Academic literature on the topic 'Elasto-Capillary length'

For a broad class of soft materials their surface stress can strongly influence mechanical behaviour. For example, a line force applied to the surface of an elastic substrate is locally supported by surface stress over an elasto-capillary length l c (surface stress/elastic modulus). Surface stress regularizes the otherwise highly singular stress and strain fields. However, surface such as lipid bilayer interfaces can also resist deformation by bending. This has not been studied either by experiments or theories. We analyse a theoretical model of the response of a half-space to a line force when the surface carries both a stress and resistance to bending. We find that surface bending further regularizes the singular fields. The local stress field near the line load can be separated into three regions. Region 1 occupies distances from the line load smaller than an elasto-capillary bending length l b (bending stiffness/elastic modulus to the 1/3 power) where surface bending dominates and the elastic stress and strains are continuous. Region 2 occupies intermediate distances between l b and l c ( > l b ) where surface stress dominates. At distances larger than l c we retrieve the classical elasticity solution. The size of region 2 depends on κ = l c / l b and vanishes for small l c .

The motility mechanism of certain prokaryotes has long been a mystery, since their motion, known as gliding, involves no external appendages. The physical principles behind gliding still remain poorly understood. Using myxobacteria as an example of such organisms, we identify here the physical principles behind gliding motility and develop a theoretical model that predicts a 2-regime behavior of the gliding speed as a function of the substrate stiffness. Our theory describes the elasto-capillary–hydrodynamic interactions between the membrane of the bacteria, the slime it secretes, and the soft substrate underneath. Defining gliding as the horizontal translation under zero net force, we find the 2-regime behavior is due to 2 distinct mechanisms of motility thrust. On mildly soft substrates, the thrust arises from bacterial shape deformations creating a flow of slime that exerts a pressure along the bacterial length. This pressure in conjunction with the bacterial shape provides the necessary thrust for propulsion. On very soft substrates, however, we show that capillary effects must be considered that lead to the formation of a ridge at the slime–substrate–air interface, thereby creating a thrust in the form of a localized pressure gradient at the bacterial leading edge. To test our theory, we perform experiments with isolated cells on agar substrates of varying stiffness and find the measured gliding speeds in good agreement with the predictions from our elasto-capillary–hydrodynamic model. The mechanisms reported here serve as an important step toward an accurate theory of friction and substrate-mediated interactions between bacteria proliferating in soft media.

The equilibrium configuration of a liquid drop on a solid is determined by local energy balance. For a very stiff substrate, energy balance is represented by Young's equation. The equilibrium configuration near a line separating three fluids, in contrast, is determined by a balance of forces—their surface tensions—which is represented graphically by Neumann's triangle. We argue that these two are limiting cases of the more general situation of a drop on an elastic substrate in which both configurational energy balance and force balance must be satisfied independently. By analysing deformation close to the contact line of a liquid drop on an elastic substrate, we show that the transition from the surface tension-dominated regime to the elasticity-dominated regime is controlled by a dimensionless parameter: the ratio of an elasto-capillary length to the characteristic length scale over which surface tension acts. Because of the influence of substrate elasticity, the contact angle is not necessarily given by Young's equation. For compliant solids, we show that the local deformation and stress fields near the contact line are governed by surface tensions. However, if surface tension happens to be different from surface energy, configurational energy balance may not be consistent with force balance.

We explore air invasion in a dead-end compliant water-filled microchannel containing a constriction. The phenomenon is driven by the pervaporation of the liquid present in the channel through the surrounding medium. The penetration is intermittent, jerky and characterised by a stop-and-go dynamics as the bubble escapes the constriction. We demonstrate that this sequence of arrest and jump of the bubble is due to an elasto-capillary coupling between the air–liquid interface and the elastic medium. When the interface enters the constriction, its curvature increases strongly, leading to a depressurisation within the liquid-filled channel that drives a compression of the channel. As the interface is forced to leave the constriction at a given threshold pressure, due to the ongoing loss of liquid content by pervaporation, the pressure is suddenly released, which gives rise to a rapid propagation of the air bubble away from the constriction, and a restoration of the rest shape of the channel. Combining macroscopic observations and confocal imaging, we present a comprehensive experimental study of this phenomenon. In particular, the effect of the channel geometry on the time of arrest in the constriction and the jump length is investigated. Our novel microfluidic design succeeds in mimicking the role of inter-vessel pits in plants, which transiently stop the propagation of air embolisms during long and severe droughts. It is expected to serve as a building block for further biomimetic studies in more complex leaf-like architectures, in order to recover this universal phenomenon of intermittent propagation reported in real leaves.

Les matériaux ultra-mous présentent des caractéristiques de déformation et de fracture différentes de celles des matériaux mous ordinaires, en raison des effets anticipés de leur tension superficielle et de leur hétérogénéité de structure. Dans ce contexte, nous avons systématiquement étudié les propriétés de fracture d’hydrogels ultra-mous en utilisant des méthodes de ponction et de cavitation. Pour le polyacrylamide, le PDMS et le carraghénane, la résistance à la fracture est dominée par l'élasticité non linéaire au-dessus de l'échelle de longueur élasto-capillaire. En-dessous cette échelle spécifique, la résistance à la fracture augmente puisque la capillarité joue un rôle dans le début de la fracture. En synthétisant des hydrogels de poly(alcool vinylique) (PVA) à faible degré d'hydrolyse à partir de deux voies de percolation (percolation de liens et percolation de site), nous avons découvert que les gels formés par percolation de site, étudiés par diffusion dynamique de la lumière, possèdent une plus forte hétérogénéité de structure et entraînent une plus faible résistance à la fracture. Étonnamment, une cristallisation extrême induite par déformation pendant la ponction a été observée dans l'hydrogel de PVA avec un degré d'hydrolyse élevé. En effet, le réseau de cet hydrogel est renforcé localement autour de la pointe de l'aiguille et déplace le point d'initiation de la fissure de la pointe de l'aiguille vers le bord. Cette structure anisotrope donne lieu à une cavité sphérique irrégulière dans la méthode de cavitation et augmente significativement son énergie de fracture. En outre, nous avons constaté que l’augmentation de la masse moléculaire, l'ajout d'un tensioactif ou le dépôt d'une couche d'huile en surface augmentent chacun la résistance à la fracture de l’hydrogel. Enfin, nous avons mis au point une nouvelle technique optique : l'imagerie par corrélation de photons, qui permet de déterminer quantitativement la distribution des déformations en compression et en tension autour de l'aiguille. Ces nouvelles connaissances et avancées méthodologiques fourniront des informations utiles pour la conception de matériaux souples mais résistants aux fractures, et de robots assistant chirurgicaux dans les applications médicales
Ultra-soft material exhibits different deformation and fracture characteristics compared to common soft material due to anticipated surface tension effects and structural heterogeneity. To this end, we systematically investigated fracture properties of ultra-soft hydrogels using puncture and cavitation methods. For soft polyacrylamide, PDMS, and carrageenan, fracture resistance is dominated by the non-linear elasticity above the elasto-capillary length scale. Below this particular scale, fracture resistance is improved since capillarity must play a role in the onset of fracture. By synthesizing poly(vinyl alcohol) (PVA) hydrogels with low hydrolysis degree from two percolation paths (bond-percolation and site percolation), we discovered that gels formed by site-percolation possess stronger structural heterogeneity studied via dynamic light scattering and thus result in lower fracture resistance. Surprisingly, an extremely large strain-induced crystallization during puncture was discovered in PVA hydrogel with high hydrolysis degree, which locally reinforces the network around the needle tip and displaces the crack initiation point from the needle tip to the edge. This anisotropic structure results in an irregular spherical cavity in the cavitation experiment and largely improves its fracture energy. In addition, we found that increasing the molecular weight, adding surfactant, and placing an oil layer on hydrogel surfaces could each increase their fracture resistance. In the end, we developed a novel optical technique - photon correlation imaging - in which compression and tension strain distribution around the needle is quantitatively revealed. These new insights and methodological advances will provide useful information to design soft but fracture-resistant materials and surgical assistant robots in medical applications