Session W52: Focus Session: Extreme Mechanics - Fluid-Structure Interactions and Swelling

Capillary rise between exible walls

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 $t^{1/3}$, a characteristic of capillary imbibition in a wedge.   

Motion of a rigid sphere through an elastic tube

The transport of soft objects through small rigid channels is a common problem in the biological world : red blood cells are deformed when passing through small capillaries and polymer coils can make their way through minute pores. We study the opposite model problem of a rigid sphere moving in a narrower elastic tube. Geometry, mechanical properties of the tube and friction or lubrication conditions determine the dynamics of the entrapped sphere. We present experimental results on this problem, together with scaling law analysis.   

Equilibrium and stability of an elastic meniscus

A liquid-air interface touching a solid wall gives rise to a liquid meniscus, whose shape has been well known for two centuries and results from the balance between capillarity and gravity. We investigate the case in which a portion of the liquid interface has been replaced by a soft strip, adding the elastic ingredient to this physical problem. We experimentally study the equilibrium configurations, from small to high non-linear deformations, and we compare to a 2D theoretical model. Stability of the system involving 3D corrections is also addressed.   

Capillary-Induced Self-Organization of Soft Pillar Arrays into Moir\'{e} Patterns by Dynamic Feedback Process

We report a self-organized pattern formation of polymer nanopillar arrays by dynamic feedback: two nanopillar arrays collectively structure a sandwiched liquid and pattern the menisci, which bend the pillars into Moir\'{e} patterns as it evaporates. Like the conventional Moir\'{e} phenomenon, the patterns are deterministic and tunable by mismatch angle, yet additional behaviors---chirality from achiral starting motifs and preservation of the patterns after the surfaces are separated---appear from the feedback process. Patterning menisci based on this mechanism provides a simple, scalable approach for making a series of complex, long-range-ordered structures. Reference: Sung H. Kang, Ning Wu, Alison Grinthal, and Joanna Aizenberg, Phys. Rev. Lett., \textbf{107}, 177802 (2011).~   

Study of waving of grass using a soap film model

Wind blowing over a grass field incites synchronized response from the grass blades, which appear as waves. This effect is called Mo-nami in a terrestrial setting, while in an aquatic setting it is termed as Ho-nami. We use a combination of experimental observations, numerical simulations and theoretical analysis to understand this effect. The experiment is conducted in two-dimensional realization of these phenomena in a gravity driven soap film tunnel. Nylon filaments attached to the boundaries of the soap film play the role of the grass. We provide a preliminary characterization of this analog model for the synchronized oscillations of grass.   

Direct measurements of flow and deformation of a free reed

The free reed, responsible for producing sound in a family of air-driven musical instruments, is an example of a coupled fluid-structure system engineered to vibrate efficiently at a controllable frequency. In Western free reed instruments, a flexible metal plate is clamped at one end above a slot cut into a rigid support plate. This geometry allows a constant driving pressure to produce and sustain large-amplitude vibrations. The mechanism behind this has been discussed by several investigators. However, it has yet to be verified experimentally with direct measurements of the flow speed. We present simultaneous measurements of the reed motion and the flow speed in the downstream jet, which enable characterization of the relationship between the finite-amplitude deformation of the reed and the flow.   

Control and Manipulation of Fluid Flow Using Elastic Deformations

In this work, we utilize elastic deformations within a flexible microfluidic device via mechanical actuation to control and direct fluid flow. The device consists of a microchannel with a flexible arch prepared by buckling a thin elastic film. The deflection of the arch can be predicted and controlled using the classical theory of Euler buckling. We controlled the fluid flow rate by coupling the elastic deformation of the arch to the gap within the microchannel, and matched these experimental results analytically with a perturbation of lubrication theory and with computational simulations. These results illustrate an experimental design paradigm for the preparation of portable microchannels for chemical mixing, self-healing, and in situ diagnostics.   

Curling paper

As many soft materials, paper is mechanically sensitive to humidity. Owing to its hygroscopic cellulose-based structure, it is known to wrinkle when subject to humidity fluctuations. Here, we present experimental results on the more extreme deformations observed when a sheet of tracing paper is put on a bath of water. After contact with the liquid surface, water diffuses into the hygroscopic material from below and induces differential swelling, resulting in the curling of the paper. Within seconds, a spectacular roll-up motion follows. We explain the observed shapes and curling dynamics.   

Walking and jumping spores

The Equisetum plants, more commonly called ``horsetail,'' emit 50-microns spores that are spherical in shape and present four hygroscopic arms. Under high humidity, the arms are retracted. But under lower humidity, less than 70\%, the four arms deploy beautifully. With time-lapse image recordings, we show that under repeated cycles of dry and high humidity, the spores behave as random walkers, since they move by about their size in a different direction at every cycle. The process is apparently stochastic because of the complex shape of the arms and hysteretic friction of the arms on the ground. For some spores, a decrease in humidity level results in very fast jumps, the spores taking off at a typical velocity of a meter per second, as recorded on high-speed camera. With these jumps, they reach centimetric elevations, much larger than their size. The physical mechanism at the root of these ``Levy-flight'' jumps is still under investigation. The walking and jumping phenomena thus provide motility, which we believe is helpful for the understanding of the biological dispersion of the spores. It could also bring biomimetic inspiration to engineer new motile elastic structures.   

Mechanic instabilities of swelling gels

While the study of gels takes undoubtedly its roots within the field of physico-chemistry, the interest for gels has flourished and they progressively became an important object in the study of the mechanics of polymeric materials and volumetric growth, rising some fascinating problems, some of them remaining unsolved. Because gels are multiphase objects, their study represents an important step in the understanding of the mechanics of complex soft matter as well as for the process of shape generation in biological bodies. I will present here experiments and models of swelling gels mainly in the cylindrical geometry which mimic various growth instabilities from tumors up to the morphogenesis of tubular organs.   

Patterns formed by swelling-induced folding of films

The solvent swelling of a thin polymer film attached to a rigid substrate is known to induce a creasing pattern on the free surface of the film. Here we show that if the film is weakly attached to the substrate, the swelling-induced compressive stress nucleates buckle delamination of the film from the substrate. Surprisingly, the buckles do not have a sinusoidal profile, instead, the film near the delamination buckles slides towards the buckles causing growth of sharp folds of high aspect ratio. The folds persist even after the solvent evaporates. Such fold formation depends on the size of the region of the film exposed to solvent. A very small region of exposure (realized by placing a small drop of solvent on the film) does not induce delamination. Remarkably, with moderate sized drops, the delamination and folding occurs around the perimeter of the drop, thus culminating in a corral with tall walls. We quantify the parameters (drop volume, film thickness) which demarcate the transitions between no fold formation, corral formation, and multiple fold formation.   

Swelling-Driven Shaping of Thermally Responsive Photo-Patterned Gel Sheets

Swelling-mediated shaping of patterned non-Euclidean plates offers a powerful route to design and engineer complex 3-D structures, with possible applications in biomedicine, robotics, and tunable micro-optics. We have studied the behavior of poly(N-isopropyl acrylamide) (PNIPAm) copolymers containing pendent benzophenone units that allow the degree of crosslinking to be tuned by varying the dose of ultraviolet light. A halftone (gray) gel lithography approach, wherein two photomasks enable patterning of highly-crosslinked domains within a lightly-crosslinked matrix, is shown to provide effectively continuous variations in swelling in truly two-dimensional patterns. We show how this technique can be harnessed to form complex, reversibly actuating, 3-D structures through patterned growth.   

Dynamical Actuation and Pattern Formation with Local Swelling in Microgels

In this invited talk, we present a set of study on swelling-induced actuation and pattern formation in hydrogels of three dimensional microstructures. For example, rapid actuation of a micro hydrogel device is observed by exploiting swelling-induced snap-buckling. Utilizing its fast actuation speed, the device can even jump by itself upon wetting. It is demonstrated that elastic energy is effectively stored and quickly released from the device by incorporating elastic instability. In our experiment, the micro device could generate a snapping motion within 12 milliseconds, releasing power at a rate of 34 mW/g. We also captured the evolution circumferential buckling of tubular shaped microgels. Inhomogeneous stress develops as gel swells under mechanical constraints, which gives rise to buckling instability. A simple analytical model is developed using elastic energy to predict stability and post-buckling patterns upon swelling. Our experiment demonstrates that circumferential buckling of desired mode can be created in a prescribed manner. Our study on the mechanics of three-dimensionally microstructured gels might provide new insights for in morphogenesis in tissue engineering, and provide new gateways in many emerging fields such as soft robotics and tunable matamaterials.   

Separating Viscoelasticity and Poroelasticity of Gels with Different Length and Time Scales

Viscoelasticity and poroelasticity commonly coexist in polymer gels. We propose a method capable of separating the viscoelasticity and poroelasticity of gels in various mechanical tests. The viscoelastic characteristic times and the poroelastic diffusivities of a gel can define intrinsic material length scales of the gel. The experimental setup can give sample length scales, over which the solvent migrates in the gel. By setting the sample lengths to be much larger or smaller than the material lengths, the viscoelasticity and poroelasticity of the gel will manifest at different time scales in a test. Therefore, the viscoelastic and poroelastic properties of the gel can be probed separately at different time scales of the test.   

A constitutive theory for visco-hyperelastic gels

Many gels operate in chemically saturated environments in a variety of applications. Most constitutive theories for gels are formulated using large deformation hyperelasticity coupled with fluid transport. However, in most cases the mechanical response of such gels show hysteresis and other dissipative effects which are not accounted for in present constitutive theories. We have recently developed a three dimensional continuum level theory to describe the coupled fluid permeation and large deformation response of visco-hyperelastic materials. In this work, we apply our theory and numerical simulation capability to study the indentation response among others of visco-hyperelastic gels.