Session B40: Fluids and Elasticity

Direct measurement of surface stress of stretched soft solids.

The wetting profile of liquid droplets on soft solids is determined by the competition between elasticity and solid surface stress. Near the contact point, the bulk elasticity becomes negligible such that Neumann's classic analysis nicely captures the wetting geometry and provides us an effective approach to directly measure the solid surface stress. Here, we report our experiments using confocal microscopy in studying the wetting of liquids on soft PDMS gels. While the droplets are sitting on the top, the substrates are biaxially strained. We observe that the wetting profiles and the three-phase contact angles are changing dramatically as the substrate is stretched. With Neumann's principle, we obtain the quantitative relation between surface stress of the PDMS and the applied strain. These results suggest a significant strain-dependence of surface energy and surface stress for our PDMS.   

A numerical modeling capability for the interplay between surface energy and elasticity in soft materials

Surface energy is an important factor in the deformation of fluids but is typically a minimal or negligible effect in solids. However, when a solid is soft and its characteristic dimension is small, forces due to surface energy can become important and induce significant elastic deformation. The interplay between surface energy and elasticity can lead to interesting elasto-capillary phenomena. We have developed a finite-element formulation for problems involving these effects in both 2D and 3D settings and will demonstrate the simulation capability by examining two elasto-capillary problems. (1) The Rayleigh-Plateau instability in an elastic material -- In a fluid, this instability causes fluid jets to break up into droplets; however, as shown in recent experiments (Mora et al., PRL, 2010), break-up is prohibited in an elastic material, resulting in a stable undulatory configuration. (2) The effect of fluid-filled droplet inclusions on a soft solid -- When the matrix material is stiff, the presence of fluid-filled inclusions leads to a more compliant composite material; however, recent experiments (Style, et al., Nature Physics, 2014) have shown that when the matrix material is more compliant, the presence of droplets leads to stiffening. In this talk, we will show that our simulation capability predicts all experimentally observed phenomena and provides a straightforward route for describing nonlinear aspects of elasto-capillarity, which are difficult to address via analytics.   

Elastocapillary Deformations and Fracture of Soft Gels

When a droplet is placed on the surface of a soft gel, the surface deforms by an amount proportional to the elastocapillary length calculated from the ratio of surface tension and elastic modulus. For sufficiently large deformations, the gel can fracture due to the forces generated under the liquid-gel contact line. We observe that a starburst of channel fractures forms at the surface of the gel, driven by fluid propagating away from the central droplet. To understand the initiation of these cracks, we model the substrate as an incompressible, linear-elastic solid and quantify the elastic response. This provides quantitative agreement with experimental measurements of the number of fracture arms as a function of material properties and geometric parameters. In addition, we find that the initiation process is thermally-activated, with delay time that decreases as a function of the elastocapillary length.   

Surface tension and deformation in soft adhesion

Modern contact mechanics was originally developed to account for the competition between adhesion and elasticity for relatively stiff deformable materials like rubber, but much softer sticky materials are ubiquitous in biology, engineering, and everyday consumer products. In such soft materials, the solid surface tension can also play an important role in resisting shape change, and significantly modify the physics of contact with soft matter. We report indentation and pull-off experiments that bring small, rigid spheres into adhesive contact with compliant silicone gel substrates, varying both the surface functionalization of the spheres and the bulk elastic properties of the gels. We map the resulting deformation profiles using optical microscopy and image analysis. We examine the substrate geometry in light of capillary and elastic theories in order to explore the interplay of surface tension and bulk elasticity in governing soft adhesion.   

Elastocapillary Swelling: When coalesced structures curl apart

We consider the elastocapillary rise between swellable structures using a favorable solvent. We study the elastocapillary rise and subsequent swelling-induced bending, and characterize the dynamic deformations and resulting equilibrium configurations for various beam geometries. Our analysis highlights the importance of two characteristic length scales, and uses these lengths to predict both the elastocapillary rise and the critical curvature for peeling. We predict the transition between coalescence dominated beams and bending dominated beams using a balance of bending, stretching, and surface energies, and use a relaxed constraint on Euler's elastica to describe the fluid ratcheting.   

Effects of elasto-capillarity on periodic films folding and unfolding

Thin films interact with liquid surfaces through elastocapillary forces. These forces can control structural deformations of wetted thin films. Deformations arise from the interplay between the elastic strain energy in the bulk of the films, and the energy on the surface. In this work, we study the interplay between the surface tension of water and periodic patterns on different thin films. Our analysis explores the utilization of these periodically patterned films for the deployability of micro and nano-systems. The main attention is paid to the experimental results of this phenomenon and the results are supported by numerical analysis.   

Wrinkles and folds in a compressed granular raft

Wrinkles and folds occur in a wide variety of situations, we find them in Nature but also in man-made products. They typically appear when a thin sheet bound to a foundation is compressed. Here we demonstrate that particle ladden interfaces, despite being made of discrete very hard particles, can form wrinkles and folds like a soft elastic solid. We call granular raft a close packed monolayer of heavy, athermal particles at the interface between two fluids. We use beads of different materials with diameters ranging from $30\:\mu m$ to $0.8\:mm$ dispersed at a planar oil/water interface. Upon uniaxial compression the raft buckles out of plane like a soft elastic solid and forms a periodic wrinkling pattern, then the deformation localizes in a large unique fold/crease. This behavior is reminiscent of a compressed elastic sheet floating on water. We will highlight similarities and differences between the mechanical properties of our discrete heavy granular raft and a continuous elastic floating film. Finally we will show how elasticity and gravity contribute to rationalize the original shape of the fold we observe.   

Wrapping with a splash

Ultrathin sheets have been used to encapsulate drops of one fluid in another. When the sheet is thin enough that bending energies are much smaller than interfacial energies, experiment and theory show that optimal wrappings are achieved without any special sheet design [1]. Here we study wrappings generated by the impact of an oil droplet onto an ultrathin (30-200 nm) polystyrene film floating on water. Depending on the energy of impact, a large deformation of the air-water interface is followed by formation of an oil phase wrapped around by the polymer film, submerged in the water. Even though the energetic cost of bending of the polymer film is very small, we find that successful wrapping requires an impact energy much larger than the energy difference between the initial and final configurations. We explore the dynamics of the fluid and the sheet in this process with a view to devising an efficient method to create optimal wrappings. [1] J.D. Paulsen, V. Démery, C.D. Santangelo, T.P. Russell, B. Davidovitch, and N. Menon, doi:10.1038/nmat4397 (2015).   

Deformation of flexible micro helices under flow

The interaction of small helices with fluids is important because of its relevance to both fundamental science and technological applications, such as swimming microrobots or microflow sensors. Helically shaped flagella are also exploited by swimming microorganisms to move through their surrounding fluids. Here we study experimentally the deformation of flexible helical ribbons under flow in a microfluidic channel. The size of the helix is typically microscale for the diameter and nanoscale for the thickness. We focus on two different aspects: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive force theory. Deformation of helices by viscous flow is well-described by non-linear finite extensibility. Due to the non-uniform distribution of the pitch under distributed loading, we identify both linear and nonlinear behavior along the contour length of a single helix. Utilizing our system, we explore the impact of non-Newtonian fluid properties on the mechanics of helix-fluid interactions.   

Dynamics and propulsion of a rotating flexible helical rod near a no-slip rigid boundary

We study the effect of a no-slip rigid boundary on the locomotion of uni-flagellar bacteria in a viscous fluid at low Reynolds number conditions, through a combination of computer simulations and experiments. In our analogue model experiments, we exploit the prominence of geometry in this class of problems to rescale the original micron-scale system onto the desktop-scale. We manufacture elastomeric filaments with fully customizable geometric and material properties, and rotate them in a glycerin bath at a finite distance away from a rigid boundary. The experimental results are compared against numerical simulations that combine the Discrete Elastic Rods method in conjunction with Lighthill Slender Body Theory. The no-slip boundary condition on the wall is implemented by the method of images. We first show that the filament buckles above a critical rotation frequency due to fluid loading, and then quantify the dependence of this critical threshold on the distance from the boundary. Excellent agreement is found between experiments and simulations, with no fitting parameters. Moreover, we find that the generated propulsion force is strongly affected by the presence of a nearby boundary.   

Fluid-structure interaction of reticulated porous wings

Insects of the orders \textit{Neuroptera} and \textit{Hymenoptera} locomote via flapping flight with reticulated wings that have porous structures that confers them with remarkable lightweight characteristics. Yet these porous wings still perform as contiguous plates to provide the necessary aerodynamic lift and drag required for flight. Even though the fluid flow past the bulk of these insects may be in high Reynolds conditions, viscosity can dominate over inertia in the flow through the porous sub-features. Further considering the flexibility of these reticulated wings yields a highly nonlinear fluid-structure interaction problem. We perform a series of dynamically-scaled precision model experiments to gain physical insight into this system. Our experiments are complemented with computer simulations that combine the Discrete Elastic Rods method and a model for the fluid loading that takes into account the `leakiness' through the porous structure. Our results are anticipated to find applications in micro-air vehicle aerodynamics.   

Switchable and Tunable Aerodynamic Drag on Cylinders

We report results on the performance of Smart Morphable Surfaces (Smporhs) that can be mounted onto cylindrical structures to actively reduce their aerodynamic drag. Our system comprises of an elastomeric thin shell with a series of carefully designed subsurface cavities that, once depressurized, lead to a dramatic deformation of the surface topography, on demand. Our design is inspired by the morphology of the giant cactus (\textit{Carnegiea gigantea}) which possesses an array of axial grooves, thought to help reduce aerodynamic drag, thereby enhancing the structural robustness of the plant under wind loading. We perform systematic wind tunnel tests on cylinders covered with our Smorphs and characterize their aerodynamic performance. The switchable and tunable nature of our system offers substantial advantages for aerodynamic performance when compared to static topographies, due to their operation over a wider range of flow conditions.   

Fanning the Optimal Breeze with an Abanico

Flexible hand-held fans, or abanicos, are universally employed as cooling devices that are both portable and sustainable. Their to and fro axial motion about one's hand generates an airflow that increases the evaporation rate near the skin and refreshes. We study this problem in the context of fluid-structure interaction, through precision model experiments. We first characterize the elastic properties of a semi-circular thin plates with various thickness and evaluate their aerodynamic performance in a custom built apparatus. The air velocity profile that results from the flapping motion of the fan is characterized for different driving conditions. A systematic variation of the geometric and elastic parameters, along with an exploration of the parameter space of the periodic driving motion (amplitude and frequency), allows us to establish optimal design and operational conditions for maximal output of the generated airflow, while minimizing the input power.