Obstructed swelling and fracture of hydrogels.

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Unidirectional Freezing of Polymer Solution Droplets.

Ice templating provides a means of generating textures with a well-defined topography. Recent applications involve the freezing of water droplets, with or without colloids, on flat or textured surfaces. An interesting feature of water droplets freezing on a substrate is the formation of a pointy tip at a constant angle, regardless of the substrate temperature, surface energy, or droplet volume. Here, by adding the polymer to water, we demonstrate how to manipulate and even prevent the formation of such an icy tip. We find that the sharpness of the tip decreases with increasing polymer concentration until completely disappearing above the overlap concentration, while the total freezing time increases concomitantly. Building on these observations, we combined simple geometrical arguments with heat flux measurements to model and connect the spatial and temporal evolution of polymer droplets under unidirectional freezing. Together our results provide new ways to control the shape of frozen droplets for ice templating or microstructure fabrication, with applications in tissue engineering, separation membranes, and soft robotics.

An energy-optimization method to study gel-swelling in confinement.

We recast the problem of hydrogel swelling under physical constraints as an energy optimization problem. We apply this approach to compute equilibrium shapes of hydrogel spheres confined within a jammed matrix of rigid beads and interpret the results to determine how confinement modifies the mechanics of swollen hydrogels. In contrast to the unconfined case, we find a spatial separation of strains within the bulk of the hydrogel as the strain becomes localized to an outer region. We also explore the contact mechanics of the gel, finding a transition from Hertzian behavior to non-Hertzian behavior as a function of swelling. Our model, implemented in the Morpho shape optimization environment and validated against an experimentally demonstrated prototypical scenario, can be applied in any dimension, readily adapted to diverse swelling scenarios and extended to use other energies in conjunction.

Poroelastic plant-inspired structures & materials to sense, regulate flow, and move.

Despite their lack of a nervous system and muscles, plants are able to feel, regulate flow, and move. Such abilities are achieved through complex multi-scale couplings between biology, chemistry, and physics, making them difficult to decipher. A promising approach is to decompose plant responses in different blocks that can be modeled independently, and combined later on for a more holistic view. In this perspective, we examine the most recent strategies for designing plant-inspired soft devices that leverage poroelastic principles to sense, manipulate flow, and even generate motion. We will start at the organism scale, and study how plants can use poroelasticity to carry informationin-lieuof a nervous system. Then, we will go down in size and look at how plants manage to passively regulate flow at the microscopic scale using valves with encoded geometric non-linearities. Lastly, we will see at an even smaller scale, at the nanoscopic scale, how fibers orientation in plants' tissues allow them to induce motion using water instead of muscles.

Poroelastic shape relaxation of hydrogel particles.

Hydrogels are commonly used in research and energy, manufacturing, agriculture, and biomedical applications. These uses typically require hydrogel mechanics and internal water transport, described by the poroelastic diffusion coefficient, to be characterized. Sophisticated indentation-based approaches are typically used for this purpose, but they require expensive instrumentation and are often limited to planar samples. Here, we present Shape Relaxation (SHARE), an alternative way to assess the poroelastic diffusion coefficient of hydrogel particles that is cost-effective, straightforward, and versatile. This approach relies on first indenting a hydrogel particle via swelling within a granular packing, and then monitoring how the indented shape of the hydrogel relaxes after it is removed from the packing. We validate this approach using experiments in packings with varying grain sizes and confining stresses; these yield measurements of the poroelastic diffusion coefficient of polyacrylamide hydrogels that are in good agreement with those previously obtained using indentation approaches. We therefore anticipate that the SHARE approach will find broad use in a range of applications of hydrogels and other swellable soft materials.

Under pressure: Hydrogel swelling in a granular medium.

Hydrogels hold promise in agriculture as reservoirs of water in dry soil, potentially alleviating the burden of irrigation. However, confinement in soil can markedly reduce the ability of hydrogels to absorb water and swell, limiting their widespread adoption. Unfortunately, the underlying reason remains unknown. By directly visualizing the swelling of hydrogels confined in three-dimensional granular media, we demonstrate that the extent of hydrogel swelling is determined by the competition between the force exerted by the hydrogel due to osmotic swelling and the confining force transmitted by the surrounding grains. Furthermore, the medium can itself be restructured by hydrogel swelling, as set by the balance between the osmotic swelling force, the confining force, and intergrain friction. Together, our results provide quantitative principles to predict how hydrogels behave in confinement, potentially improving their use in agriculture as well as informing other applications such as oil recovery, construction, mechanobiology, and filtration.

Bending and Stretching of Soft Pores Enable Passive Control of Fluid Flows.

Programmable valves and actuators are widely used in man-made systems to provide sophisticated control of fluid flows. In nature, however, this process is frequently achieved using passive soft materials. Here we study how elastic deformations of cylindrical pores embedded in a flexible membrane enable passive flow control. We develop biomimetic valves with variable pore radius, membrane radius, and thickness. Our experiments reveal a mechanism where small deformations bend the membrane and constrict the pore-thus reducing flow-while larger deformations stretch the membrane, expand the pore, and enhance flow. We develop a theory capturing this highly nonmonotonic behavior, and validate the scaling across a broad range of material and geometric parameters. Our results suggest that intercompartmental flow control in living systems can be encoded entirely in the physical attributes of soft materials. Moreover, this design could enable autonomous flow control in man-made systems.

Author Correction: How wind drives the correlation between leaf shape and mechanical properties.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Drying of channels by evaporation through a permeable medium.

We study the drying of isolated channels initially filled with water moulded in a water-permeable polymer (polydimethylsiloxane, PDMS) by pervaporation, when placed in a dry atmosphere. Channel drying is monitored by tracking a meniscus, separating water from air, advancing within the channels. The role of two geometrical parameters, the channel width and the PDMS thickness, is investigated experimentally. All data show that drying displays a truncated exponential dynamics. A fully predictive analytical model, in excellent agreement with the data, is proposed to explain such a dynamics, by solving water diffusion both in the PDMS layer and in the gas inside the channel. This drying process is crucial in geological or biological systems, such as rock disintegration or the drying of plant leaves after cavitation and embolism formation.

How wind drives the correlation between leaf shape and mechanical properties.

From a geometrical point of view, a non-sessile leaf is composed of two parts: a large flat plate called the lamina, and a long beam called the petiole which connects the lamina to the branch/stem. While wind is exerting force (e.g. drag) on the lamina, the petiole undergoes twisting and bending motions. To survive in harsh abiotic conditions, leaves may have evolved to form in different shapes, resulting from a coupling between the lamina geometry and the petiole mechanical properties. In this study, we measure the shape of laminae from 120 simple leaf species (no leaflets). Leaves of the same species are found to be geometrically similar regardless of their size. From tensile/torsional tests, we characterize the bending rigidity (EI) and the twisting rigidity (GJ) of 15 petioles of 4 species in the Spring/Summer: Red Oak (Quercus Rubra), American Sycamore (Platanus occidentalis), Yellow Poplar (Liriodendron tulipifera), and Sugar Maple (Acer saccharum). A twist-to-bend ratio EI/GJ is found to be around 4.3, within the range in previous studies conducted on similar species (EI/GJ = 2.7~8.0 reported in S. Vogel, 1992). In addition, we develop a simple energetic model to find a relation between geometrical shapes and mechanical properties (EI/GJ = 2LL/WC where LL is the laminar length and WC is the laminar width), verified with experimental data. Lastly, we discuss leaf's ability to reduce stress at the stem-petiole junction by choosing certain geometry, and also present exploratory results on the effect that seasons have on the Young's and twisting moduli.