Travelling waves are hydrodynamically optimal for long-wavelength flagella

Flagella-induced transitions in the collective behavior of confined microswimmers

Bacteria exist in a free-swimming state or in a sessile biofilm state. The transition from free-swimming to sessile mode is characterized by changes in gene expression which alter, among others,the mechanics of flagellar motility. In this paper, we propose an idealized physical model to investigate the effects of flagellar activity on the hydrodynamic interactions among a population of microswimmers. We show that decreasing flagellar activity induces a hydrodynamically-triggered transition in confined microswimmers from turbulent-like swimming to aggregation and clustering. These results sugge…

低雷诺数流体中流体动力学耦合的球形振子的输运效率

Transportation efficiency of hydrodynamically coupled spherical oscillators in low Reynolds number fluids

本文提出基于球形振子的简化模型，研究低雷诺数流体中流体动力学相互作用对振子链输运效率的影响，发现珠子间流体相互作用增强流动且珠子数量增加可提升输运效率。

Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molec…

The optimal elastic flagellum

Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (non-smooth). Physically, biological organisms (or engineered micro-swimmers) must expend internal energy in order to produce the waves of deformation respo…

Small-amplitude swimmers can self-propel faster in viscoelastic fluids

Many small organisms self-propel in viscous fluids using travelling wave-like deformation of their bodies or appendages. Examples include small nematodes moving through soil using whole-body undulations or spermatozoa swimming through mucus using flagellar waves. When self-propulsion occurs in a non-Newtonian fluid, one fundamental question is whether locomotion will occur faster or slower than in a Newtonian environment. Here we consider the general problem of swimming using small-amplitude periodic waves in a viscoelastic fluid described by the classical Oldroyd-B constitutive relationship. …

Long-range interactions and phase defects in chains of fluid-coupled oscillators

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface; hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly effects the global dynamics, due to variations in…