Soft Deployable Structures via Core-Shell Inflatables.

Deployable structures capable of significant geometric reconfigurations are ubiquitous in nature. While engineering contraptions typically comprise articulated rigid elements, soft structures that experience material growth for deployment mostly remain the handiwork of biology, e.g., when winged insects deploy their wings during metamorphosis. Here we perform experiments and develop formal models to rationalize the previously unexplored physics of soft deployable structures using core-shell inflatables. We first derive a Maxwell construction to model the expansion of a hyperelastic cylindrical core constrained by a rigid shell. Based on these results, we identify a strategy to obtain synchronized deployment in soft networks. We then show that a single actuated element behaves as an elastic beam with a pressure-dependent bending stiffness which allows us to model complex deployed networks and demonstrate the ability to reconfigure their final shape. Finally, we generalize our results to obtain three-dimensional elastic gridshells, demonstrating our approach's applicability to assemble complex structures using core-shell inflatables as building blocks. Our results leverage material and geometric nonlinearities to create a low-energy pathway to growth and reconfiguration for soft deployable structures.

Instability mediated self-templating of drop crystals.

The breakup of liquid threads into droplets is prevalent in engineering and natural settings. While drop formation in these systems has a long-standing history, existing studies typically consider axisymmetric systems. Conversely, the physics at play when multiple threads are involved and the interaction of a thread with a symmetry breaking boundary remain unexplored. Here, we show that the breakup of closely spaced liquid threads sequentially printed in an immiscible bath locks into crystal-like lattices of droplets. We rationalize the hydrodynamics at the origin of this previously unknown phenomenon. We leverage this knowledge to tune the lattice pattern via the control of injection flow rate and nozzle translation speed, thereby overcoming the limitations in structural versatility typically seen in existing fluid manipulations paradigms. We further demonstrate that these drop crystals have the ability to self-correct and propose a simple mechanism to describe the convergence toward a uniform pattern of drops.

Formation of Pixelated Elastic Films via Capillary Suction of Curable Elastomers in Templated Hele-Shaw Cells.

Natural materials are highly organized, frequently possessing intricate and sophisticated hierarchical structures from which superior properties emerge. In the wake of biomimicry, there is a growing interest in designing architected materials in the laboratory as such structures could enable myriad functionalities in engineering. Yet, their fabrication remains challenging despite recent progress in additive manufacturing. In particular, soft materials are typically poorly suited to form the requisite structures consisting of regular geometries. Here, a new frugal methodology is reported to fabricate pixelated soft materials. This approach is conceptually analogous to the watershed transform used in image analysis and allows the passive assembly of complex geometries through the capillary-mediated flow of curable elastomers in confined geometries. Emerging from sources distributed across a Hele-Shaw cell consisting of two parallel flat plates separated by an infinitesimally small gap, these flows eventually meet at the "dividing lines" thereby forming Voronoi tesselations. After curing is complete, these structures turn into composite elastic sheets. Rationalizing the fluid mechanics at play allows the structural geometry of the newly formed sheets to be tailored and thereby their local material properties to be tuned.

Bubble casting soft robotics.

Inspired by living organisms, soft robots are developed from intrinsically compliant materials, enabling continuous motions that mimic animal and vegetal movement1. In soft robots, the canonical hinges and bolts are replaced by elastomers assembled into actuators programmed to change shape following the application of stimuli, for example pneumatic inflation2-5. The morphing information is typically directly embedded within the shape of these actuators, whose assembly is facilitated by recent advances in rapid prototyping techniques6-11. Yet, these manufacturing processes have limitations in scalability, design flexibility and robustness. Here we demonstrate a new all-in-one methodology for the fabrication and the programming of soft machines. Instead of relying on the assembly of individual parts, our approach harnesses interfacial flows in elastomers that progressively cure to robustly produce monolithic pneumatic actuators whose shape can easily be tailored to suit applications ranging from artificial muscles to grippers. We rationalize the fluid mechanics at play in the assembly of our actuators and model their subsequent morphing. We leverage this quantitative knowledge to program these soft machines and produce complex functionalities, for example sequential motion obtained from a monotonic stimulus. We expect that the flexibility, robustness and predictive nature of our methodology will accelerate the proliferation of soft robotics by enabling the assembly of complex actuators, for example long, tortuous or vascular structures, thereby paving the way towards new functionalities stemming from geometric and material nonlinearities.

Drops on the Underside of a Slightly Inclined Wet Substrate Move Too Fast to Grow.

Pendant drops suspended on the underside of a wet substrate are known to accumulate fluid from the surrounding thin liquid film, a process that often results in dripping. The growth of such drops is hastened by their ability to translate over an otherwise uniform horizontal film. Here we show that this scenario is surprisingly reversed when the substrate is slightly tilted (≈2°); drops become too fast to grow and shrink over the course of their motion. Combining experiments and numerical simulations, we rationalize the transition between the conventional growth regime and the previously unknown decay regime we report. Using an analytical treatment of the Landau-Levich meniscus that connects the drop to the film, we quantitatively predict the drop dynamics in the two flow regimes and the value of the critical inclination angle where the transition between them occurs.

Elastic amplification of the Rayleigh-Taylor instability in solidifying melts.

The concomitant mechanical deformation and solidification of melts are relevant to a broad range of phenomena. Examples include the preparation of cotton candy, the atomization of metals, the manufacture of glass fibers, and the formation of elongated structures in volcanic eruptions known as Pele's hair. Usually, solid-like deformations during solidification are neglected as the melt is much more malleable in its initial liquid-like form. Here we demonstrate how elastic deformations in the midst of solidification, i.e., while the melt responds as a very soft solid ([Formula: see text] Pa), can lead to the formation of previously unknown periodic structures. Namely, we generate an array of droplets on a thin layer of liquid elastomer melt coated on the outside of a rotating cylinder through the Rayleigh-Taylor instability. Then, as the melt cures and goes through its gelation point, the rotation speed is increased and the drops stretch into hairs. The ongoing solidification eventually hardens the material, permanently "freezing" these elastic deformations into a patterned solid. Using experiments, simulation, and theory, we demonstrate that the formation of our two-step patterns can be rationalized when combining the tools from fluid mechanics, elasticity, and statistics. Our study therefore provides a framework to analyze multistep pattern formation processes and harness them to assemble complex materials.

Marangoni flows drive the alignment of fibrillar cell-laden hydrogels.

When a sessile droplet containing a solute in a volatile solvent evaporates, flow in the droplet can transport and assemble solute particles into complex patterns. Transport in evaporating sessile droplets has largely been examined in solvents that undergo complete evaporation. Here, we demonstrate that flow in evaporating aqueous sessile droplets containing type I collagen-a self-assembling polymer-can be harnessed to engineer hydrated networks of aligned collagen fibers. We find that Marangoni flows direct collagen fiber assembly over millimeter-scale areas in a manner that depends on the rate of self-assembly, the relative humidity of the surrounding environment, and the geometry of the droplet. Skeletal muscle cells that are incorporated into and cultured within these evaporating droplets collectively orient and subsequently differentiate into myotubes in response to aligned networks of collagen. Our findings demonstrate a simple, tunable, and high-throughput approach to engineer aligned fibrillar hydrogels and cell-laden biomimetic materials.

Printing on liquid elastomers.

In recent years the research community has paid significant attention to geometrically engineered materials. These materials derive their unique properties from their structure rather than their chemistry alone. Despite their success in the laboratory, the assembly of such soft functional materials remains an outstanding challenge. Here, we propose a robust fluid-mediated route for the rapid fabrication of soft elastomers architected with liquid inclusions. Our approach consists of depositing water drops at the surface of an immiscible liquid elastomer bath. As the elastomer cures, the drops are encapsulated in the polymer and impart shape and function to the newly formed elastic matrix. Using the framework of fluid mechanics, we show how this type of composite material can be tailored.

Curvature Regularization near Contacts with Stretched Elastic Tubes.

Inserting a rigid object into a soft elastic tube produces conformal contact between the two, resulting in contact lines. The curvature of the tube walls near these contact lines is often large and is typically regularized by the finite bending rigidity of the tube. Here, it is demonstrated using experiments and a Föppl-von Kármán-like theory that a second, independent, mechanism of curvature regularization occurs when the tube is axially stretched. In contrast with the effects of finite bending rigidity, the radius of curvature obtained increases with the applied stretching force and decreases with sheet thickness. The dependence of the curvature on a suitably rescaled stretching force is found to be universal, independent of the shape of the intruder, and results from an interplay between the longitudinal stresses due to the applied stretch and hoop stresses characteristic of curved geometry. These results suggest that curvature measurements can be used to infer the mechanical properties of stretched tubular structures.

An unbounded approach to microfluidics using the Rayleigh-Plateau instability of viscous threads directly drawn in a bath.

We study the droplet-forming instability of a thin jet extruded from a nozzle moving horizontally below the surface of an isoviscous immiscible fluid bath. While this interfacial instability is a classic problem in fluid mechanics, it has never been studied in the context of the deposition of a thread into a reservoir, an open-sky version of microfluidics. As the nozzle translates through the reservoir, drops may form at the nozzle (dripping) or further downstream (jetting). We first focus on rectilinear printing paths and derive a scaling law to rationalize the transition between dripping and jetting. We then leverage the flexibility of our system and study the dynamics of breakup when printing sinusoidal paths. We unravel a methodology to control both the size of the drops formed by the instability and the distance that separates them.

Microextrusion printing cell-laden networks of type I collagen with patterned fiber alignment and geometry.

Type I collagen self-assembles into three-dimensional (3D) fibrous networks. These dynamic viscoelastic materials can be remodeled in response to mechanical and chemical signals to form anisotropic networks, the structure of which influences tissue development, homeostasis, and disease progression. Conventional approaches for fabricating anisotropic networks of type I collagen are often limited to unidirectional fiber alignment over small areas. Here, we describe a new approach for engineering cell-laden networks of aligned type I collagen fibers using 3D microextrusion printing of a collagen-Matrigel ink. We demonstrate hierarchical control of 3D-printed collagen with the ability to spatially pattern collagen fiber alignment and geometry. Our data suggest that collagen alignment results from a combination of molecular crowding in the ink and shear and extensional flows present during 3D printing. We demonstrate that human breast cancer cells cultured on 3D-printed collagen constructs orient along the direction of collagen fiber alignment. We also demonstrate the ability to simultaneously bioprint epithelial cell clusters and control the alignment and geometry of collagen fibers surrounding cells in the bioink. The resulting cell-laden constructs consist of epithelial cell clusters fully embedded in aligned networks of collagen fibers. Such 3D-printed constructs can be used for studies of developmental biology, tissue engineering, and regenerative medicine.

The fingerprint of a flow: wrinkle patterns in nonuniform coatings on pre-stretched soft foundations.

We study the wrinkle patterns obtained when applying a thin polymeric film on a uniaxially prestretched soft foundation. The film is coated onto a substrate where it drains under the action of gravity, thereby introducing a continuous variation in its thickness. We first study the fluid mechanics component of the problem and derive the coating profile as a function of the curing properties of the polymeric solution. Upon polymerization, the prestretch is released and yields the formation of wrinkles, which are arranged in organized patterns, including fractals. We study a variety of scenarios depending on the relative orientation of the gradient of film thickness and the stretching direction. In particular, we characterize and rationalize the distribution of singular events in our problem where wrinkles merge to allow a variation of the average value of the wrinkle wavelength across the sample.

The interaction of a walking droplet and a submerged pillar: From scattering to the logarithmic spiral.

Millimetric droplets may walk across the surface of a vibrating fluid bath, propelled forward by their own guiding or "pilot" wave field. We here consider the interaction of such walking droplets with a submerged circular pillar. While simple scattering events are the norm, as the waves become more pronounced, the drop departs the pillar along a path corresponding to a logarithmic spiral. The system behavior is explored both experimentally and theoretically, using a reduced numerical model in which the pillar is simply treated as a region of decreased wave speed. A trajectory equation valid in the limit of weak droplet acceleration is used to infer an effective force due to the presence of the pillar, which is found to be a lift force proportional to the product of the drop's walking speed and its instantaneous angular speed around the post. This system presents a macroscopic example of pilot-wave-mediated forces giving rise to apparent action at a distance.

Designing soft materials with interfacial instabilities in liquid films.

Natural soft materials harness hierarchy and structures at all scales to build function. Adapting this paradigm to our technological needs, from mechanical, phononic and photonic metamaterials to functional surfaces prompts the development of new fabrication pathways with improved scalability, design flexibility and robustness. Here we show that the inherent periodicity of the Rayleigh-Taylor instability in thin polymeric liquid films can be harnessed to spontaneously fabricate structured materials. The fluidic instability yields pendant drops lattices, which become solid upon curing of the polymer, thereby permanently sculpting the interface of the material. We solve the inverse design problem, taming the instability, so that the structures we form can be tailored, over a range of sizes spanning over two decades. This all-in-one methodology could potentially be extended down to the scales where continuum mechanics breaks down, while remaining scalable.

Fluid dynamic instabilities: theory and application to pattern forming in complex media.

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'.

The molten glass sewing machine.

We present a fluid-instability-based approach for digitally fabricating geometrically complex uniformly sized structures in molten glass. Formed by mathematically defined and physically characterized instability patterns, such structures are produced via the additive manufacturing of optically transparent glass, and result from the coiling of an extruded glass thread. We propose a minimal geometrical model-and a methodology-to reliably control the morphology of patterns, so that these building blocks can be assembled into larger structures with tailored functionally and optically tunable properties.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'.

The surprising dynamics of a chain on a pulley: lift off and snapping.

The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain when one of the weights is removed and, thus, one end is pulled with constant acceleration. This simple change has dramatic consequences for the ensuing motion: at a finite time, the chain 'lifts off' from the pulley, and the free end subsequently accelerates faster than the end that is pulled. Eventually, the chain undergoes a dramatic reversal of curvature reminiscent of the crack or snap, of a whip. We combine experiments, numerical simulations and theoretical arguments to explain key aspects of this dynamical problem.

Rising beyond elastocapillarity.

We consider the elastocapillary rise between swellable structures using a favorable solvent. We characterize the dynamic deformations and resulting equilibrium configurations for various beams. Our analysis reveals the importance of the spacing between the two beams, and the elastocapillary length lec, which prescribes the relative magnitude of surface tension and bending stiffness in the system. In particular, we rationalize the transition between coalescence-dominated, bending-dominated, and swelling-dominated regimes, and enumerate the subtle interfacial mechanisms at play in the ratcheting of a fluid droplet trapped between the curling beams.

Fabrication of slender elastic shells by the coating of curved surfaces.

Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.