whether these shape changes are beneficial for locomotion, for food capture, or some other purpose. Restricting our attention to our model, we show that passive shape changes can result in both faster and slower swimming, and that this response depends on the swimmer's elasticity. The theory accurately predicts both the regimes, where the shape changes respectively promote and hinder the motion, that are visible in the simulations.In chapter 5 we look at active effects of shape, by studying the different swimming speeds of swimmers with rigid beads of different shapes. For this we allow the beads to be ellipsoids of revolution, and calculate the optimal aspect ratios of the ellipsoids (given a fixed volume or surface area) that maximize the swimming velocity for equal driving forces. We find that depending on the stiffness coefficient of the springs, the same shape (for instance, the ellipsoid of the lowest drag coefficient) may result in the fastest or the slowest swimmer, owing to the different energy costs of deforming springs of low and high stiffness. We show that this happens due to the swimming in the two cases being dominated either by a reduction in the drag force opposing the beads or by the hydrodynamic interaction amongst them.In chapter 6 we expand the scope of our study to incorporate the onset of non-Stokesian effects in microswimming. Using the Walberla simulation system, we systematically increase the forces driving the beads, thereby raising the Reynolds number of motion and ultimately pushing the swimmer beyond the Stokes regime. We show that the limit of this regime may be determined by matching the coasting exhibited by the swimmer to that of an underdamped harmonic oscillator, with the damping constant arising from the Stokes drag law. The effective radius of the swimmer thus found agrees excellently with that obtained from theory, and indicates that inertial effects in microswimming set in at increased driving forces (or, equivalently, larger swimming strokes) or at increased swimmer masses. Building on this heuristic investigation, we modify our theoretical model by adding a mass acceleration term in the governing equations of motion of the three beads, and show that solution of the resultant system predicts swimmer velocities which are in good agreement with those observed in simulations (and which differ significantly from the Stokes-regime calculation results). These calculations confirm the identification of the Stokes, non-Stokes and intermediate regimes seen in the simulations.We conclude in chapter 7 by a discussion of the main results presented in our work, and future possibilities for its extension." @default.
• W3163578627 created "2021-05-24" @default.
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• W3163578627 date "2016-01-01" @default.
• W3163578627 modified "2023-09-27" @default.
• W3163578627 title "Analytical and numerical study of microswimming using the 'bead-spring model'" @default.
• W3163578627 hasPublicationYear "2016" @default.
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