An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.

When a soft hydrogel sphere is placed on a rigid hydrophilic substrate, it undergoes arrested spreading by forming an axisymmetric foot near the contact line, while conserving its global spherical shape. In contrast, liquid water (that constitutes greater than 90% of the hydrogel's volume) spreads into a thin film on the same surface. We study systematically this elastowetting of gel spheres on substrates of different surface energies, and find that their contact angle increases as the work of adhesion between the gel and the substrate decreases, as one would observe for drops of pure water - albeit being larger than in the latter case. This difference in the contact angles of gel and water appears to be due to the elastic shear stresses that develop in the gel and oppose its spreading. Indeed, by increasing the elastic modulus of the gel spheres, we find that their contact angle also increases. In addition, the length of the contact foot increases with the work of adhesion and sphere size, while it decreases when the elastic modulus of the gel is increased. We discuss those experimental results in light of a minimal analysis based on energy minimization, volume conservation, and scaling arguments.

Soft elastic solids play an important role in a wide range of applications such as in tissue scaffolds to grow artificial organs, in wearable contact lenses, as adhesives, in soft robotics and even as prototypical models to understand the mechanics of growth and morphology of organs. For a soft elastic material like hydrogel with its shear modulus in the range of tens of pascals, its surface tension also contributes to the mechanics of its deformation in addition to its elasticity. As opposed to a hard solid that is very difficult to deform, for the case of these soft solids, even a weak force like gravity can bring about significant deformation. Many of these aspects of the deformation and behavior of these ultrasoft materials are still not very well understood. Thus, the objectives of this dissertation were to understand the role of elastocapillarity (i.e, joint roles of solid surface tension and elasticity) and elastobuoyancy (i.e, joint roles of gravity and elasticity) that manifest in such solids. In this dissertation, we studied the role elastocapillarity in adhesion-induced instability in thin elastic films bonded to rigid substrates and also in surface oscillation modes of soft gel spheres set to vibration; the elastobuoyancy effect; elasticity mediated interaction of particles in soft solids as well as on thin films supported over a pool of liquid. We also presented some new results on how soft spherical gels undergo restricted spreading on rigid substrates with varying surface energies. In the first section, we studied how a thin confined layer of a soft elastic film loses adhesion from a rigid substrate by forming interfacial instabilities when a tensile stress is applied to it. We performed experiments to quantify the characteristic lengthscale of the patterns formed and found that they were significantly larger than the wavelengths of purely elastic instabilities. A linear stability analysis of the elastic field equations by taking into account the role of surface tension showed that the amplification of the wavelength is due to the role of elastocapillarity where the surface tension, elasticity, and film thickness contribute jointly in a non-trivial way. In addition, we found experimentally as well as theoretically that the stress required to adhesively fracture these films is much larger than Griffith’s fracture stress for stiffer elastic films, which is also due to the effect of elastocapillarity. We also studied the surface fluctuation of sessile hydrogel spheres subjected to mechanically-induced Gaussian white noise to understand the role of elastocapillarity in their oscillation modes. An important finding of this study is that they give a direct evidence that the surface tension of these elastic hydrogels is almost like that of water, which is the integral solvent in the swollen network of the polymeric gel. In the subsequent section, we introduced the new phenomenon of Elastobuoyancy. When a rigid sphere is placed on the surface of an ultrasoft hydrogel, it plunges into the soft substrate to an equilibrium depth where the elastic strain energy of the surrounding medium balances its weight. We refer to this state of the sphere as ‘Elastobuoyant’. By performing systematic experiments where we varied the sphere size and the elasticity of the substrate, we obtained scaling laws of the depth as a function of the radii, elastic modulus and the spheres buoyant weight, which were also supported by asymptotic analyses of the same. Following the section on elastobuoyancy, we reported a new set of principles to design self-assembly of particles by using the combined roles of surface tension, elasticity, and gravity in soft substrates. We used three different systems to study this elastic interaction macroscopically: (i) elastobuoyant assembly of particles suspended inside a soft elastic gel, (ii) elastocapillary assembly of particles floating on the surface of soft gels analogous to capillary attraction of objects on the surface of liquids, and (iii) assembly of particles on the surface of thin elastic membranes supported over a viscous liquid. In the second last chapter in this thesis, we presented some results on how soft elastic gel spheres spread on rigid substrates with different surface energies. Our observations indicate that their contact angles are slightly greater than those of equivalent liquid drops on similar substrates. The contact angles of these gel spheres increase as a function of elasticity and decrease when surface energy increases. We derived an expression for the excess elastic tension in the gel spheres at the crack tip by using an approach that is similar to estimating the viscous dissipation at the contact line during spreading of liquids. By using a general constitutive law where the elastic energy is not limited to the square of the strains, the singularity at the crack tip is artificially removed thereby forcing the gel to assume a liquid-like behavior. Our experimental results agreed reasonably well with the model. In the last chapter, we summarized the doctoral research and presented suggestions for future investigations. There are several appendices in this thesis that have interesting observations from partially completed projects that need additional research and analysis in the future.

A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elasticity. When such a confined film is subjected to a continually increasing normal displacement, the morphological patterns evolve into cracks, which, in turn, govern the adhesive fracture behavior of the interface. While, in general, the thickness provides the relevant length scale underlying the well-known Griffith-Kendall criterion of debonding of a rigid disc from a confined film, it is modified non-trivially by the elasto-capillary number for an ultra-soft film. Depending upon the degree of confinement and the spatial distribution of external stress, various analogs of the canonical instability patterns in liquid systems can also be reproduced with thin confined elastic films.

We study the interaction of two parallel rigid cylinders on the surface of a thin elastic film supported on a pool of liquid. The excess energy of the surface due to the curvature of the stretched film induces attraction of the cylinders that can be quantified by the variation of their gravitational potential energies as they descend into the liquid while still floating on the film. Although the experimental results follow the trend predicted from the balance of the gravitational and elastic energies of the system, they are somewhat underestimated. The origin of this discrepancy is the hysteresis of adhesion between the cylinder and the elastic film that does not allow the conversion of the total available energy into gravitational potential energy, as some part of it is recovered in stretching the film behind the cylinders while they approach each other. A modification of the model accounting for the effects of adhesion hysteresis improves the agreement between theoretical and experimental results. The contribution of the adhesion hysteresis can be reduced considerably by introducing a thin hydrogel layer atop the elastic film that enhances the range of attraction of the cylinders (as well as rigid spheres) in a dramatic way. Morphological instabilities in the gel project corrugated paths to the motion of small spheres, thus leading to a large numbers of particles to aggregate along their defects. These observations suggest that a thin hydrogel layer supported on a deformable elastic film affords an effective model system to study elasticity and defects mediated interaction of particles on its surface.

A liquid drop moves on a solid surface if it is subjected to a gradient of wettability or temperature. However, the pinning defects on the surface manifested in terms of a wetting hysteresis, or first-order nonlinear friction, limit the motion in the sense that a critical size has to be exceeded for a drop to move. The effect of hysteresis can, however, be mitigated by an external vibration that can be either structured or stochastic, thereby creating a directed motion of the drop. Many of the well-known features of rectification, amplification, and switching that are generic to electronics can be engineered with such types of movements. A specific case of interest is the random coalescence of drops on a surface that gives rise to self-generated noise. This noise overcomes the pinning potential, thereby generating a random motion of the coalesced drops. Randomly moving coalesced drops themselves exhibit a directed diffusive flux when a boundary is present to eliminate them by absorption. With the presence of a bias, the coalesced drops execute a diffusive drift motion that can have useful applications in various water and thermal management technologies.

In the classic theory of solid adhesion, surface energy drives deformation to increase contact area while bulk elasticity opposes it. Recently, solid surface stress has been shown also to play an important role in opposing deformation of soft materials. This suggests that the contact line in soft adhesion should mimic that of a liquid droplet, with a contact angle determined by surface tensions. Consistent with this hypothesis, we observe a contact angle of a soft silicone substrate on rigid silica spheres that depends on the surface functionalization but not the sphere size. However, to satisfy this wetting condition without a divergent elastic stress, the gel separates from its solvent near the contact line. This creates a four-phase contact zone with two additional contact lines hidden below the surface of the substrate. While the geometries of these contact lines are independent of the size of the sphere, the volume of the phase-separated region is not, but rather depends on the indentation volume. These results indicate that theories of adhesion of soft gels need to account for both the compressibility of the gel network and a non-zero surface stress between the gel and its solvent.

A new mechanism for the passive removal of drop on a horizontal surface is described that does not require pre-fabrication of a surface energy gradient. The method relies upon the preparation of alternate hydrophilic/hydrophobic stripes on a surface. When one side of this surface is exposed to steam, with its other surface convectively cooled with cold water, steam condenses as a continuous film on the hydrophilic stripes but as droplets on the hydrophobic stripes. Coalescence leads to a self-generated noise that in turn leads to a random motion of the center of mass of the fused drops on the surface, which are readily removed as they reach near the boundary of the hydrophobic and hydrophilic zones thus resulting in a net diffusive flux of the coalesced drops moving from the hydrophobic to the hydrophilic stripes on the surface. This phenomenon is, indeed, similar to that of the random walk of particles with an absorbing wall. This method of creating directed motion of drops does not require a pre-existing wettability gradient and may have useful applications in thermal management devices.

Sessile drops of soft hydrogels were vibrated vertically by subjecting them to a mechanically-induced Gaussian white noise. Power spectra of the surface fluctuation of the gel allowed identification of its resonant frequency that decreases with their mass, but increases with its shear modulus (??). The principal resonant frequencies of the spheroidal modes of the gel of shear moduli ranging from 55 Pa to 290 Pa were closest to the lowest Rayleigh mode of vibration of a drop of pure water. These observations coupled with the fact that the resonance frequency varies inversely as the mass with an exponent close to 0.5 suggest that they primarily correspond to the capillary (or a pseudo-capillary) mode of drop vibration. The contact angles of the gel drops also increase with the modulus of the gel. When the resonance frequencies are plotted against a fundamental frequency scale (??/??P2h)0.5 (expressed in terms of its surface tension (??), density (??), perimeter (P) and mean thickness (h)) all the data collapse nicely on a single plot provided that the latter is shifted by a shear modulus dependent factor (1+??h/2??). We believe that this method has the potential to measure directly the surface tension of soft elastic gels.

An adhesively stressed thin film of a soft hydrogel confined between two rigid flat substrates autoroughens with its dominant wavelength ($łambda$) exhibiting pronounced dependence on the film thickness (H). A linear stability analysis confirmed that this long wavelength instability ($łambda$ \~ 7H) is due to an elastocapillary effect, the implementation of which required direct measurements of the surface tension and the elasticity of the gel. The surface tension of the gel was estimated from the fundamental spherical harmonic of a hemispherical cap of the gel that was excited by an external noise. The shear modulus ($μ$) of the gel was determined from its resonant shear mode in a confined geometry. During the course of this study, it was found that a high density steel ball submerges itself inside the gel by balancing its excess weight with the accumulated strain induced elastic force that allows another estimation of its elastic modulus. The large ratio (1.8 mm) of the surface tension to its elasticity ascertains the role of elastocapillarity in the adhesion-induced pattern formation with such gels. Experimental results are in accord with a linear stability analysis that predicts that the rescaled wavelength $łambda$($μ$H/$\gamma$)(0.27) is linear with H, which also modifies the conventional stress to pull a flat rigid object out of a very soft film by a multiplicative factor: ($\gamma$/$μ$H)(1/4). The analysis also suggests some new results related to the role of the finite dilation of a material in interfacial pattern formation that may have nontrivial consequences in the adhesive delamination of very thin and/or soft elastic films via self-generated cracks.