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The rupture of soap films is traditionally described by a law accounting for a balance between momentum and surface tension forces, derived independently by Taylor and Culick in the 1960s. This law is highly relevant to the dynamics of thin liquid films of jets when viscous effects are negligible. However, the minute amounts of surfactant molecules present in soap films play a major role in interfacial rheology, and may result in complex behaviour. Petit et al. (J. Fluid Mech., vol. 774, 2015, R3) challenge standard thin film dynamics via intriguing experiments conducted with highly elastic surfactants. Unexpected structures reminiscent of faults are observed. [ABSTRACT FROM PUBLISHER]

We study, through model experiments, the buckling under tension of an elastic membrane reinforced with a more rigid strip or fiber. In these systems, the compression of the rigid layer is induced through Poisson contraction as the membrane is stretched perpendicularly to the strip. Although strips always lead to out-of-plane wrinkles, we observe a transition from out-of-plane to in-plane wrinkles beyond a critical strain in the case of fibers embedded into elastic membranes. We describe through scaling laws the evolution of the morphology of the wrinkles and the different transitions as a function of material properties and stretching strain [ABSTRACT FROM AUTHOR]

We report experimental work on capillary rise of a liquid in a cell formed by parallel plates, one of which is flexible. We show that above a critical width, the cell collapses under the negative capillary pressure in the liquid. This collapse allows the liquid to rise virtually without limit between the plates. The height of the rising front is found to increase with time as t1/3, a characteristic of capillary imbibition in a wedge. [ABSTRACT FROM AUTHOR]

This paper discusses the breakup of capillary jets of dilute polymer solutions and the dynamics associated with the transition from dripping to jetting. High-speed digital video imaging reveals a new scenario of transition and breakup via periodic growth and detachment of large terminal drops. The underlying mechanism is discussed and a basic theory for the mechanism of breakup is also presented. The dynamics of the terminal drop growth and trajectory prove to be governed primarily by mass and momentum balances involving capillary, gravity and inertial forces, whilst the drop detachment event is controlled by the kinetics of the thinning process in the viscoelastic ligaments that connect the drops. This thinning process of the ligaments that are subjected to a constant axial force is driven by surface tension and resisted by the viscoelasticity of the dissolved polymeric molecules. Analysis of this transition provides a new experimental method to probe the rheological properties of solutions when minute concentrations of macromolecules have been added. [ABSTRACT FROM AUTHOR]

A spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is coated with a thin layer (of order 50–100 μm) of a viscous liquid. The steady motion of the sphere under gravity involves a combination of rotation and sliding. We examine the dependence of the experimentally observed steady translational and rotational speeds on the physical parameters in the system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial exponents for the scaling of the speeds with the characteristics of the sphere and the viscous liquid. The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane, is also examined. In this case, the steady motion is still observed for a certain range of angles and bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces. Such a force should also play a role in other problems of lubrication mechanics such as humid granular flows. [ABSTRACT FROM AUTHOR]

We investigate the rheological properties of microliter quantities of the spinning material extracted ex vivo from the major ampullate gland of a Nephila clavipes spider using two new micro-rheometric devices. A sliding plate micro-rheometer is employed to measure the steady-state shear viscosity of ~1 µl samples of silk dope from individual biological specimens. The steady shear viscosity of the spinning solution is found to be highly shear- thinning, with a power-law index consistent with values expected for liquid crystalline solutions. Calculations show that the viscosity of the fluid decreases 10-fold as it flows through the narrow spinning canals of the spider. By contrast, measurements in a microcapillary extensional rheometer show that the transient extensional viscosity (i.e. the viscoelastic resistance to stretching) of the spinning fluid increases more than 100-fold during the spinning process. Quantifying the properties of native spinning solutions provides new guidance for adjusting the spinning processes of synthetic or genetically engineered silks to match those of the spider. [ABSTRACT FROM AUTHOR]

Adjusting the wetting properties of water through the addition of a miscible liquid is commonly used in a wide variety of industrial processes involving interfaces. We investigate experimentally the evolution of a drop of water and volatile alcohol deposited on a bath of oil: The drop spreads and spontaneously fragments into a myriad of minute droplets whose size strongly depends on the initial concentration of alcohol. Marangoni flows induced by the evaporation of alcohol play a key role in the overall phenomenon. The intricate coupling of hydrodynamics, wetting, and evaporation is well captured by analytical scaling laws. Our scenario is confirmed by experiments involving other combinations of liquids that also lead to this fascinating phenomenon. [ABSTRACT FROM AUTHOR]

On a flat map of the Earth, continents are inevitably distorted. Reciprocally, curving a plate simultaneously in two directions requires a modification of in-plane distances, as Gauss stated in his seminal theorem. Although emerging architectured materials with programmed in-plane distortions are capable of such shape morphing, an additional control of local bending is required to precisely set the final shape of the resulting three-dimensional surface. Inspired by bulliform cells in leaves of monocotyledon plants, we show how the internal structure of flat panels can be designed to program bending and in-plane distortions simultaneously when pressurized, leading to a targeted shell shape. These surfaces with controlled stiffness and fast actuation are manufactured using consumer-grade materials and open a route to large-scale shape-morphing robotics applications.

Viscosity, which impacts the rate of haemolymph circulation and heat transfer, is one of the transport properties that affects the performance of an insect. Measuring the viscosity of insect fluids is challenging because of the small amount available per specimen. Using particle tracking microrheology, which is well suited to characterise the rheology of the fluid part of the haemolymph, we studied the plasma viscosity in the bumblebee Bombus terrestris. In a sealed geometry, the viscosity exhibits an Arrhenius dependence with temperature, with an activation energy comparable to that previously estimated in hornworm larvae. In an open to air geometry, it increases by 4-5 orders of magnitude during evaporation. Evaporation times are temperature dependent and longer than typical insect haemolymph coagulation times. Unlike standard bulk rheology, microrheology can be applied to even smaller insects, paving the way to characterise biological fluids such as pheromones, pad secretions or cuticular layers., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2023. Published by The Company of Biologists Ltd.)

The crystal structure of atomically defined colloidal II-VI semiconductor nanoplatelets (NPLs) induces the self-assembly of organic ligands over thousands of square nanometers on the top and bottom basal planes of these anisotropic nanoparticles. NPLs curl into helices under the influence of the surface stress induced by these ligands. We demonstrate the control of the radii of NPL helices through the ligands described as an anchoring group and an aliphatic chain of a given length. A mechanical model accounting for the misfit strain between the inorganic core and the surface ligands predicts the helices' radii. We show how the chirality of the helices can be tuned by the ligands anchoring group and inverted from one population to another.

We show that ribbed elastic strips under tension present large spontaneous curvature and may close into tubes. In this single material architectured system, transverse bending results from a bilayer effect induced by Poisson contraction as the textured ribbon is stretched. Surprisingly, the induced curvature may reverse if ribs of different orientations are considered. Slender ribbed structures may also undergo a nontrivial buckling transition. We use analytical calculations to describe the evolution of the morphology of the ribbon and the transitions between the different experimental regimes as a function of material properties, geometrical parameters, and stretching strain. This scale-independent phenomenon may help the manufacturing of tubular textured structures or easily controllable grippers at small scale.

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented., (© 2021 The Authors. Advanced Materials published by Wiley-VCH GmbH.)

Lack of stiffness often limits thin shape-shifting structures to small scales. The large in-plane transformations required to distort the metrics are indeed commonly achieved by using soft hydrogels or elastomers. We introduce here a versatile single-step method to shape-program stiff inflated structures, opening the door for numerous large scale applications, ranging from space deployable structures to emergency shelters. This technique relies on channel patterns obtained by heat-sealing superimposed flat quasi-inextensible fabric sheets. Inflating channels induces an anisotropic in-plane contraction and thus a possible change of Gaussian curvature. Seam lines, which act as a director field for the in-plane deformation, encode the shape of the deployed structure. We present three patterning methods to quantitatively and analytically program shells with non-Euclidean metrics. In addition to shapes, we describe with scaling laws the mechanical properties of the inflated structures. Large deployed structures can resist their weight, substantially broadening the palette of applications.

Inflatable structures offer a path for light deployable structures in medicine, architecture, and aerospace. In this study, we address the challenge of programming the shape of thin sheets of high-stretching modulus cut and sealed along their edges. Internal pressure induces the inflation of the structure into a deployed shape that maximizes its volume. We focus on the shape and nonlinear mechanics of inflated rings and more generally, of any sealed curvilinear path. We rationalize the stress state of the sheet and infer the counterintuitive increase of curvature observed on inflation. In addition to the change of curvature, wrinkles patterns are observed in the region under compression in agreement with our minimal model. We finally develop a simple numerical tool to solve the inverse problem of programming any 2-dimensional (2D) curve on inflation and illustrate the application potential by moving an object along an intricate target path with a simple pressure input., Competing Interests: The authors declare no conflict of interest.

We study the sedimentation of highly viscous droplets confined inside Hele-Shaw cells with textured walls of controlled topography. In contrast with common observations on superhydrophobic surfaces, roughness tends here to significantly increase viscous friction, thus substantially decreasing the droplets mobility. However, reducing confinement induces a jump in the velocity as droplets can slide on a lubricating layer of the surrounding fluid thicker than the roughness features. We demonstrate that increasing the viscosity of the surrounding liquid may counterintuitively enhance the mobility of a droplet sliding along a rough wall. Similarly, a sharp change of the droplet mobility is observed as the amplitude of the roughness is modified. These results illustrate the nontrivial friction processes at the scale of the roughness, and the coupling between viscous dissipation in the drop, in the front meniscus, and in the lubricating film. They could enable one to specifically control the speed of droplets or capsules in microchannels, based on their rheological properties.

Dielectric elastomer sheets undergo in-plane expansion when stimulated by a transverse electric field. We study experimentally how dielectric plates subjected to a non-uniform voltage distribution undergo buckling instabilities. Two different configurations involving circular plates are investigated: plates freely floating on a bath of water, and plates clamped on a frame. We describe theoretically the out-of-plane deformation of the plates within the framework of weakly non-linear plate equations. This study constitutes a first step of a route to control the 3D activation of dielectric elastomers.

We show the self-assembly through twisting and bending of side by side ribbons under the action of capillary forces. Micro-ribbons made of silicon nitride are batch assembled at the wafer scale. We study their assembly as a function of their dimensions and separating distance. Model experiments are carried out at the macroscopic scale where the tension in ribbons can easily be tuned. The process is modeled considering the competition between capillary, elastic and tension forces. Theory shows a good agreement for macroscale assemblies, while the accuracy is within 30% at the micrometer scale. This simple self-assembly technique yields highly symmetric and controllable structures which could be used for batch fabrication of functional 3D micro-structures.

We describe the peeling of an elastomeric strip adhering to a glass plate through van der Waals interactions in the limit of a zero peeling angle. In contrast to classical studies that predict a saturation of the pulling force, in this lap test configuration the force continuously increases, while a sliding front propagates along the tape. The strip eventually detaches from the substrate when the front reaches its end. Although the evolution of the force is reminiscent of recent studies involving a compliant adhesive coupled with a rigid backing, the progression of a front is in contradiction with such a mechanism. To interpret this behavior, we estimate the local shear stress at the interface by monitoring the deformation of the strip. Our results are consistent with a nearly constant friction stress in the sliding zone in agreement with other experimental observations where adhesion and friction are observed.

Straight cracks are observed in thin coatings under residual tensile stress, resulting into the classical network pattern observed in china crockery, old paintings, or dry mud. Here, we present a novel fracture mechanism where delamination and propagation occur simultaneously, leading to the spontaneous self-replication of an initial template. Surprisingly, this mechanism is active below the standard critical tensile load for channel cracks and selects a robust interaction length scale on the order of 30 times the film thickness. Depending on triggering mechanisms, crescent alleys, spirals, or long bands are generated over a wide range of experimental parameters. We describe with a simple physical model, the selection of the fracture path and provide a configuration diagram displaying the different failure modes.

We report how cell rheology measurements can be performed by monitoring the deformation of a cell in a microfluidic constriction, provided that friction and fluid leaks effects between the cell and the walls of the microchannels are correctly taken into account. Indeed, the mismatch between the rounded shapes of cells and the angular cross-section of standard microfluidic channels hampers efficient obstruction of the channel by an incoming cell. Moreover, friction forces between a cell and channels walls have never been characterized. Both effects impede a quantitative determination of forces experienced by cells in a constriction. Our study is based on a new microfluidic device composed of two successive constrictions, combined with optical interference microscopy measurements to characterize the contact zone between the cell and the walls of the channel. A cell squeezed in a first constriction obstructs most of the channel cross-section, which strongly limits leaks around cells. The rheological properties of the cell are subsequently probed during its entry in a second narrower constriction. The pressure force is determined from the pressure drop across the device, the cell velocity, and the width of the gutters formed between the cell and the corners of the channel. The additional friction force, which has never been analyzed for moving and constrained cells before, is found to involve both hydrodynamic lubrication and surface forces. This friction results in the existence of a threshold for moving the cells and leads to a non-linear behavior at low velocity. The friction force can nevertheless be assessed in the linear regime. Finally, an apparent viscosity of single cells can be estimated from a numerical prediction of the viscous dissipation induced by a small step in the channel. A preliminary application of our method yields an apparent loss modulus on the order of 100 Pa s for leukocytes THP-1 cells, in agreement with the literature data.

It is often postulated that quasistatic cracks propagate along the direction allowing fracture for the lowest load. Nevertheless, this statement is debated, in particular for anisotropic materials. We performed tearing experiments in anisotropic brittle thin sheets that validate this principle in the case of weak anisotropy. We also predict the existence of forbidden directions and facets in strongly anisotropic materials, through an analogy with the description of equilibrium shapes in crystals. However, we observe cracks that do not necessarily follow the easiest direction but can select a harder direction, which is only locally more advantageous than neighboring paths. These results challenge the traditional description of fracture propagation, and we suggest a modified, less restrictive criterion compatible with our experimental observations.

We study the peculiar wrinkling pattern of an elastic plate stamped into a spherical mold. We show that the wavelength of the wrinkles decreases with their amplitude, but reaches a minimum when the amplitude is of the order of the thickness of the plate. The force required for compressing the wrinkled plate presents a maximum independent of the thickness. A model is derived and verified experimentally for a simple one-dimensional case. This model is extended to the initial situation through an effective Young modulus representing the mechanical behavior of the wrinkled state. The theoretical predictions are shown to be in good agreement with the experiments. This approach provides a complement to the "tension field theory" developed for wrinkles with unconstrained amplitude.

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

We study the adhesion of an elastic sheet on a rigid spherical substrate. Gauss's Theorema Egregium shows that this operation necessarily generates metric distortions (i.e., stretching) as well as bending. As a result, a large variety of contact patterns ranging from simple disks to complex branched shapes are observed as a function of both geometrical and material properties. We describe these different morphologies as a function of two nondimensional parameters comparing, respectively, bending and stretching energies to adhesion. A complete configuration diagram is finally proposed.

The wrinkling and delamination of stiff thin films adhered to a polymer substrate have important applications in "flexible electronics." The resulting periodic structures, when used for circuitry, have remarkable mechanical properties because stretching or twisting of the substrate is mostly accommodated through bending of the film, which minimizes fatigue or fracture. To date, applications in this context have used substrate patterning to create an anisotropic substrate-film adhesion energy, thereby producing a controlled array of delamination "blisters." However, even in the absence of such patterning, blisters appear spontaneously, with a characteristic size. Here, we perform well-controlled experiments at macroscopic scales to study what sets the dimensions of these blisters in terms of the material properties and explain our results by using a combination of scaling and analytical methods. Besides pointing to a method for determining the interfacial toughness, our analysis suggests a number of design guidelines for the thin films used in flexible electronic applications. Crucially, we show that, to avoid the possibility that delamination may cause fatigue damage, the thin film thickness must be greater than a critical value, which we determine.

Aggregation processes generally lead to broad distributions of sizes involving exponential tails. Here, experiments on the capillary-driven coalescence of regularly spaced flexible structures yields a self-similar distribution of sizes with no tail. At a given step, the physical process imposes a maximal size for the aggregates, which appears as the relevant scale for the distribution. A simple toy model involving the aggregation of nearest neighbors exhibits the same statistics. A mean-field theory accounting for a maximal size is in agreement with both experiments and numerics. This approach is extended to iterative fragmentation processes where the largest object is broken at each step.

The interaction between elasticity and capillarity is used to produce three-dimensional structures through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tailoring the initial geometry of the flat membrane. Balancing interfacial energy with elastic bending energy provides a critical length scale below which encapsulation cannot occur, which is verified experimentally. This length is found to depend on the thickness as h3/2, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nanoscale objects.

We investigated why wet hair clumps into bundles by dunking a model brush of parallel elastic lamellae into a perfectly wetting liquid. As the brush is withdrawn, pairs of bundles aggregate successively, forming complex hierarchical patterns that depend on a balance between capillary forces and the elasticity of the lamellae. This capillary-driven self-assembly of flexible structures, which occurs in the tarsi of insects and in biomimetic adhesives but which can also damage micro-electromechanical structures or carbon nanotube 'carpets', represents a new type of coalescence process.

When a fiber is brought into contact with a soft etching liquid, a conical tip is generally shaped. We show here that the use of corrosive liquids which release gases during the etching reaction may lead to original self-similar shapes, because of successive pinning and detachment of the meniscus. The conditions for the formation of this shape and its evolution are described. In particular, we stress the effect of convection due to released bubbles.

We discuss the rise of a liquid inside an angular capillary tube. It is shown that for a wetting liquid, the height of the rise is (as usually) inversely proportional to the length which characterizes the confinement. The exact laws deduced from energetic considerations are found to be in excellent agreement with the data. We then show how such tubes can be used to prevent bubbles from being trapped. The rising velocity of a bubble is finally discussed, in the particular case of a square tube.