Bendability parameter for twisted ribbons to describe longitudinal wrinkling and delineate the near-threshold regime.

We propose a dimensionless bendability parameter, ε^{-1}=[(h/W)^{2}T^{-1}]^{-1}, for wrinkling of thin, twisted ribbons with thickness h, width W, and tensional strain T. Bendability permits efficient collapse of data for wrinkle onset, wavelength, critical stress, and residual stress, demonstrating longitudinal wrinkling's primary dependence on this parameter. This parameter also allows us to distinguish the highly bendable range (ε^{-1}>20) from moderately bendable samples (ε^{-1}∈(0,20]). We identify scaling relations to describe longitudinal wrinkles that are valid across our entire set of simulated ribbons. When restricted to the highly bendable regime, simulations confirm theoretical near-threshold (NT) predictions for wrinkle onset and wavelength.

Energetics of twisted elastic filament pairs.

We investigate the elastic energy stored in a filament pair as a function of applied twist by measuring torque under prescribed end-to-end separation conditions. We show that the torque increases rapidly to a peak with applied twist when the filaments are initially separate, then decreases to a minimum as the filaments cross and come into contact. The torque then increases again while the filaments form a double helix with increasing twist. A nonlinear elasto-geometric model that combines the effect of geometrical nonlinearities with large stretching and self-twist is shown to capture the evolution of the helical geometry, torque profile, and stored energy with twist. We find that a large fraction of the total energy is stored in stretching the filaments, which increases with separation distance and applied tension. We find that only a small fraction of energy is stored in the form of bending energy, and that the contribution due to contact energy is negligible. Further, we provide analytical formulas for the torque observed as a function of the applied twist and the inverse relation of the observed angle for a given applied torque in the Hookean limit. Our study highlights the consequences of stretchablility on filament twisting, which is a fundamental topological transformation relevant to making ropes, tying shoelaces, actuating robots, and the physical properties of entangled polymers.

Computational model of twisted elastic ribbons.

We develop an irregular lattice mass-spring model to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally observed modes, including transitions from helicoids to longitudinal wrinkles, creased helicoids and loops with self-contact, and transverse wrinkles to accordion self-folds. Our simulations also show that the twist angles at which the primary longitudinal and transverse wrinkles appear are well described by various analyses of the Föppl-von Kármán equations, but the characteristic wavelength of the longitudinal wrinkles has a more complex relationship to applied tension than previously estimated. The clamped edges are shown to suppress longitudinal wrinkling over a distance set by the applied tension and the ribbon width, but otherwise have no apparent effect on measured wavelength. Further, by analyzing the stress profile, we find that longitudinal wrinkling does not completely alleviate compression, but caps the magnitude of the compression. Nonetheless, the width over which wrinkles form is observed to be wider than the near-threshold analysis predictions: the width is more consistent with the predictions of far-from-threshold analysis. However, the end-to-end contraction of the ribbon as a function of twist is found to more closely follow the corresponding near-threshold prediction as tension in the ribbon is increased, in contrast to the expectations of far-from-threshold analysis. These results point to the need for further theoretical analysis of this rich thin elastic system, guided by our physically robust and intuitive simulation model.

Density-mediated spin correlations drive edge-to-bulk flow transition in active chiral matter.

We demonstrate that edge currents develop in active chiral matter due to boundary shielding over a wide range of densities corresponding to a gas, fluid, and crystal. The system is composed of spinning disk-shaped grains with chirally arranged tilted legs confined in a circular vibrating chamber. The edge currents are shown to increasingly drive circulating bulk flows with area fraction as percolating clusters develop due to increasing spin-coupling between neighbors mediated by frictional contacts. Edge currents are observed even in the dilute limit. While, at low area fraction, the average flux vanishes except within a distance that is of the order of a particle diameter of the boundary, the penetration depth grows with increasing area fraction until a solid-body rotation is achieved corresponding to the highest packing, where the particles are fully caged with hexagonal order and spin in phase with the entire packing. A coarse-grained model, based on the increased collisional interlocking of the particles with area fraction and the emergence of order, captures the observed flow fields.

Dissolution-driven propulsion of floating solids.

We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.

Escape dynamics of confined undulating worms.

We investigate the escape dynamics of oligochaeta Lumbriculus variegatus by confining them to a quasi-2D circular chamber with a narrow exit passage. The worms move by performing undulatory and peristaltic strokes and use their head to actively probe their surroundings. We show that the worms follow the chamber boundary with occasional reversals in direction and with velocities determined by the orientation angle of the body with respect to the boundary. The average time needed to reach the passage decreases with its width before approaching a constant, consistent with a boundary-following search strategy. We model the search dynamics as a persistent random walk along the boundary and demonstrate that the head increasingly skips over the passage entrance for smaller passage widths due to body undulations. The simulations capture the observed exponential time-distributions taken to reach the exit and their mean as a function of width when starting from random locations. Even after the head penetrates the passage entrance, we find that the worm does not always escape because the head withdraws rhythmically back into the chamber over distances set by the dual stroke amplitudes. Our study highlights the importance of boundary following and body strokes in determining how active matter escapes from enclosed spaces.

Nonadditive drag of tandem rods drafting in granular sediments.

We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between the leading and following body is observed in both dry granular beds and while immersed in viscous Newtonian fluids across the quasistatic and the rate-dependent regimes. Through refractive index matching, we visualize the sediment flow past the two rods and show that a stagnant region develops in their reference frame between the rods for small separations. Thus, the following rod is increasingly shielded from the granular flow with decreasing separation distance, leading to a lower net drag. Care should be exercised in applying resistive force theory to multicomponent objects moving in granular sediments based on our result that drag is not additive at short separation distances.

Tensional twist-folding of sheets into multilayered scrolled yarns.

Twisting sheets as a strategy to form functional yarns relies on millennia of human practice in making catguts and fabric wearables, but it still lacks overarching principles to guide their intricate architectures. We show that twisted hyperelastic sheets form multilayered self-scrolled yarns, through recursive folding and twist localization, that can be reconfigured and redeployed. We combine weakly nonlinear elasticity and origami to explain the observed ordered progression beyond the realm of perturbative models. Incorporating dominant stretching modes with folding kinematics, we explain the measured torque and energetics originating from geometric nonlinearities due to large displacements. Complementarily, we show that the resulting structures can be algorithmically generated using Schläfli symbols for star-shaped polygons. A geometric model is then introduced to explain the formation and structure of self-scrolled yarns. Our tensional twist-folding framework shows that origami can be harnessed to understand the transformation of stretchable sheets into self-assembled architectures with a simple twist.

Mitigating exhalation puffs during oxygen therapy for respiratory disease.

We investigate the dispersal of exhalations corresponding to a patient experiencing shortness of breath while being treated for a respiratory disease with oxygen therapy. Respiration through a nasal cannula and a simple O2 mask is studied using a supine manikin equipped with a controllable mechanical lung by measuring aerosol density and flow with direct imaging. Exhalation puffs are observed to travel 0.35 ± 0.02 m upward while wearing a nasal cannula, and 0.29 ± 0.02 m laterally through a simple O2 mask, posing a higher direct exposure risk to caregivers. The aerosol-laden air flows were found to concentrate in narrow conical regions through both devices at several times their concentration level compared with a uniform spreading at the same distance. We test a mitigation strategy by placing a surgical mask loosely over the tested devices. The mask is demonstrated to alleviate exposure by deflecting the exhalations from being launched directly above a supine patient. The surgical mask is found to essentially eliminate the concentrated aerosol regions above the patient over the entire oxygenation rates used in treatment in both devices.

Unstable Invasion of Sedimenting Granular Suspensions.

We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the timescale over which the instability develops is given by the volume fraction dependent settling timescale of the grains in the cell. We then show that the mobility inversion and the nonequilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

Birth and decay of tensional wrinkles in hyperelastic sheets.

We demonstrate with experiments that wrinkling in stretched latex sheets occurs over finite strains, and that their amplitudes grow and then decay to zero over a greater range of applied strains compared with linear elastic materials. The wrinkles occur provided the sheet is sufficiently thin compared to its width, and only over a finite range of length-to-width ratios. We show with simulations that the Mooney-Rivlin hyperelastic model describes the observed growth and decay of the wrinkles in our experiments. The decrease of wavelength with applied tension is found to be consistent with a far-from-threshold scenario proposed by Cerda and Mahadevan in 2003. However, the amplitude is observed to decrease with increasing tensile load, in contrast with the prediction of their original model. We address the crucial assumption of collapse of compressive stress, as opposed to collapse of compressive strain, underlying the far-from-threshold analysis, and test it by measuring the actual arc-length of the stretched sheet in the transverse direction and its difference from the width of a planar projection of the wrinkled shape. Our experiments and numerical simulations indicate a collapse of the compressive stress and reveal that a proper implementation of the far-from-threshold analysis is consistent with the nonmonotonic dependence of the amplitude on applied tensile load observed in experiments and simulations. Thus, our work support and extend far-from-threshold analysis to the stretching problem of rectangular hyperelastic sheets.

Burrowing dynamics of aquatic worms in soft sediments.

We investigate the dynamics of Lumbriculus variegatus in water-saturated sediment beds to understand limbless locomotion in the benthic zone found at the bottom of lakes and oceans. These slender aquatic worms are observed to perform elongation-contraction and transverse undulatory strokes in both water-saturated sediments and water. Greater drag anisotropy in the sediment medium is observed to boost the burrowing speed of the worm compared to swimming in water with the same stroke using drag-assisted propulsion. We capture the observed speeds by combining the calculated forms based on resistive-force theory of undulatory motion in viscous fluids and a dynamic anchor model of peristaltic motion in the sediments. Peristalsis is found to be effective for burrowing in noncohesive sediments which fill in rapidly behind the moving body inside the sediment bed. Whereas the undulatory stroke is found to be effective in water and in shallow sediment layers where anchoring is not possible to achieve peristaltic motion. We show that such dual strokes occur as well in the earthworm Eisenia fetida which inhabits moist sediments that are prone to flooding. Our analysis in terms of the rheology of the medium shows that the dual strokes are exploited by organisms to negotiate sediment beds that may be packed heterogeneously and can be used by active intruders to move effectively from a fluid through the loose bed surface layer which fluidizes easily to the well-consolidated bed below.

Effective drag of a rod in fluid-saturated granular beds.

We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of the depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction µ_{e} encountered over six orders of magnitude of speeds. While a constant µ_{e} is found when the grain size, rod depth, and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze µ_{e} in terms of the inertial number I and viscous number J to understand the relative importance of inertia and viscous forces, respectively. For sufficiently high fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function µ_{e}=µ_{o}+kJ^{n}, where µ_{o} is the effective friction measured in the quasistatic limit, and k and n are material constants. The drag is then analyzed in terms of the effective viscosity η_{e} and found to decrease systematically as a function of J. We further show that η_{e} as a function of J is directly proportional to the fluid viscosity and the µ_{e} encountered by the rod.

Publisher's Note: Drag law for an intruder in granular sediments [Phys. Rev. E 95, 032901 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.032901.

Persistence of Perfect Packing in Twisted Bundles of Elastic Filaments.

It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of twist due to a subtle counteraction of geometric expansion with elastic contraction. Using x-ray scanning and by locating each filament in the bundle, we show the remarkable persistence of order even as the twist is increased well above 360°, by measuring the spatial correlation function across the bundle cross section. We introduce a model which analyzes the combined effects of elasticity including filament stretching and radial and hoop compression necessary to explain this generic preservation of order observed with Hookean filaments.

Dynamic Wrinkling and Strengthening of an Elastic Filament in a Viscous Fluid.

We investigate the wrinkling dynamics of an elastic filament immersed in a viscous fluid submitted to compression at a finite rate with experiments and by combining geometric nonlinearities, elasticity, and slender body theory. The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time. We discover a new dynamical regime characterized by a time scale with a nontrivial dependence on the loading rate, where the growth of the instability is superexponential and the wave number is an increasing function of the loading rate. We find that this time scale can be interpreted as the characteristic time over which the filament transitions from the extensible to the inextensible regime. In contrast with our analysis with moving boundary conditions, Biot's analysis in the limit of infinitely fast loading leads to rate independent exponential growth and wavelength.

Measuring geometric frustration in twisted inextensible filament bundles.

We investigate with experiments and mapping the structure of a hexagonally ordered filament bundle that is held near its ends and progressively twisted around its central axis. The filaments are free to slide relative to each other and are further held under tension-free boundary conditions. Measuring the bundle packing with micro x-ray imaging, we find that the filaments develop the helical rotation Ω imposed at the boundaries. We then show that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We further demonstrate that the mean interfilament distance is minimal on the surface, which can be approximated by a hemisphere with an effective curvature K_{eff}=3Ω^{2}. Examining the packing on the dual surface, we analyze the geometric frustration of packing in twisted bundles and find the core to remain relatively hexagonally ordered with interfilament strains growing from the bundle center, driving the formation of defects at the exterior of highly twisted bundles.

Drag law for an intruder in granular sediments.

We investigate the drag experienced by a spherical intruder moving through a medium consisting of granular hydrogels immersed in water as a function of its depth, size, and speed. The medium is observed to display a yield stress with a finite force required to move the intruder in the quasistatic regime at low speeds before rapidly increasing at high speeds. In order to understand the relevant time scales that determine drag, we estimate the inertial number I given by the ratio of the time scales required to rearrange grains due to the overburden pressure and imposed shear and the viscous number J given by the ratio of the time scales required to sediment grains in the interstitial fluid and imposed shear. We find that the effective friction µ_{e} encountered by the intruder can be parametrized by I=sqrt[ρ_{g}/P_{p}]v_{i}, where ρ_{g} is the density of the granular hydrogels, v_{i} is the intruder speed, and P_{p} is the overburden pressure due to the weight of the medium, over a wide range of I where the Stokes number St=I^{2}/J≫1. We then show that µ_{e} can be described by the function µ_{e}(I)=µ_{0}+αI^{ß}, where µ_{0}, α, and ß are constants that depend on the medium. This formula can be used to predict the drag experienced by an intruder of a different size at a different depth in the same medium as a function of its speed.

Headward growth and branching in subterranean channels.

We investigate the erosive growth of channels in a thin subsurface sedimentary layer driven by hydrodynamic drag toward understanding subterranean networks and their relation to river networks charged by ground water. Building on a model based on experimental observations of fluid-driven evolution of bed porosity, we focus on the characteristics of the channel growth and their bifurcations in a horizontal rectangular domain subject to various fluid source and sink distributions. We find that the erosion front between low- and high-porosity regions becomes unstable, giving rise to branched channel networks, depending on the spatial fluctuations of the fluid flow near the front and the degree to which the flow is above the erodibility threshold of the medium. Focusing on the growth of a network starting from a single channel, and by identifying the channel heads and their branch points, we find that the number of branches increases sublinearly and is affected by the source distribution. The mean angles between branches are found to be systematically lower than river networks in humid climates and depend on the domain geometry.

Evolution of Porosity and Channelization of an Erosive Medium Driven by Fluid Flow.

We demonstrate that a homogeneous porous medium composed of sedimentary particles develops channels due to curvature driven growth of fluid flow coupled with an increase in porosity. While the flux is increased linearly, the evolution of porosity is observed to be intermittent with erosion occurring at the boundaries between low and high porosity regions. Calculating the spatial distribution of the flow within the medium and the fluid stress given by the product of the fluid flux and the volume fraction of the particles, we find that the system organizes itself to be locally near the threshold needed to erode the weakest particles. A statistical model simulating the coupling of the erosion, transport, and deposition of the particles to the local fluid flow and porosity is found to capture the overall development of the observed channels.