Wetting and phase separation in soft adhesion

Unravelling soft interfaces: Visualization of gel ridges

HYPOTHESIS

Soft materials, particularly elastomers, are extensively studied, but investigations into purely soft gel contact systems are limited due to their complex dual phases consisting of polymer and free liquids. While Dual Wavelength-Reflection Interference Confocal Microscopy (DW-RICM) is effective for noninvasively visualizing interfaces from a bottom view, it faces challenges in gel studies due to close refractive indices of polymeric networks and free liquids. We hypothesize that modulating the refractive index of soft gels using nanoparticles (NPs) enhances the visualization of contact zone beneath the free surface, providing insights into the configuration of phase-separated free oil within gel-on-gel contact systems.

EXPERIMENTS

Gel-on-gel contact systems were fabricated using immiscible organogels and hydrogels. Titanium dioxide (TiO2) NPs were introduced into the organogel to modulate refractive indices. Given the lack of prior studies on the hidden contact zone between gels, various techniques, including DW-RICM, side-view imaging, and inverted optical microscopy, were employed to observe and validate our findings. Comparative analyses were conducted with elastomer-on-rigid, elastomer-on-gel, and gel-on-rigid contact systems.

FINDINGS

Our investigation demonstrated that a minimal amount of TiO2 NPs effectively delineates the direct contact radius between organogel polymeric networks and hydrogel surfaces. Comparative experiments showed that TiO2 addition did not alter the gels' mechanical and surface properties but significantly enhanced information on gel contact deformation. This enhanced visualization technique has the potential to advance our understanding of adhesive contacts in gels, providing valuable insights into interface phenomena involving biological soft tissues and cells.

Phase separation dynamics in wetting ridges of polymer surfaces swollen with oils of different viscosities

When drops are placed on a sufficiently soft surface, the drop surface tension drives an out of plane deformation around the contact line (i.e., a wetting ridge). For soft elastomeric surfaces that are swollen with a liquid, capillarity from a drop can induce a phase separation in the wetting ridge. Using confocal microscopy, we study the dynamics of phase separation at the wetting ridge of glycerol drops on silicone elastomers, which are swollen with silicone oils of varying viscosity (i.e., molecular weight). We show that the viscosity of the swelling oil plays a large role in the oil separation size and separation rate. For networks swollen to near their maximum swelling (i.e., saturated), lower viscosity oil separates more and separates faster at early times compared to larger viscosity oil. During late-stage wetting, the growth rate of the separation is a function of viscosity and swelling ratio, which can be described by a simple diffusive model and a defined wetting ridge geometry. In this late-stage wetting, the higher viscosity oil evidently grows faster, likely because it is further from reaching equilibrium. Interestingly, the separated oil phase region grows with a nearly constant, geometrically similar shape. Understanding how phase separation occurs on swollen substrates should provide information on how to control drop spreading, sliding, adhesion, or friction on such surfaces.

Flexible hydrogels connecting adhesion and wetting

Raindrops falling on window-panes spread upon contact, whereas hail can cause dents or scratches on the same glass window upon contact. While the former phenomenon resembles classical wetting, the latter is dictated by contact and adhesion theories. The classical Young-Dupre law applies to the wetting of pure liquids on rigid solids, whereas conventional contact mechanics theories account for rigid-on-soft or soft-on-rigid contacts with small deformations in the elastic limit. However, the crossover between adhesion and wetting is yet to be fully resolved. The key lies in the study of soft-on-soft interactions with material properties intermediate between liquids and solids. In this work, we translate adhesion to wetting by experimentally probing the static signature of hydrogels in contact with soft PDMS of varying elasticity of both the components. Consequently, we probe this transition across six orders of magnitude in terms of the characteristic elasto-adhesive parameter of the system. In doing so, we reveal previously unknown phenomenology and a theoretical model which smoothly bridges adhesion of glass spheres with total wetting of pure liquids on any given substrate.

From a distance: Shuttleworth revisited

The Shuttleworth equation: a linear stress-strain relation ubiquitously used in modeling the behavior of soft surfaces. Its validity in the realm of materials subject to large deformation is a topic of current debate. Here, we allow for large deformation by deriving the constitutive behavior of the surface from the general framework of finite kinematics. We distinguish cases of finite and infinitesimal surface relaxation preceding an infinitesimal applied deformation. The Shuttleworth equation identifies as the Cauchy stress measure in the fully linearized setting. We show that both in finite and linearized cases, measured elastic constants depend on the utilized stress measure. In addition, we discuss the physical implications of our results and analyze the impact of surface relaxation on the estimation of surface elastic moduli in the light of two different test cases.

Wetting on silicone surfaces

Silicone is frequently used as a model system to investigate and tune wetting on soft materials. Silicone is biocompatible and shows excellent thermal, chemical, and UV stability. Moreover, the mechanical properties of the surface can be easily varied by several orders of magnitude in a controlled manner. Polydimethylsiloxane (PDMS) is a popular choice for coating applications such as lubrication, self-cleaning, and drag reduction, facilitated by low surface energy. Aiming to understand the underlying interactions and forces, motivated numerous and detailed investigations of the static and dynamic wetting behavior of drops on PDMS-based surfaces. Here, we recognize the three most prevalent PDMS surface variants, namely liquid-infused (SLIPS/LIS), elastomeric, and liquid-like (SOCAL) surfaces. To understand, optimize, and tune the wetting properties of these PDMS surfaces, we review and compare their similarities and differences by discussing (i) the chemical and molecular structure, and (ii) the static and dynamic wetting behavior. We also provide (iii) an overview of methods and techniques to characterize PDMS-based surfaces and their wetting behavior. The static and dynamic wetting ridge is given particular attention, as it dominates energy dissipation, adhesion, and friction of sliding drops and influences the durability of the surfaces. We also discuss special features such as cloaking and wetting-induced phase separation. Key challenges and opportunities of these three surface variants are outlined.

Dynamics of Droplets Moving on Lubricated Polymer Brushes

Understanding the dynamics of drops on polymer-coated surfaces is crucial for optimizing applications such as self-cleaning materials or microfluidic devices. While the static and dynamic properties of deposited drops have been well characterized, a microscopic understanding of the underlying dynamics is missing. In particular, it is unclear how drop dynamics depends on the amount of uncross-linked chains in the brush, because experimental techniques fail to quantify those. Here we use coarse-grained simulations to study droplets moving on a lubricated polymer brush substrate under the influence of an external body force. The simulation model is based on the many body dissipative particle dynamics (MDPD) method and designed to mimic a system of water droplets on poly(dimethylsiloxane) (PDMS) brushes with chemically identical PDMS lubricant. In agreement with experiments, we find a sublinear power law dependence between the external force F and the droplet velocity v, F ∝ vα with α < 1; however, the exponents differ (α ∼ 0.6-0.7 in simulations versus α ∼ 0.25 in experiments). With increasing velocity, the droplets elongate and the receding contact angle decreases, whereas the advancing contact angle remains roughly constant. Analyzing the flow profiles inside the droplet reveals that the droplets do not slide but roll, with vanishing slip at the substrate surface. Surprisingly, adding lubricant has very little effect on the effective friction force between the droplet and the substrate, even though it has a pronounced effect on the size and structure of the wetting ridge, especially above the cloaking transition.

Soft wetting: Substrate softness- and time-dependent droplet/bubble adhesion

HYPOTHESIS

The droplet/bubble adhesion characteristics depend on the length of the droplet/bubble three-phase contact line. Since the deformation caused by the liquid-gas interfacial tension on the soft substrate, referred as to the wetting ridge, retards contact line spreading and retraction, we conjecture that the droplet/bubble adhesion characteristics depend also on the substrate softness.

EXPERIMENTS

Soft substrates with various shear moduli are prepared and characterized by the spreading and receding dynamics of water droplets and underwater bubbles. Snap-in and normal adhesion forces of droplets/bubbles on such soft substrates are directly measured along with the visualized droplet/bubble shape profiles.

FINDINGS

The droplet/bubble snap-in force, which corresponds to the short-time spreading dynamics, decreases with a decrease in the substrate shear modulus because of the retarded contact line spreading. The droplet maximal adhesion force on a soft substrate can be counterintuitively either smaller or larger than its counterpart on the rigid substrate depending on different dwelling times, i.e., the droplet/bubble-substrate contact time before droplet/bubble-substrate separation. The former is attributed to the retarded contact line spreading, whereas the latter is attributed to the retarded contact line retraction. The substrate softness- and dwelling time-dependent droplet/bubble adhesion reported in this study will benefit various applications related to soft substrates.

Enhancement of the Rate of Surface Reactions by the Elastocapillary Effect

We examined the effect of deformability of a solid substrate on the kinetics of a surface reaction that occurs between chemical species present in it and a liquid dispensed on it. In particular, we have dispensed aqueous solutions of gold and silver salt as sessile drops or as a liquid pool on a cross-linked film of poly(dimethylsiloxane) (PDMS). The PDMS surface contains organosilane (SiH), which reduces the salt, producing metallic nanoparticles at the solid-liquid interface. These experiments reveal that, for a sufficiently soft solid, the reaction proceeds about three times faster in the drop mode than in the pool mode. The reaction conditions in both cases remain exactly identical except that, for the drop, the vertical component of the liquid surface tension deforms the solid substrate at the three-phase contact line. We have estimated the solid-liquid and solid-air interfacial energy, which along with the surface energy of the liquid gives an estimate of excess free energy. This energy is found to be different for the drop and pool modes. By considering that this excess free energy decreases the activation energy barrier for the reaction, we have shown that the reaction rate constant in the drop mode should indeed exceed that in the pool mode by about three times.

Adhesion and Contact Aging of Acrylic Pressure-Sensitive Adhesives to Swollen Elastomers

Fluid-infused (or swollen) elastomers are known for their antiadhesive properties. The presence of excess fluid at their surface is the main contributor to limiting contact formation and minimizing adhesion. Despite their potential, the mechanisms for adhesion and contact aging to fluid-infused elastomers are poorly understood beyond contact with a few materials (ice, biofilms, glass). This study reports on adhesion to a model fluid-infused elastomer, poly(dimethylsiloxane) (PDMS), swollen with silicone oil. The effects of oil saturation, contact time, and the opposing surface are investigated. Specifically, adhesion to two different adherents with comparable surface energies but drastically different mechanical properties is investigated: a glass surface and a soft viscoelastic acrylic pressure-sensitive adhesive film (PSA, modulus ∼25 kPa). Adhesion between the PSA and swollen PDMS [with 23% (w/w) silicone oil] retains up to 60% of its value compared to contact with unswollen (dry) PDMS. In contrast, adhesion to glass nearly vanishes in contact with the same swollen elastomer. Adhesion to the PSA also displays stronger contact aging than adhesion to glass. Contact aging with the PSA is comparable for dry and unsaturated PDMS. Moreover, load relaxation when the PSA is in contact with the PDMS does not correlate with contact aging for contact with the dry or unsaturated elastomer, suggesting that contact aging is likely caused by chain interpenetration and polymer reorganization within the contact region. Closer to full saturation of the PDMS with oil, adhesion to the PSA decreases significantly and shows a delay in the onset of contact aging that is weakly correlated to the poroelastic relaxation of the elastomer. Additional confocal imaging suggests that the presence of a layer of fluid trapped at the interface between the two solids could explain the delayed (and limited) contact aging to the oil-saturated PDMS.

Morphology and stability of droplets sliding on soft viscoelastic substrates

We show that energy dissipation partition between a liquid and a solid controls the shape and stability of droplets sliding on viscoelastic gels. When both phases dissipate energy equally, droplet dynamics is similar to that on rigid solids. When the solid is the major contributor to dissipation, we observe an apparent contact angle hysteresis of viscoelastic origin. We find excellent agreement between our data and a non-linear model of the wetting of gels of our own that also indicates the presence of significant slip. Our work opens general questions on the dynamics of curved contact lines on compliant substrates.

Experimental characterization of elastocapillary and osmocapillary effects on multi-scale gel surface topography

Surface topography significantly affects various surface properties of polymer gels. Unlike conventional materials where surface topography is largely a geometric property, the surface topography of a polymer gel is governed by the competition between capillary, elastic, and osmotic effects, which leads to complex stimuli-responsive effects. Elastocapillary deformation and osmocapillary phase separation are two phenomena that are known to flatten gel surface topography. Here we experimentally quantify how osmocapillary phase separation affects gel surface topography by fabricating ionogels with multi-scale topography and characterizing the swelling-dependent surface flattening. Our observation confirms the vital role of the osmocapillary length in governing the surface behavior of swollen ionogels. This study provides the first quantitative experimental verification of the osmocapillary phase separation and shows the insufficiency of the previous studies based on elastocapillary deformation alone.

An energy-optimization method to study gel-swelling in confinement

We recast the problem of hydrogel swelling under physical constraints as an energy optimization problem. We apply this approach to compute equilibrium shapes of hydrogel spheres confined within a jammed matrix of rigid beads and interpret the results to determine how confinement modifies the mechanics of swollen hydrogels. In contrast to the unconfined case, we find a spatial separation of strains within the bulk of the hydrogel as the strain becomes localized to an outer region. We also explore the contact mechanics of the gel, finding a transition from Hertzian behavior to non-Hertzian behavior as a function of swelling. Our model, implemented in the Morpho shape optimization environment and validated against an experimentally demonstrated prototypical scenario, can be applied in any dimension, readily adapted to diverse swelling scenarios and extended to use other energies in conjunction.

Capillary detachment of a microparticle from a liquid-liquid interface

The attachment and detachment of microparticles at a liquid-liquid interface are common in many material systems, from Pickering emulsions and colloidal assemblies to capillary suspensions. Properties of these systems rely on how the particles interact with the liquid-liquid interface, including the detachment process. In this study, we simultaneously measure the capillary detachment force of a microparticle from a liquid-liquid interface and visualize the shape of the meniscus by combining colloidal probe microscopy and confocal microscopy. The capillary behavior is studied on both untreated (hydrophilic) and fluorinated (hydrophobic) glass microparticles. The measured force data show good agreement with theoretical calculations based on the extracted geometric parameters from confocal images of the capillary bridge. It is also evident that contact line pinning is an important aspect of detachment for both untreated and fluorinated particles.

Reversal of Solvent Migration in Poroelastic Folds

Polymer networks and biological tissues are often swollen by a solvent such that their properties emerge from a coupling between swelling and elastic stress. This poroelastic coupling becomes particularly intricate in wetting, adhesion, and creasing, for which sharp folds appear that can even lead to phase separation. Here, we resolve the singular nature of poroelastic surface folds and determine the solvent distribution in the vicinity of the fold tip. Surprisingly, two opposite scenarios emerge depending on the angle of the fold. In obtuse folds such as creases, it is found that the solvent is completely expelled near the crease tip, according to a nontrivial spatial distribution. For wetting ridges with acute fold angles, the solvent migration is reversed as compared to creasing, and the degree of swelling is maximal at the fold tip. We discuss how our poroelastic fold analysis offers an explanation for phase separation, fracture, and contact angle hysteresis.

Preparation of ultra-thin elastomeric films

When polydimethylsiloxane elastomers are produced, in the absence of great care, chains remain that are unbound to the cross-linked matrix. Due to the unbound chains swelling the crosslinked matrix, these materials are gels. We have developed a simple process to prepare well-controlled elastomeric thin films which do not rely on unknown commercial formulations.

Studying kinetics of a surface reaction using elastocapillary effect

HYPOTHESIS

When a liquid is inserted inside a microfluidic channel, embedded within a soft elastomeric layer, e.g. poly(dimethylsiloxane) (PDMS), the thin wall of the channel deforms, due to change in solid-liquid interfacial energy. This phenomenon is known as Elastocapillary effect. The evolution of a new species at this interface too alters the interfacial energy and consequently the extent of deformation. Hence, it should be possible to monitor dynamics of physical and chemical events occurring near to the solid-liquid interface by measuring this deformation by a suitable method, e.g., optical profilometer.

EXPERIMENTS

Aqueous solution of a metal salt inserted into these channels reacts with Silicon-hydride present in PDMS, yielding metallic nanoparticles at the channel surface. The kinetics of this reaction was captured in real time, by measuring the wall deformation. Similarly, physical adsorption of a protein: Bovine Serum Albumin, on PDMS surface too was monitored.

FINDING

The rate of change in deformation can be related to rate of these processes to extract the respective reaction rate constant. These results show that Elastocapillary effect can be a viable analytical tool for in-situ monitoring of many physical and chemical processes for which, the reaction site is inaccessible to conventional analytical methods.

Creasing in microscale, soft static friction

Utilizing colloidal probe, lateral force microscopy and simultaneous confocal microscopy, combined with finite element analysis, we investigate how a microparticle starts moving laterally on a soft, adhesive surface. We find that the surface can form a self-contacting crease at the leading front, which results from a buildup of compressive stress. Experimentally, creases are observed on substrates that exhibit either high or low adhesion when measured in the normal direction, motivating the use of simulations to consider the role of adhesion energy and interfacial strength. Our simulations illustrate that the interfacial strength plays a dominating role in the nucleation of a crease. After the crease forms, it progresses through the contact zone in a Schallamach wave-like fashion. Interestingly, our results suggest that this Schallamach wave-like motion is facilitated by free slip at the adhesive, self-contacting interface within the crease.

Phase Separation in Wetting Ridges of Sliding Drops on Soft and Swollen Surfaces

Drops in contact with swollen, elastomeric substrates can induce a capillary mediated phase separation in wetting ridges. Using confocal microscopy, we visualize phase separation of oligomeric silicone oil from a cross-linked silicone network during steady-state sliding of water drops. We find an inverse relationship between the oil tip height and the drop sliding speed, which is rationalized by competing transport timescales of the oil molecules: separation rate versus drop-advection speed. Separation rates in highly swollen networks are as fast as diffusion in pure melts.

The crucial role of elasticity in regulating liquid-liquid phase separation in cells

Liquid-liquid phase separation has emerged as a fundamental mechanism underlying intracellular organization, with evidence for it being reported in numerous different systems. However, there is a growing concern regarding the lack of quantitative rigor in the techniques employed to study phase separation, and their ability to account for the complex nature of the cellular milieu, which affects key experimentally observable measures, such as the shape, size and transport dynamics of liquid droplets. Here, we bridge this gap by combining recent experimental data with theoretical predictions that capture the subtleties of nonlinear elasticity and fluid transport. We show that within a biologically accessible range of material parameters, phase separation is highly sensitive to elastic properties and can thus be used as a mechanical switch to rapidly transition between different states in cellular systems. Furthermore, we show that this active mechanically mediated mechanism can drive transport across cells at biologically relevant timescales and could play a crucial role in promoting spatial localization of condensates; whether cells exploit such mechanisms for transport of their constituents remains an open question.

Adhesion of fluid infused silicone elastomer to glass

Elastomers swollen with non-polar fluids show potential as anti-adhesive materials. We study the effect of oil fraction and contact time on the adhesion between swollen spherical probes of PDMS (polydimethylsiloxane) and flat glass surfaces. The PDMS probes are swollen with pre-determined amount of 10 cSt silicone oil to span the range where the PDMS is fluid free (via solvent extraction) up to the limit where it is oil saturated. Probe tack measurements show that adhesion decreases rapidly with an increase in oil fraction. The decrease in adhesion is attributed to excess oil present at the PDMS-air interface. Contact angle measurements and optical microscopy images support this observation. Adhesion also increases with contact time for a given oil fraction. The increase in adhesion with contact time can be interpreted through different competing mechanisms that depend on the oil fraction where the dominant mechanism changes from extracted to fully swollen PDMS. For partially swollen PDMS, we observe that adhesion initially increases because of viscoelastic relaxation and at long times increases because of contact aging. In contrast, adhesion between fully swollen PDMS and glass barely increases over time and is mainly due to capillary forces. While the relaxation of PDMS in contact is well-described by a visco-poroelastic model, we do not see evidence that poroelastic relaxation of the PDMS contributes to an increase of adhesion with glass whether it is partially or fully swollen.

Capillary pressure mediated long-term dynamics of thin soft films

HYPOTHESIS

The conventional solid-solid contact is well studied in the literature. However, a number of practical applications, such as adhesive patches and biomimetic surfaces, require a much deeper understanding of soft contact where there is a distinct time-dependent adhesion behavior due to the dual-phase structure (solids and liquids). To understand this, currently existing solid-solid contact behavior is extrapolated to soft contact, wherein the size-effect of the gel film and the preload are typically neglected. When introducing the finite-size effect and preload, gels could experience distinctive long-term contact dynamics in contact with another material.

EXPERIMENTS

We reconstruct the evolving surface profile of the gel films intercalated between a glass sphere and glass slide using dual wavelength-reflection interference contrast microscopy. The macro-sized glass sphere compresses the gel. The indentation depth is comparable to the gel film thickness, wherein the conventional contact theories are inapplicable.

FINDINGS

The gel surface experiences two deformation stages. The natural preload and elastic force develop the contact area in the early state. In the later state, the viscous free molecules of the gel develop the ridge. We discover that the residual surface stress relaxes over 85 hr. Our findings on the long-term gel deformation provide a new perspective on soft adhesion, from developing soft adhesives to understanding biological tissues.

How liquid-liquid phase separation induces active spreading

The interplay between phase separation and wetting of multicomponent mixtures is ubiquitous in nature and technology and recently gained significant attention across scientific disciplines, due to the discovery of biomolecular condensates. It is well understood that sessile droplets, undergoing phase separation in a static wetting configuration, exhibit microdroplet nucleation at their contact lines, forming an oil ring during later stages. However, very little is known about the dynamic counterpart, when phase separation occurs in a nonequilibrium wetting configuration, i.e., spreading droplets. Here we show that liquid-liquid phase separation strongly couples to the spreading motion of three-phase contact lines. Thus, the classical Cox-Voinov law is not applicable anymore, because phase separation adds an active spreading force beyond the capillary driving. Intriguingly, we observe that spreading starts well before any visible nucleation of microdroplets in the main droplet. Using high-speed ellipsometry, we further demonstrate that the evaporation-induced enrichment, together with surface forces, causes an even earlier nucleation in the wetting precursor film around the droplet, initiating the observed wetting transition. We expect our findings to improve the fundamental understanding of phase separation processes that involve dynamical contact lines and/or surface forces, with implications in a wide range of applications, from oil recovery or inkjet printing to material synthesis and biomolecular condensates.

Wetting dynamics of viscoelastic solid films

We study the wetting phenomena of a soft viscoelastic solid film on a smooth and flat substrate. A poly-dimethylsiloxane (PDMS) rubber film is suspended from a stage at both ends, and the wetting behavior of the film against a glass substrate is observed while lowering the stage at a constant velocity. We find that the dynamics of the rubber-glass-air contact lines vary with the lowering velocity of the stage. When the stage velocity is sufficiently low, the film wets the substrate smoothly and the contact lines are straight throughout. Consequently, the contact line velocity is proportional to the lowering velocity. As the stage velocity is increased, the contact line velocity reaches a maximum at the critical stage velocity and then subsequently decreases. The contact lines are wavy and sensitive to the defects above the critical velocity, resulting in the trapping of air bubbles at the interface. We reproduce the wetting behavior using a simple numerical model, assuming an upper limit for the contact line velocity. The wetting behavior observed in our experiments is attributed to the transition in the in-plane stress state from tensile to compressive along the film, leading to buckling of the film above the critical stage velocity. Our results suggest the existence and importance of the maximum wetting velocity for viscoelastic solids.

Temperature-dependent soft wetting on amorphous, uncrosslinked polymer surfaces

The wetting of polymer melts at high temperatures is studied by placing a glycerol drop on a poly(n-butyl methacrylate) film and measuring the wetting ridge. The height of the wetting ridge grows continuously over time. These wetting ridge growth rates can be explained by polymer chain dynamics occurring at the molecular level, determined using oscillatory shear rheology of the polymer melt. The shape of wetting ridge profile can be modeled using an equation previously used for elastomers, with a simple modification that incorporates the time-dependent storage modulus of the uncrosslinked melts.

The role of crosslinking density in surface stress and surface energy of soft solids

Surface stress and surface energy are two fundamental parameters that determine the surface properties of any material. While it is commonly believed that the surface stress and surface energy of liquids are identical, the relationship between the two parameters in soft polymeric gels remains debatable. In this work, we measured the surface stress and surface energy of soft silicone gels with varying weight ratios of crosslinkers in soft wetting experiments. Above a critical density, k₀, the surface stress was found to increase significantly with crosslinking density while the surface energy remained unchanged. In this regime, we can estimate a non-zero surface elastic modulus that also increases with the ratio of crosslinkers. By comparing the surface mechanics of the soft gels with their bulk rheology, the surface properties near the critical density k₀ were found to be closely related to the underlying percolation transition of the polymer networks.

Reduced Pressure Drop in Viscoelastic Polydimethylsiloxane Wall Channels

Polydimethylsiloxane (PDMS) is an important viscoelastic material that finds applications in a large number of engineering systems, particularly lab-on-chip microfluidic devices built with a flexible substrate. Channels made of PDMS, used for transporting analytes, are integral to these applications. The PDMS viscoelastic nature can induce additional hydrodynamic contributions at the soft wall/fluid interface compared to rigid walls. In this research, we investigated the pressure drop within PDMS channels bounded by rigid tubes (cellulose tubes). The bulging effect of the PDMS was limited by the rigid tubes under flowing fluids. The PDMS viscoelasticity was modulated by changing the ratio of the base to the cross-linker from 10:1 to 35:1. We observed that the pressure drop of the flowing fluids within the channel decreased with the increased loss tangent of the PDMS in the examined laminar regime [Reynolds number (Re) ∼ 23-58.6 for water and Re ∼ 0.69-8.69 for glycerol solution]. The elastic PDMS 10:1 wall channels followed the classical Hagen Poiseuille's equation, but the PDMS walls with lower cross-linker concentrations and thicker walls decreased pressure drops. The friction factor (f) for the PDMS channels with the two working fluids could be approximated as f = 47/Re. We provide a correlation between the pressure drop and PDMS viscoelasticity based on experimental findings. In the correlation, the loss tangent predominates; the larger the loss tangent, the smaller is the pressure drop. The research findings appear to be unexpected if only considering the energy dissipation of viscoelastic PDMS walls. We attributed the reduction in the pressure drop to a lubricating effect of the viscoelastic PDMS walls in the presence of the working fluids. Our results reveal the importance of the subtle diffusion of the residual oligomers and water from the bulk to the soft wall/fluid interface for the observed pressure drop in soft wall channels.

Surface Tension and the Strain-Dependent Topography of Soft Solids

When stretched in one direction, most solids shrink in the transverse directions. In soft silicone gels, however, we observe that small-scale topographical features grow upon stretching. A quantitative analysis of the topography shows that this counterintuitive response is nearly linear, allowing us to tackle it through a small-strain analysis. We find that the surprising increase of small-scale topography with stretch is due to a delicate interplay of the bulk and surface responses to strain. Specifically, we find that surface tension changes as the material is deformed. This response is expected on general grounds for solid materials, but challenges the standard description of gel and elastomer surfaces.

Understanding the Wetting and Water-Induced Dewetting Behaviors of Bitumen on Rough Aggregate Surfaces

The interaction of bitumen colloidal (a form of heavy oil) with inorganic solids, for example, mineral aggregates, in both air and water environments is ubiquitous in nature and engineering. However, our knowledge of the underlying physical mechanism of bitumen-/solid-wetting phenomena is still very limited. The current study aims to reveal how the mineralogy and topography of aggregate surfaces affect the wetting and water-induced dewetting of bitumen on aggregate surfaces. For this, contact angle tests were performed to measure the surface energies of bitumen and aggregate surfaces varying in both mineralogy and roughness. Based on the measurements, both qualitative and quantitative analyses were conducted for the interaction of bitumen/aggregate interface in air and water environments. Complete wetting and complete dewetting hold for the air/bitumen/aggregate and water/bitumen/aggregate interfaces, respectively. The negative interfacial adhesive energy for the air/bitumen/aggregate interface and the interfacial debonding energy for the water/bitumen/aggregate interface imply that both bitumen wetting and water-induced bitumen dewetting on flat surfaces are thermodynamically favorable. The Wenzel model approximation holds up for the rough aggregate surface interface systems. The interfacial adhesive energy and interfacial debonding energy are enhanced geometrically by the roughness factor r, which indicates that the textured aggregate surface is in favor of force-induced interfacial cracking resistance but shows an adverse effect to moisture damage resistance. The findings from the current study provide guidelines for materials design in pavement engineering.

Friction between soft contacts at nanoscale on uncoated and protein-coated surfaces

The understanding of friction on soft sliding biological surfaces at the nanoscale is poorly understood as hard interfaces are frequently used as model systems. Herein, we studied the influence of elastic modulus on the frictional properties of model surfaces at the nanoscale for the first time. We prepared model silicone-based elastomer surfaces with tuneable modulus ranging from hundreds of kPa to a few MPa, similar to those found in real biological surfaces, and employed atomic force microscopy to characterize their modulus, adhesion, and surface morphology. Consequently, we used friction force microscopy to investigate nanoscale friction in hard-soft and soft-soft contacts using spherical colloidal probes covered by adsorbed protein films. Unprecedented results from this study reveal that modulus of a surface can have a significant impact on the frictional properties of protein-coated surfaces with higher deformability leading to lower contact pressure and, consequently, decreased friction. These important results pave the way forward for designing new functional surfaces for serving as models of appropriate deformability to replicate the mechanical properties of the biological structures and processes for accurate friction measurements at nanoscale.

Viscoelastic and Poroelastic Relaxations of Soft Solid Surfaces

Understanding surface mechanics of soft solids, such as soft polymeric gels, is crucial in many engineering processes, such as dynamic wetting and adhesive failure. In these situations, a combination of capillary and elastic forces drives the motion, which is balanced by dissipative mechanisms to determine the rate. While shear rheology (i.e., viscoelasticity) has long been assumed to dominate the dissipation, recent works have suggested that compressibility effects (i.e., poroelasticity) could play roles in swollen networks. We use fast interferometric imaging to quantify the relaxation of surface deformations due to a displaced contact line. By systematically measuring the profiles at different time and length scales, we experimentally observe a crossover from viscoelastic to poroelastic surface relaxations.

Capillary-driven indentation of a microparticle into a soft, oil-coated substrate

Small scale contact between a soft, liquid-coated layer and a stiff surface is common in many situations, from synovial fluid on articular cartilage to adhesives in humid environments. Moreover, many model studies on soft adhesive contacts are conducted with soft silicone elastomers, which possess uncrosslinked liquid molecules (i.e. silicone oil) when the modulus is low. We investigate how the thickness of a silicone oil layer on a soft substrate relates to the indentation depth of glass microspheres in contact with crosslinked PDMS, which have a modulus of <10 kPa. The particles indent into the underlying substrate more as a function of decreasing oil layer thickness. This is due to the presence of the liquid layer at the surface that causes capillary forces to pull down on the particle. A simple model that balances the capillary force of the oil layer and the minimal particle-substrate adhesion with the elastic and surface tension forces from the substrate is proposed to predict the particle indentation depth.

Spreading on viscoelastic solids: are contact angles selected by Neumann's law?

The spreading of liquid drops on soft substrates is extremely slow, owing to strong viscoelastic dissipation inside the solid. A detailed understanding of the spreading dynamics has remained elusive, partly owing to the difficulty in quantifying the strong viscoelastic deformations below the contact line that determine the shape of moving wetting ridges. Here we present direct experimental visualisations of the dynamic wetting ridge using shadowgraphic imaging, complemented with measurements of the liquid contact angle. It is observed that the wetting ridge exhibits a rotation that follows exactly the dynamic liquid contact angle - as was previously hypothesized [Karpitschka et al., Nat. Commun., 2015, 6, 7891]. This experimentally proves that, despite the contact line motion, the wetting ridge is still governed by Neumann's law. Furthermore, our experiments suggest that moving contact lines lead to a variable surface tension of the substrate. We therefore set up a new theory that incorporates the influence of surface strain, for the first time including the so-called Shuttleworth effect into the dynamical theory for soft wetting. It includes a detailed analysis of the boundary conditions at the contact line, complemented by a dissipation analysis, which shows, again, the validity of Neumann's balance.

Inherent forms and the evolution of evolution

John Bonner presented a provocative conjecture that the means by which organisms evolve has itself evolved. The elements of his postulated nonuniformitarianism in the essay under discussion-the emergence of sex, the enhanced selection pressures on larger multicellular forms-center on a presumed close mapping of genotypic to phenotypic change. A different view emerges from delving into earlier work of Bonner's in which he proposed the concept of "neutral phenotypes" and "neutral morphologies" allied to D'Arcy Thompson's analysis of physical determinants of form and studied the conditional elicitation of intrinsic organizational properties of cell aggregates in social amoebae. By comparing the shared and disparate mechanistic bases of morphogenesis and developmental outcomes in the embryos of metazoans (animals), closely related nonmetazoan holozoans, more distantly related dictyostelids, and very distantly related volvocine algae, I conclude, in agreement with Bonner's earlier proposals, that understanding the evolution of multicellular evolution requires knowledge of the inherent forms of diversifying lineages, and that the relevant causative factors extend beyond genes and adaptation to the physics of materials.

Inherency of Form and Function in Animal Development and Evolution

I discuss recent work on the origins of morphology and cell-type diversification in Metazoa – collectively the animals – and propose a scenario for how these two properties became integrated, with the help of a third set of processes, cellular pattern formation, into the developmental programs seen in present-day metazoans. Inherent propensities to generate familiar forms and cell types, in essence a parts kit for the animals, are exhibited by present-day organisms and were likely more prominent in primitive ones. The structural motifs of animal bodies and organs, e.g., multilayered, hollow, elongated and segmented tissues, internal and external appendages, branched tubes, and modular endoskeletons, can be accounted for by the properties of mesoscale masses of metazoan cells. These material properties, in turn, resulted from the recruitment of “generic” physical forces and mechanisms – adhesion, contraction, polarity, chemical oscillation, diffusion – by toolkit molecules that were partly conserved from unicellular holozoan antecedents and partly novel, distributed in the different metazoan phyla in a fashion correlated with morphological complexity. The specialized functions of the terminally differentiated cell types in animals, e.g., contraction, excitability, barrier function, detoxification, excretion, were already present in ancestral unicellular organisms. These functions were implemented in metazoan differentiation in some cases using the same transcription factors as in single-celled ancestors, although controlled by regulatory mechanisms that were hybrids between earlier-evolved processes and regulatory innovations, such as enhancers. Cellular pattern formation, mediated by released morphogens interacting with biochemically responsive and excitable tissues, drew on inherent self-organizing processes in proto-metazoans to transform clusters of holozoan cells into animal embryos and organs.

Effects of strain-dependent surface stress on the adhesive contact of a rigid sphere to a compliant substrate

Recent experiments have reported that the surface stress of soft elastic solids can increase rapidly with surface strain. For example, when a small hard sphere in adhesive contact with a soft silicone gel is slowly retracted from its rest position, it was found that the retraction force versus displacement relation cannot be explained either by the Johnson-Kendall-Roberts (JKR) theory or a recent indentation theory based on an isotropic surface stress that is independent of surface strain. In this paper, we address this problem using a finite element method to simulate the retraction process. Our numerical model does not have the restrictions of the aforementioned theories; that is, it can handle large nonlinear elastic deformation as well as a surface-strain-dependent surface stress. Our simulation is in good agreement with experimental force versus displacement data with no fitting parameters. Therefore, our results lend further support to the claim that significant strain-dependent surface stresses can occur in simple soft elastic gels. However, significant challenges remain in the reconciliation of theory and experiments, particularly regarding the geometry of the contact and substrate deformation.

Singular dynamics in the failure of soft adhesive contacts

We characterize the mechanical recovery of compliant silicone gels following adhesive contact failure. We establish broad, stable adhesive contacts between rigid microspheres and soft gels, then stretch the gels to large deformations by pulling quasi-statically on the contact. Eventually, the adhesive contact begins to fail, and ultimately slides to a final contact point on the bottom of the sphere. Immediately after detachment, the gel recoils quickly with a self-similar surface profile that evolves as a power law in time, suggesting that the adhesive detachment point is singular. The singular dynamics we observe are consistent with a relaxation process driven by surface stress and slowed by viscous flow through the porous, elastic network of the gel. Our results emphasize the importance of accounting for both the liquid and solid phases of gels in understanding their mechanics, especially under extreme deformation.

Extraction of Silicone Uncrosslinked Chains at Air-Water-Polydimethylsiloxane Triple Lines

Silicone elastomers such as polydimethylsiloxane (PDMS) are convenient materials routinely used in laboratories that combine ease of preparation, flexibility, transparency, and gas permeability. However, these elastomers are known to contain a small fraction of uncrosslinked low-molecular-weight oligomers, the effects of which are not completely understood, particularly when used in contact with liquids. Here, we show that triple lines involving air, water, and PDMS elastomers are responsible for the contamination of water-air interfaces by uncrosslinked silicone oligomers through a capillarity-induced extraction mechanism. We investigate both the case of static and moving contact lines and study various geometries ranging from partially immersed PDMS plates to water droplets or air bubbles deposited on PDMS plates, all involving air-water-elastomer triple lines. We demonstrate experimentally that the contamination timescale is strikingly shorter for moving contact lines than in the static case. Eventually, we propose a simple poroelastic model capturing the main features of contamination observed in experiments.

3D patient-specific numerical modeling of the soft palate considering adhesion from the tongue

Collapse of the soft palate in the upper airway contributes to obstructive sleeping apnea (OSA). In this study, we investigate the influence of the adhesion from the tongue on the soft palate global response. This is achieved using a cohesive zone finite element approach. A traction-separation law is determined to describe the adhesion effect from the surface tension of the lining liquid between the soft palate and the tongue. According to pull-off experimental tests of human lining liquid from the oral surface of the soft palate, the corresponding cohesive properties, including the critical normal traction stress and the failure separation displacement, are obtained. The 3D patient-specific soft palate geometry is accounted for, based on one specific patient's computed tomography (CT) images. The calculation results show that influence of the adhesion from the tongue surface on the global response of the soft palate depends on the length ratio between the cohesive length and the soft palate length. When the length of the cohesive zone is smaller than half of the soft palate length, the adhesion's influence is negligible. When the adhesion length is larger than 70 percent of soft palate length, the adhesion force contributes to preventing the soft palate from collapsing towards to the pharynx wall, i.e. the closing pressure is more negative than in the no adhesion case. These results may provide useful information to the clinical treatment of OSA patients.

The contact mechanics challenge: tribology meets soft matter

In the fall of 2015, Martin Müser suggested a Contact Mechanics Challenge for the Tribology community. The challenge was an ambitious effort to compare a wide variety of theoretical and computational contact-mechanics approaches, and involved researchers voluntarily tackling the same hypothetical contact problem. The result is an impressive collection of innovative approaches - including a surprise experimental effort - that highlight the continuing importance of surface contact mechanics and the challenges of solving these large-scale problems. Here, we describe how the Contact Mechanics Challenge also reveals exciting opportunities for the Soft Matter community to engage intensely with classical and emerging problems in tribology, surface science, and contact mechanics.

The mechanical equilibrium of soft solids with surface elasticity

Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the appropriate boundary condition, showing that it simplifies significantly in certain cases. We show that surface elasticity's main role is to stiffen a solid surface's response to in-plane tractions, in particular at length-scales smaller than a characteristic elastocapillary length. We also investigate how surface elasticity affects the Green's-function problem of a line force on a flat, incompressible, linear-elastic substrate. There are significant changes to this solution, especially in that the well-known displacement singularity is regularised. This raises interesting implications for soft phenomena like wetting contact lines, adhesion and friction. Finally, we discuss open questions, future directions, and close ties with existing fields of research.

Contact mechanics for polydimethylsiloxane: from liquid to solid

Adhesion between a glass ball and a polydimethylsiloxane (PDMS) sample is dependent on the PDMS cross-link density, and the transformation of the material from the uncrosslinked liquid state to the fully crosslinked solid state is investigated in this study. The physical picture reflected a gradual transition from capillary forces driven contact mechanics to the classical Johnson-Kendall-Roberts (JKR)-type contact mechanics. PDMS was produced by mixing the base fluid and a cross-linker at a ratio of 10 : 1 and allowed to slowly cross-link at room temperature with simultaneous measurement of the ball-PDMS interaction force. The PDMS sample was in the liquid state during the first ≈16 hours, and in this case the ball-PDMS interaction was purely adhesive, i.e., no repulsive interaction was observed. Later at the PDMS gel-point the cross-linked PDMS clusters percolate, converting the fluid into a soft (fluid-filled) poroelastic solid. In the transition period, PDMS appears similar to pressure-sensitive adhesives. There we observe so-called "stringing" and permanent deformation of the material impacted by the ball. At room temperature, it takes more than ∼100 hours for PDMS to fully cross-link that can be confirmed by the comparison with the earlier-studied reference PDMS produced at elevated temperatures.

Growth and relaxation of a ridge on a soft poroelastic substrate

Elastocapillarity describes the deformations of soft materials by surface tensions and is involved in a broad range of applications, from microelectromechanical devices to cell patterning on soft surfaces. Although the vast majority of elastocapillarity experiments are performed on soft gels, because of their tunable mechanical properties, the theoretical interpretation of these data has been so far undertaken solely within the framework of linear elasticity, neglecting the porous nature of gels. We investigate in this work the deformation of a thick poroelastic layer with surface tension subjected to an arbitrary distribution of time-dependent axisymmetric surface forces. Following the derivation of a general analytical solution, we then focus on the specific problem of a liquid drop sitting on a soft poroelastic substrate. We investigate how the deformation and the solvent concentration field evolve in time for various droplet sizes. In particular, we show that the ridge height beneath the triple line grows logarithmically in time as the liquid migrates toward the ridge. We then study the relaxation of the ridge following the removal of the drop and show that the drop leaves long-lived footprints after removal which may affect surface and wetting properties of gel layers and also the motion of living cells on soft materials. Preliminary experiments performed with water droplets on soft PDMS gel layers are in excellent agreement with the theoretical predictions.

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 surface stresses can play a dominant role in solid mechanics at larger length scales than previously anticipated.Solid surface stress is a fundamental property of solid interfaces. Here authors measure the solid surface stress of a gel, and show its dependence on surface strain through a surface modulus.

Analyzing the Molecular Kinetics of Water Spreading on Hydrophobic Surfaces via Molecular Dynamics Simulation

In this paper, we report molecular kinetic analyses of water spreading on hydrophobic surfaces via molecular dynamics simulation. The hydrophobic surfaces are composed of amorphous polytetrafluoroethylene (PTFE) with a static contact angle of ~112.4° for water. On the basis of the molecular kinetic theory (MKT), the influences of both viscous damping and solid-liquid retarding were analyzed in evaluating contact line friction, which characterizes the frictional force on the contact line. The unit displacement length on PTFE was estimated to be ~0.621 nm and is ~4 times as long as the bond length of C-C backbone. The static friction coefficient was found to be ~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{-3}$$\end{document}10−3 Pa·s, which is on the same order of magnitude as the dynamic viscosity of water, and increases with the droplet size. A nondimensional number defined by the ratio of the standard deviation of wetting velocity to the characteristic wetting velocity was put forward to signify the strength of the inherent contact line fluctuation and unveil the mechanism of enhanced energy dissipation in nanoscale, whereas such effect would become insignificant in macroscale. Moreover, regarding a liquid droplet on hydrophobic or superhydrophobic surfaces, an approximate solution to the base radius development was derived by an asymptotic expansion approach.