arXiv subjects

Robert W. Style

Publications and source records attributed to Robert W. Style.

At least 55 records · Page 3Linked to original sources

arXiv2017

Liquid-Liquid Phase Separation in an Elastic Network

Living and engineered systems rely on the stable coexistence of two interspersed liquid phases. Yet surface tension drives their complete separation. Here we show that stable droplets of uniform and tuneable size can be produced through arrested phase separation in an elastic matrix. Starting with an elastic polymer network swollen by a solvent mixture, we change the temperature or composition to drive demixing. Droplets nucleate and grow to a stable size that is tuneable by the network cross-linking density, the cooling rate, and the composition of the solvent mixture. We discuss thermodynamic and mechanical constraints on the process. In particular, we show that the threshold for macroscopic phase separation is altered by the elasticity of the polymer network, and we highlight the role of internuclear correlations in determining the droplet size and polydispersity. This phenomenon has potential applications ranging from colloid synthesis and structural colour to phase separation in biological cells.

cond-mat.soft↗

arXiv2017

Strain-dependent solid surface stress and the stiffness of soft contacts

Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving deformation to establish contact and bulk elasticity resisting this. However, it has recently been shown that surface stresses provide an additional restoring force that can compete with and even dominate over elasticity in highly compliant materials, especially when length scales are small compared to the ratio of the surface stress to the elastic modulus, $Υ/E$. Here, we investigate experimentally the contribution of surface stresses to the force of adhesion. We find that the elastic and capillary contributions to the adhesive force are of similar magnitude, and that both are required to account for measured adhesive forces between rigid silica spheres and compliant, silicone gels. Notably, the strain-dependence of the solid surface stress contributes significantly to the stiffness of soft solid contacts.

cond-mat.soft↗

arXiv2017

Direct Measurement of Strain-dependent Solid Surface Stress

Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very challenging. Consequently, our understanding relies heavily on untested theories, especially regarding the strain dependence of this property. Here, we take advantage of the high compliance and large elastic deformability of a soft polymer gel to directly measure solid surface stress as a function of strain. As anticipated by theoretical work for metals, we find that the surface stress depends on the strain via a surface modulus. Remarkably, the surface modulus of our soft gels is many times larger than the zero-strain surface tension. This suggests that surfaces stresses can play a dominant role in solid mechanics at much larger length scales than previously anticipated.

cond-mat.mtrl-sci↗

arXiv2016

It's harder to splash on soft solids

Droplets splash when they impact dry, flat substrates above a critical velocity that depends on parameters such as droplet size, viscosity and air pressure. By imaging ethanol drops impacting silicone gels of different stiffnesses we show that substrate stiffness also affects the splashing threshold. Splashing is reduced or even eliminated: droplets on the softest substrates need over 70\% more kinetic energy to splash than they do on rigid substrates. We show that this is due to energy losses caused by deformations of soft substrates during the first few microseconds of impact. We find that solids with Young's moduli $\lesssim 100$kPa reduce splashing, in agreement with simple scaling arguments. Thus materials like soft gels and elastomers can be used as simple coatings for effective splash prevention. Soft substrates also serve as a useful system for testing splash-formation theories and sheet-ejection mechanisms, as they allow the characteristics of ejection sheets to be controlled independently of the bulk impact dynamics of droplets.

physics.flu-dyn↗

arXiv2016

Mechanical stability of particle-stabilized droplets under micropipette aspiration

We investigate the mechanical behavior of particle-stabilized droplets using micropipette aspiration. We observe that droplets stabilized with amphiphilic dumbbell-shaped particles exhibit a two-stage response to increasing suction pressure. Droplets first drip, then wrinkle and buckle like an elastic shell. While particles have a dramatic impact on the mechanism of failure, the mechanical strength of the droplets is only modestly increased. On the other hand, droplets coated with the molecular surfactant Sodium Dodecyl Sulfate are even weaker than bare droplets. In all cases, the magnitude of the critical pressure for the onset of instabilities is set by the fluid surface tension.

cond-mat.soft↗

arXiv2016

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play an central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses causes dramatic departures from classic theories for wetting (Young-Dupré), adhesion (Johnson-Kendall-Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

cond-mat.soft↗

arXiv2015

Solid Capillarity: When and How does Surface Tension Deform Soft Solids?

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement.

cond-mat.soft↗

arXiv2015

Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids

Eshelby's theory is the foundation of composite mechanics, allowing calculation of the effective elastic moduli of composites from a knowledge of their microstructure. However it ignores interfacial stress and only applies to very dilute composites -- i.e. where any inclusions are widely spaced apart. Here, within the framework of the Mori-Tanaka multiphase approximation scheme, we extend Eshelby's theory to treat a composite with interfacial stress in the non-dilute limit. In particular we calculate the elastic moduli of composites comprised of a compliant, elastic solid hosting a non-dilute distribution of identical liquid droplets. The composite stiffness depends strongly on the ratio of the droplet size, $R$, to an elastocapillary length scale, $L$. Interfacial tension substantially impacts the effective elastic moduli of the composite when $R/L\lesssim 100$. When $R < 3L/2$ ($R=3L/2$) liquid inclusions stiffen (cloak the far-field signature of) the solid.

cond-mat.soft↗

arXiv2015

Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids

In the dilute limit Eshelby's inclusion theory captures the behavior of a wide range of systems and properties. However, because Eshelby's approach neglects interfacial stress, it breaks down in soft materials as the inclusion size approaches the elastocapillarity length $L$. Here, we use a three-phase generalized self-consistent method to calculate the elastic moduli of composites comprised of an isotropic, linear-elastic compliant solid hosting a spatially random monodisperse distribution of spherical liquid droplets. As opposed to similar approaches, we explicitly capture the liquid-solid interfacial stress when it is treated as an isotropic, strain-independent surface tension. Within this framework, the composite stiffness depends solely on the ratio of the elastocapillarity length $L$ to the inclusion radius $R$. Independent of inclusion volume fraction, we find that the composite is stiffened by the inclusions whenever $R < 3L/2$. Over the same range of parameters, we compare our results with alternative approaches (dilute and Mori-Tanaka theories that include surface tension). Our framework can be easily extended to calculate the composite properties of more general soft materials where surface tension plays a role.

cond-mat.soft↗

arXiv2015

Adsorption of soft particles at fluid interfaces

Soft particles can be better emulsifiers than hard particles because they stretch at fluid interfaces. This deformation can increase adsorption energies by orders of magnitude relative to rigid particles. The deformation of a particle at an interface is governed by a competition of bulk elasticity and surface tension. When particles are partially wet by the two liquids, deformation is localized within a material-dependent distance $L$ from the contact line. At the contact line, the particle morphology is given by a balance of surface tensions. When the particle radius $R \ll L$, the particle adopts a lenticular shape identical to that of an adsorbed fluid droplet. Particle deformations can be elastic or plastic, depending on the relative values of the Young modulus, $E$, and yield stress, $σ_p$. When surface tensions favour complete spreading of the particles at the interface, plastic deformation can lead to unusual fried-egg morphologies. When deformable particles have surface properties that are very similar to one liquid phase, adsorption can be extremely sensitive to small changes of their affinity for the other liquid phase. These findings have implications for the adsorption of microgel particles at fluid interfaces and the performance of stimuli-responsive Pickering emulsions.

cond-mat.soft↗

arXiv2014

Surface tension and the mechanics of liquid inclusions in compliant solids

Eshelby's theory of inclusions has wide-reaching implications across the mechanics of materials and structures including the theories of composites, fracture, and plasticity. However, it does not include the effects of surface stress, which has recently been shown to control many processes in soft materials such as gels, elastomers and biological tissue. To extend Eshelby's theory of inclusions to soft materials, we consider liquid inclusions within an isotropic, compressible, linear-elastic solid. We solve for the displacement and stress fields around individual stretched inclusions, accounting for the bulk elasticity of the solid and the surface tension (\textit{i.e.} isotropic strain-independent surface stress) of the solid-liquid interface. Surface tension significantly alters the inclusion's shape and stiffness as well as its near- and far-field stress fields. These phenomenon depend strongly on the ratio of inclusion radius, $R$, to an elastocapillary length, $L$. Surface tension is significant whenever inclusions are smaller than $100L$. While Eshelby theory predicts that liquid inclusions generically reduce the stiffness of an elastic solid, our results show that liquid inclusions can actually stiffen a solid when $R<3L/2$. Intriguingly, surface tension cloaks the far-field signature of liquid inclusions when $R=3L/2$. These results are have far-reaching applications from measuring local stresses in biological tissue, to determining the failure strength of soft composites.

cond-mat.soft↗

arXiv2014

Stiffening solids with liquid inclusions

From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and engineering materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is strongly size-dependent with the smallest droplets mimicking the behaviour of solid inclusions. Furthermore, in opposition to the predictions of conventional composite theory, we find that finite concentrations of small liquid inclusions enhance the stiffness of soft solids. A straight-forward extension of Eshelby's theory, accounting for the surface tension of the solid-liquid interface, explains our experimental observations. The counterintuitive effect of liquid-stiffening of solids is expected whenever droplet radii are smaller than an elastocapillary length, given by the ratio of the surface tension to Young's modulus of the solid matrix.

cond-mat.soft↗

arXiv2013

Surface tension and contact with soft elastic solids

Johnson-Kendall-Robert (JKR) theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. However, it does not include solid surface tension, which also opposes adhesion by acting to flatten the surface of soft solids. We tested JKR theory to see if solid surface tension affects indentation behaviour. Using confocal microscopy, we characterised the indentation of glass particles into soft, silicone substrates. While JKR theory held for particles larger than a critical, elastocapillary lengthscale, it failed for smaller particles. Instead, adhesion of small particles mimicked the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalised version of Young's law. A simple theory quantitatively captures this behaviour, and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials.

cond-mat.soft↗

arXiv2013

Patterning droplets with durotaxis

Numerous cell-types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate -- a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical or topographical gradients. This enables a new approach to large-scale droplet patterning and is potentially useful for many applications, such as microfluidics, thermal control and microfabrication.

cond-mat.soft↗

arXiv2012

Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses

Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Young's law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Young's law.

cond-mat.soft↗

arXiv2012

Static wetting on deformable substrates, from liquids to soft solids

Young's law fails on soft solid and liquid substrates where there are substantial deformations near the contact line. On liquid substrates, this is captured by Neumann's classic analysis, which provides a geometrical construction for minimising the interfacial free energy. On soft solids, the total free energy includes an additional contribution from elasticity. A linear-elastic model incorporating an out-of-plane restoring force due to solid surface tension was recently shown to accurately predict the equilibrium shape of a thin elastic film due to a large sessile droplet. Here, we extend this model to find substrate deformations due to droplets of arbitrary size. While the macroscopic contact angle matches Young's law for large droplets, it matches Neumann's prediction for small droplets. The cross-over droplet size is roughly given by the ratio of the solid's surface tension and elastic modulus. At this cross-over, the macroscopic contact angle increases, indicating that the substrate is effectively less wetting. For droplets of all sizes, the microscopic behaviour near the contact line follows the Neumann construction giving local force balance.

cond-mat.soft↗

arXiv2012

Evaporatively driven morphological instability

Simple observations of evaporating solutions reveal a complex hierarchy of spatio-temporal instabilities. We analyze one such instability suggested by the qualitative observations of Du and Stone and find that it is driven by a novel variant of the classical {\em morphological instability} in alloy solidification. In the latter case a moving solid-liquid interface is accompanied by a solutally enriched boundary layer that is thermodynamically metastable due to {\em constitutional supercooling}. Here, we consider the evaporation of an impure film adjacent to a solid composed of the nonvolatile species. In this case, constitutional supercooling within the film is created by evaporation at the solution-vapor interface and this drives the corrugation of the solid--solution interface across the thickness of the film. The principal points of this simple theoretical study are to suggest an instability mechanism that is likely operative across a broad range of technological and natural systems and to focus future quantitative experimental searches.

cond-mat.stat-mech↗

arXiv2012

Surface Transport in Pre--Melted Films with Application to Grain--Boundary Grooving

We present a new model of surface transport in premelted films that is applicable to a wide range of materials close to their melting point. We illustrate its use by applying it to the evolution of a grain boundary groove in a high vapour pressure material and show that Mullins's classical equation describing transport driven by gradients in surface curvature is reproduced asymptotically. The microscopic contact angle at the groove root is found to be modified over a thin boundary layer, and the apparent contact angle is determined. An explicit transport coefficient is derived that governs the evolution rate of systems controlled by surface transport through premelted films. The transport coefficient is found to depend on temperature and diverges as the bulk melting temperature is approached.

physics.flu-dyn↗