Development of an Elastic, Electrically Conductive Coating for TPU Filaments

Electrically conductive filaments are used in a wide variety of applications, for example, in smart textiles and soft robotics. Filaments that conduct electricity are required for the transmission of energy and information, but up until now, most electrically conductive fibers, filaments and wires offer low mechanical elongation. Therefore, they are not well suited for the implementation into elastomeric composites and textiles that are worn close to the human body and have to follow a wide range of movements. In order to overcome this issue, the presented study aims at the development of electrically conductive and elastic filaments based on a coating process suited for multifilament yarns made of thermoplastic polyurethane (TPU). The coating solution contains TPU, carbon nanotubes (CNT) and N-Methyl-2-pyrrolidone (NMP) with varied concentrations of solids and electrically conductive particles. After applying the coating to TPU multifilament yarns, the mechanical and electrical properties are analyzed. A special focus is given to the electromechanical behavior of the coated yarns under mechanical strain loading. It is determined that the electrical conductivity is maintained even at elongations of up to 100%.

Stable Knots and Links in Electromagnetic Fields

Persistent topological structures in physical systems have become increasingly important over the last years. Electromagnetic fields with knotted field lines play a special role among these, since they can be used to transfer their knottedness to other systems like plasmas and quantum fluids. In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time, so that all knotted closed field lines maintain their knot type. We use an approach due to Bateman to prove that for every link L there is such an electromagnetic field that satisfies Maxwell’s equations in free space and that has closed electric and magnetic field lines in the shape of L for all time. The knotted and linked field lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.

Coordination in Coupled Arrays of Stiff Filaments—Modelling and Simulation

We present the mechanical model of an array of elastic filaments and simulate the response with different mechanical couplings. This class of systems is inspired by robust and elegant solutions for locomotion mechanics that have emerged in several small-scale biological entities in the form of beating protrusions, such as cellular cilia and eukaryotic flagella. The collective dynamics of cilia arrays reveals important features such as array alignments, two-phase asymmetric beating of individual filaments, and the emergence of metachronal coordination, which make them suitable for bio-inspired terrestrial and aquatic locomotion. The model presented here is the basis for further developments towards the design of terrestrial and aquatic locomotion systems for general purpose robotic devices.

Synchronized oscillations, metachronal waves, and jammed clusters in sterically interacting active filament arrays

Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. A striking example is ciliary arrays in the mammalian respiratory tract; here individual filaments communicate through direct interactions and through the surrounding fluid to generate metachronal traveling waves crucial for mucociliary clearance. The mechanisms underlying this collective response and the essential ingredients for stable synchronization remain a mystery. In this article, we describe Brownian dynamics simulations of multi-filament arrays, demonstrating that short-range steric inter-filament interactions and surface-roughness are sufficient to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. Starting from results for the collective dynamics of two- and three-filament systems, we identify parameter ranges in which inter-filament interactions lead to synchronized oscillations. We then study how these results generalize to large one-dimensional arrays of many interacting filaments. The phase space characterizing the multi-filament array dynamics and deformations exhibits rich behaviors, including oscillations and traveling metachronal waves, depending on the interplay between geometric spacing between filaments, activity, and elasticity of the filaments. Interestingly, the existence of metachronal waves is nonmonotonic with respect to the inter-filament spacing. We also find that the degree of filament surface roughness significantly affects the dynamics — roughness on scales comparable to the filament thickness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Our simulations suggest that short-ranged steric inter-filament interactions are sufficient and perhaps even critical for the development, stability and regulation of collective patterns.

Flapping, swirling and flipping: Non-linear dynamics of pre-stressed active filaments

Initially straight slender elastic filaments and rods with geometrically constrained ends buckle and form stable two-dimensional shapes when compressed by bringing the ends together. It is known that beyond a critical value of this pre-stress, clamped rods transition to bent, twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such pre-stressed, initially twisted filaments subject to active follower forces and dissipative fluid drag. We find that degree of boundary constraint and the directionality of active forces determines if oscillatory instabilities can arise. When filaments are clamped at one end and pinned at the other with follower forces directed towards the clamped end, stable planar flapping oscillations result; reversing the directionality of the active forces quenches the instability. When both ends are clamped however, computations reveal a novel secondary instability wherein planar oscillations are destabilized by off-planar perturbations resulting in three-dimensional swirling patterns with periodic flips. These swirl-flip transitions are characterized by two distinct and time-scales. The first corresponds to unidirectional swirling rotation around the end-to-end axis. The second captures the time between flipping events when the direction of swirling reverses. We find that this spatiotemporal dance resembles relaxation oscillations with each cycle initiated by a sudden jump in torsional deformation and then followed by a period of gradual decrease in net torsion until the next cycle of variations. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by non-conservative active forces. Practically, our results suggest avenues by which pre-stress, elasticity and activity may be used to design synthetic fluidic elements to pump or mix fluid at macroscopic length scales.