Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale

Observation of Brownian elastohydrodynamic forces acting on confined soft colloids

Confined motions in complex environments are ubiquitous in microbiology. These situations invariably involve the intricate coupling between fluid flow, soft boundaries, surface forces, and fluctuations. In the present study, such a coupling is investigated using a method combining holographic microscopy and advanced statistical inference. Specifically, the Brownian motion of soft micrometric oil droplets near rigid walls is quantitatively analyzed. All the key statistical observables are reconstructed with high precision, allowing for nanoscale resolution of local mobilities and femtonewton inference of conservative or nonconservative forces. Strikingly, the analysis reveals the existence of a novel, transient, but large, soft Brownian force. The latter might be of crucial importance for microbiological and nanophysical transport, target finding, or chemical reactions in crowded environments, and hence the whole life machinery.

Polymer time crystal: Mechanical activation of reversible bonds by low-amplitude high frequency excitations

Reversible supramolecular bonds play an important role in materials science and in biological systems. The equilibrium between open and closed bonds and the association rate can be controlled thermally, chemically, by mechanical pulling, by ultrasound, or by catalysts. In practice, these intrinsic equilibrium methods either suffer from a limited range of tunability or may damage the material. Here, we present a nonequilibrium strategy that exploits the dissipative properties of the system to control and change the dynamic properties of sacrificial and reversible networks. We show theoretically and numerically how high-frequency mechanical oscillations of very low amplitude can open or close bonds. This mechanism indicates how reversible bonds could alleviate mechanical fatigue of materials especially at low temperatures where they are fragile. In another area, it suggests that the system can be actively modified by the application of ultrasound to induce gel-fluid transitions and to activate or deactivate adhesion properties.

Lift at low Reynolds number

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Effect of fluid viscoelasticity, shear stress, and interface tension on the lift force in lubricated contacts

We consider a cylinder immersed in viscous fluid moving near a flat substrate covered by an incompressible viscoelastic fluid layer, and study the effect of the fluid viscoelasticity on the lift force exerted on the cylinder. The lift force is zero when the viscoelastic layer is not deformed, but becomes non-zero when it is deformed. We calculate the lift force by considering both the tangential stress and the normal stress applied at the surface of the viscoelastic layer. Our analysis indicates that as the layer changes from the elastic limit to the viscous limit, the lift force decreases with the decrease of the Deborah number (De). For small De, the effect of the layer elasticity is taken over by the surface tension and the lift force can become negative. We also show that the tangential stress and the interface slip velocity (the surface velocity relative to the substrate), which have been ignored in the previous analysis, give important contributions to the lift force. Especially for thin elastic layers, they give dominant contributions to the lift force.

Interface Stabilization in Adhesion Caused by Elastohydrodynamic Deformation

Interfacial instabilities are common phenomena observed during adhesion measurements involving viscoelastic polymers or fluids. Typical probe-tack adhesion measurements with soft adhesives are conducted with rigid probes. However, in many settings, such as for medical applications, adhesives make and break contact from soft surfaces such as skin. Here we study how detachment from soft probes alters the debonding mechanism of a model viscoelastic polymer film. We demonstrate that detachment from a soft probe suppresses Saffman-Taylor instabilities commonly encountered in adhesion. We suggest the mechanism for interface stabilization is elastohydrodynamic deformation of the probe and propose a scaling for the onset of stabilization.

Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology

When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which further complexifies the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.

Elastohydrodynamic Relaxation of Soft and Deformable Microchannels

Hydrodynamic flows in compliant channels are of great interest in physiology and microfluidics. In these situations, elastohydrodynamic coupling leads to (i) a nonlinear pressure-vs-flow-rate relation, strongly affecting the hydraulic resistance; and (ii), because of the compliance-enabled volume storage, a finite relaxation time under a stepwise change in pressure. This latter effect remains relatively unexplored, even while the timescale can vary over a decade in typical situations. In this study we provide time-resolved measurements of the relaxation dynamics for thin and soft, rectangular microfluidic channels. We describe our data using a perturbative lubrication approximation of the Stokes equation coupled to linear elasticity, while taking into account the effect of compliance and resistance of the entrance. The modeling allows us to completely describe all of the experimental results. Our Letter is relevant for any microfluidic scenario wherein a time-dependent driving is applied and provides a first step in the dynamical description of compliant channel networks.

Rotation-translation coupling of soft objects in lubricated contact

We study the coupling between rotation and translation of a submerged cylinder in lubricated contact with a soft elastic substrate. Using numerical solutions and asymptotic theory, we analyze the elastohydrodynamic problem over the entire range of substrate deformations relative to the thickness of the intervening fluid film. We find a strong coupling between the rotation and translation of the cylinder when the surface deformation of the substrate is comparable to the thickness of the lubricating fluid layer. In the limit of large deformations, we show that the bodies are in near-Hertzian contact and cylinder rolls without slip, reminiscent of dry frictional contact. When the surface deformation is small relative to the separation between the surfaces, the coupling persists but is weaker, and the rotation rate scales with the translation speed to the one-third power. We then show how the external application of a torque modifies these behaviors by generating different combinations of rotational and translational motions, including back-spinning and top-spinning states. We demonstrate that these behaviors are robust regardless of whether the elastic substrate is thick or thin relative to the length scales of the flow.

Regimes of Soft Lubrication

Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered systems. Hence it is of particular interest to relate the thickness of the lubricant layer to the entrainment (sliding/rolling) velocity, the mechanical loading exerted onto the contacting elements, and properties of the elastic boundary. In this work we provide an overview of the various regimes of soft lubrication for two-dimensional cylinders in lubricated contact with compliant walls. We discuss the limits of small and large entrainment velocity, which is equivalent to large and small elastic deformations, as the cylinder moves near thick or thin elastic layers. The analysis focusses on thin elastic coatings, both compressible and incompressible, for which analytical scaling laws are not yet available in the regime of large deformations. By analysing the elastohydrodynamic boundary layers that appear at the edge of the contact, we establish the missing scaling laws - including prefactors. As such, we offer a rather complete overview of physically relevant limits of soft lubrication.

Validity of Winkler's mattress model for thin elastomeric layers: beyond Poisson's ratio

Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point-indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness, which itself depends on the problem under consideration.

Rotation of a submerged finite cylinder moving down a soft incline

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.