Chemically active filaments: analysis and extensions of slender phoretic theory.

Autophoretic microswimmers self-propel via surface interactions with a surrounding solute fuel. Chemically-active filaments are an exciting new microswimmer design that augments traditional autophoretic microswimmers, such as spherical Janus particles, with extra functionality inherent to their slender filament geometry. Slender Phoretic Theory (SPT) was developed by Katsamba et al. to analyse the dynamics of chemically-active filaments with arbitrary three-dimensional shape and chemical patterning. SPT provides a line integral solution for the solute concentration field and slip velocity on the filament surface. In this work, we exploit the generality of SPT to calculate a number of new, non-trivial analytical solutions for slender autophoretic microswimmers, including a general series solution for phoretic filaments with arbitrary geometry and surface chemistry, a universal solution for filaments with a straight centreline, and explicit solutions for some canonical shapes useful for practical applications and benchmarking numerical code. Many common autophoretic particle designs include discrete jumps in surface chemistry; here we extend our SPT to handle such discontinuities, showing that they are regularised by a boundary layer around the jump. Since our underlying framework is linear, combinations of our results provide a library of analytic solutions that will allow researchers to probe the interplay of activity patterning and shape.

Order and information in the patterns of spinning magnetic micro-disks at the air-water interface.

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between information and structures. Here, we use, as a model experimental system, hundreds of spinning magnetic micro-disks self-organizing at the air-water interface to generate various spatiotemporal patterns with varying degrees of order. Using the neighbor distance as the information-bearing variable, we demonstrate the links among information, structure, and interactions. We establish a direct link between information and structure without using explicit knowledge of interactions. Last, we show that the Shannon entropy by neighbor distances is a powerful observable in characterizing structural changes. Our findings are relevant for analyzing natural self-organizing systems and for designing collective robots.

A note on the Stokes phenomenon in flow under an elastic sheet.

The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue 'Stokes at 200 (part 2)'.

A Light-Driven Microgel Rotor.

The current understanding of motility through body shape deformation of micro-organisms and the knowledge of fluid flows at the microscale provides ample examples for mimicry and design of soft microrobots. In this work, a 2D spiral is presented that is capable of rotating by non-reciprocal curling deformations. The body of the microswimmer is a ribbon consisting of a thermoresponsive hydrogel bilayer with embedded plasmonic gold nanorods. Such a system allows fast local photothermal heating and nonreciprocal bending deformation of the hydrogel bilayer under nonequilibrium conditions. It is shown that the spiral acts as a spring capable of large deformations thanks to its low stiffness, which is tunable by the swelling degree of the hydrogel and the temperature. Tethering the ribbon to a freely rotating microsphere enables rotational motion of the spiral by stroboscopic irradiation. The efficiency of the rotor is estimated using resistive force theory for Stokes flow. This research demonstrates microscopic locomotion by the shape change of a spiral and may find applications in the field of microfluidics, or soft microrobotics.

The near and far of a pair of magnetic capillary disks.

Control on microscopic scales depends critically on our ability to manipulate interactions with different physical fields. The creation of micro-machines therefore requires us to understand how multiple fields, such as surface capillary or electro-magnetic fields, can be used to produce predictable behaviour. Recently, a spinning micro-raft system was developed that exhibited both static and dynamic self-assembly [Wang et al., Sci. Adv., 2017, 3, e1602522]. These rafts employed both capillary and magnetic interactions and, at a critical driving frequency, would suddenly change from stable orbital patterns to static assembled structures. In this paper, we explain the dynamics of two interacting micro-rafts through a combination of theoretical models and experiments. This is first achieved by identifying the governing physics of the orbital patterns, the assembled structures, and the collapse separately. We find that the orbital patterns are determined by the short range capillary interactions between the disks, while the explanations of the other two behaviours only require the capillary far field. Finally we combine the three models to explain the dynamics of a new micro-raft experiment.

The swimming of a deforming helix.

Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induce movement by deforming a helical-shaped body. Recently, artificial devices have been created which also generate motion by deforming their helical body in a non-reciprocal way (A. Mourran et al. Adv. Mater. 29, 1604825, 2017). Inspired by these systems, we investigate the transport of a deforming helix within a viscous fluid. Specifically, we consider a swimmer that maintains a helical centreline and a single handedness while changing its helix radius, pitch and wavelength uniformly across the body. We first discuss how a deforming helix can create a non-reciprocal translational and rotational swimming stroke and identify its principle direction of motion. We then determine the leading-order physics for helices with small helix radius before considering the general behaviour for different configuration parameters and how these swimmers can be optimised. Finally, we explore how the presence of walls, gravity, and defects in the centreline allow the helical device to break symmetries, increase its speed, and generate transport in directions not available to helices in bulk fluids.

The non-Gaussian tops and tails of diffusing boomerangs.

Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter, 2016, 12, 4318]. This in turn can lead to anomalous diffusion characteristics, including mean drift. In this paper, we develop a general theoretical explanation for these measurements. The idea relies on calculating the two-dimensional probability densities at the centre of mobility of the particle, where all distributions are Gaussian, and then transforming them to a different reference point. Our model clearly captures the experimental results, without any fitting parameters, and demonstrates that the one-dimensional probability distributions may also exhibit strongly non-Gaussian tops. These results indicate that the choice of tracking point can cause a considerable departure from Gaussian statistics, potentially causing some common modelling techniques to fail.

Microscale flow dynamics of ribbons and sheets.

Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibres and ribbons. However, such theories entail restrictions on the shapes that can be studied, and often break down in regions where standard boundary element methods are still impractical. In this paper we develop a regularised stokeslet method for ribbons and sheets in order to bridge the gap between asymptotic and boundary element methods. The method is validated against the analytical solution for plate ellipsoids, as well as the dynamics of ribbon helices and an experimental microswimmer. We then demonstrate the versatility of this method by calculating the flow around a double helix, and the swimming dynamics of a microscale "magic carpet".

Rotation of slender swimmers in isotropic-drag media.

The drag anisotropy of slender filaments is a critical physical property allowing swimming in low-Reynolds number flows, and without it linear translation is impossible. Here we show that, in contrast, net rotation can occur under isotropic drag. We first demonstrate this result formally by considering the consequences of the force- and torque-free conditions on swimming bodies and we then illustrate it with two examples (a simple swimmers made of three rods and a model bacterium with two helical flagellar filaments). Our results highlight the different role of hydrodynamic forces in generating translational versus rotational propulsion.

The passive diffusion of Leptospira interrogans.

Motivated by recent experimental measurements, the passive diffusion of the bacterium Leptospira interrogans is investigated theoretically. By approximating the cell shape as a straight helix and using the slender-body-theory approximation of Stokesian hydrodynamics, the resistance matrix of Leptospira is first determined numerically. The passive diffusion of the helical cell is then obtained computationally using a Langevin formulation which is sampled in time in a manner consistent with the experimental procedure. Our results are in excellent quantitative agreement with the experimental results with no adjustable parameters.