Bowtie-Shaped Deformation Isotherm of Superhydrophobic Cylindrical Mesopores.

Deformation of superhydrophobic cylindrical mesopores is studied during a cycle of forced water filling and spontaneous drying by in situ small-angle neutron scattering. A high-pressure setup is put forward to characterize the deformation of ordered mesoporous silanized silica up to 80 MPa. Strain isotherms of individual pores are deduced from the shift of the Bragg spectrum associated with the deformation of the hexagonal pore lattice. Due to their superhydrophobic nature, pore walls are not covered with a prewetting film. This peculiarity gives the ability to use a simple mechanical model to describe both filled and empty pore states without the pitfall of disjoining pressure effects. By fitting our experimental data with this model, we measure both the Young's modulus and the Poisson ratio of the nanometric silica wall. The measurement of this latter parameter constitutes a specificity offered by superhydrophobic nanopores with respect to hydrophilic ones.

State and Rate Dependent Contact Line Dynamics over an Aging Soft Surface.

We report direct atomic-force-microscope measurements of capillary force hysteresis (CFH) of a circular contact line (CL) formed on a long glass fiber, which is coated with a thin layer of soft polymer film and intersects a water-air interface. The measured CFH shows a distinct overshoot for the depinning of a static CL, and the overshoot amplitude grows logarithmically with both the hold time τ and fiber speed V. A unified model based on the slow growth of a wetting ridge and force-assisted barrier crossing is developed to explain the observed time (or state) and speed (or rate) dependent CL depinning dynamics over an aging soft surface. The experimental findings have important implications to a common class of problems involving depinning dynamics in a defect or roughness landscape, such as friction of solid interfaces.

Large slippage and depletion layer at the polyelectrolyte/solid interface.

The slippage of polymer solutions on solid surfaces is often attributed to a depletion layer whose origin, thickness, and interaction with the flow are poorly understood. Using a Dynamic Surface Force Apparatus we report a structural and nanorheological study of the interface between hydrolyzed poly-acrylamide solutions and platinum surfaces. Polyelectrolyte chains adsorb on the surfaces in a thin charged layer, acting as a nonattractive wall for the bulk solution. We investigate the flow of the visco-elastic solution on the adsorbed layer from the nanometer to 10 micrometers, bridging microscopic to macroscopic properties. At distances larger than 200 nanometers, the flow is well described by an apparent slip boundary condition. At smaller distance the apparent slip is found to decrease with the gap. In contrast to the apparent slip model, we show that a 2-fluids model taking into account the finite thickness of depletion layers at the non-attractive wall describes accurately the dynamic forces over 4 spatial decades of confinement. Depletion layers are found to be an equilibrium property of the interface, independent on the flow and on the confinement. Their thickness is phenomenologically described by ξ + 2lD with ξ the correlation length of the semi-dilute solutions and lD the Debye length. We interpret this result in terms of screened repulsion between the charged adsorbed layer and the bulk polyions.

A Direct Sensor to Measure Minute Liquid Flow Rates.

Nanofluidics finds its root in the study of fluids and flows at the nanoscale. Flow rate is a quantity that is both central when dealing with flows and notoriously difficult to measure experimentally at the scale of an individual nanopore or nanochannel. We show in this letter that minute flow rate can be directly measured accumulating liquid over time within the compliant membrane of a commercial piezoresistive pressure sensor. Our flow rate sensor is versatile and can be operated independently of the nature of the liquid, flow profile, and type of nanochannel. We demonstrate this method by measuring the pressure-driven flow of silicon oil in a single nanochannel of average radius 200 nm. This approach gives reliable measurement of the flow rate up to 1 pL/min. Unlike other nanoscale flow measurements methods based, for instance, on particle tracking, our sensor delivers a direct voltage output suitable for nanoflow control applications.

Viscocapillary Response of Gas Bubbles Probed by Thermal Noise Atomic Force Measurement.

We present thermal noise measurements of a vibrating sphere close to microsized air bubbles in water with an atomic force microscope. The sphere was glued at the end of a cantilever with a resonance frequency of few kHz. The subangstrom thermal motion of the microsphere reveals an elastohydrodynamic coupling between the sphere and the air bubble. The results are in perfect agreement with a model incorporating macroscopic capillarity and fluid flow on the bubble surface with full slip boundary conditions.

Nano-mechanics of ionic liquids at dielectric and metallic interfaces.

Using a dynamic surface force apparatus, we investigate the nano-mechanics and the nano-rheology of an ionic liquid at dielectric and metallic solid surfaces. On smooth dielectric Pyrex surfaces, we find an ordered interfacial phase extending over less than 3 nm away from the top of the layer, with a compression modulus of 15 MPa extracted from the profile of the oscillatory forces. We discuss the boundary flow of the Newtonian bulk phase on this ordered interfacial layer. On metallic platinum surfaces, our hydrodynamic measurements evidence an interfacial soft solid layer extending up to 20 nm away from the top of the layer. The elastic modulus of this interfacial layer, derived from elasto-hydrodynamic measurements, is similar to the one found on Pyrex surfaces. Both on the dielectric and on the metal surfaces, the thickness of the interfacial phases is not found to change upon approach of the opposite surface, and does not exhibit a capillary-freezing transition.

Noncontact Viscoelastic Measurement of Polymer Thin Films in a Liquid Medium Using Long-Needle Atomic Force Microscopy.

We report the noncontact measurement of the viscoelastic property of polymer thin films in a liquid medium using frequency-modulation atomic force microscopy with a newly developed long-needle probe. The probe contains a long vertical glass fiber with one end adhered to a cantilever beam and the other end with a sharp tip placed near the liquid-film interface. The nanoscale flow generated by the resonant oscillation of the needle tip provides a precise hydrodynamic force acting on the soft surface of the thin film. By accurately measuring the mechanical response of the thin film, we obtain the elastic and loss moduli of the thin film using the linear response theory of elastohydrodynamics. The experiment verifies the theory and demonstrates its applications. The technique can be used to accurately measure the viscoelastic property of soft surfaces, such as those made of polymers, nanobubbles, live cells, and tissues.

A micro-nano-rheometer for the mechanics of soft matter at interfaces.

We present a nano-rheometer based on the dynamic drainage flow between a sphere and a plane from bulk regime to highly confined regime. The instrument gives absolute measurements of the viscosity of simple liquids in both regimes. For complex fluids, the measurements involve the viscosity and the elastic modulus. The device operates on distances ranging over four orders of magnitude from 1 nm to 10 µm, bridging rheological properties from the macroscopic to the molecular scale. This allows to measure an hydrodynamic or visco-elastic boundary condition and to explore the causes of the boundary condition at the microscopic level.

Simultaneous observation of asymmetric speed-dependent capillary force hysteresis and slow relaxation of a suddenly stopped moving contact line.

We report direct atomic-force-microscope measurements of capillary force hysteresis (CFH) and relaxation of a circular moving contact line (CL) formed on a long micron-sized hydrophobic fiber intersecting a liquid-air interface. By using eight different liquid interfaces with varying solid-liquid molecular interactions, we find a universal behavior of the asymmetric speed dependence of CFH and CL relaxation. A unified model based on force-assisted barrier crossing is used to connect the mesoscopic measurements of CFH and CL relaxation with the energy barrier height E_{b} and size λ associated with the surface defects. The experiment demonstrates that the CL pinning (relaxation) and depinning dynamics are closely related and can be described by a common microscopic framework.

Asymmetric and Speed-Dependent Capillary Force Hysteresis and Relaxation of a Suddenly Stopped Moving Contact Line.

We report on direct atomic-force-microscope measurements of capillary force hysteresis (CFH) and relaxation of a circular moving contact line (CL) formed on a long micron-sized hydrophobic fiber intersecting a water-air interface. The measured CFH and CL relaxation show a strong asymmetric speed dependence in the advancing and receding directions. A unified model based on force-assisted barrier crossing is utilized to find the underlying energy barrier Eb and size λ associated with the defects on the fiber surface. The experiment demonstrates that the pinning (relaxation) and depinning dynamics of the CL can be described by a common microscopic framework, and the advancing and receding CLs are influenced by two different sets of relatively wetting and nonwetting defects on the fiber surface.

Giant Osmotic Pressure in the Forced Wetting of Hydrophobic Nanopores.

The forced intrusion of water in hydrophobic nanoporous pulverulent material is of interest for quick storage of energy. With nanometric pores the energy storage capacity is controlled by interfacial phenomena. With subnanometric pores, we demonstrate that a breakdown occurs with the emergence of molecular exclusion as a leading contribution. This bulk exclusion effect leads to an osmotic contribution to the pressure that can reach levels never previously sustained. We illustrate, on various electrolytes and different microporous materials, that a simple osmotic pressure law accounts quantitatively for the enhancement of the intrusion and extrusion pressures governing the forced wetting and spontaneous drying of the nanopores. Using electrolyte solutions, energy storage and power capacities can be widely enhanced.

Effect of surface elasticity on the rheology of nanometric liquids.

The rheological properties of liquids confined to nanometer scales are important in many physical situations. In this Letter, we demonstrate that the long-range elastic deformation of the confining surfaces must be taken into account when considering the rheology of nanometric liquids. In the case of a squeeze-flow geometry, we show that below a critical distance D(c), the liquid is clamped by its viscosity and its intrinsic properties cannot be disentangled from the global system response. Using nanorheology experiments, we demonstrate that picometer elastic deflections of the rigid confining surfaces dominate the overall mechanical response of nanometric liquids confined between solid walls.

Capacitive detection of buried interfaces by a dynamic surface force apparatus.

We present here a new type of distance sensor mounted on a Surface Force Apparatus (SFA), able to detect the position of a buried interface and therefore the thickness of a thin solid or soft matter film coating the SFA surface(s). This sensor relies on the capacitance created by the two metallized surfaces of the SFA. An harmonic oscillation of these polarized surfaces creates a pico- to femto-amps current indicating their relative position. One of the specificities of this sensor is the relatively weak polarization used for the measurements, minimizing the electrical forces and their impact on other interactions, hydrodynamical and mechanical forces measured by the SFA. This original and simple design is of high interest for studying the viscoelastic properties of thin films, to detect adsorbed liquid layers or slippage at liquid-solid interfaces, or even to study complex fluids such as ionic liquids under polarization. We demonstrate the use of this sensor to study the flow boundary condition of silicon oil on a metal surface, and the elastic modulus of a thin elastomer layer.

Nanofluidic osmotic diodes: theory and molecular dynamics simulations.

Osmosis describes the flow of water across semipermeable membranes powered by the chemical free energy extracted from salinity gradients. While osmosis can be expressed in simple terms via the van 't Hoff ideal gas formula for the osmotic pressure, it is a complex phenomenon taking its roots in the subtle interactions occurring at the scale of the membrane nanopores. Here we use new opportunities offered by nanofluidic systems to create an osmotic diode exhibiting asymmetric water flow under reversal of osmotic driving. We show that a surface charge asymmetry built on a nanochannel surface leads to nonlinear couplings between water flow and the ion dynamics, which are capable of water flow rectification. This phenomenon opens new opportunities for water purification and complex flow control in nanochannels.

Activated drying in hydrophobic nanopores and the line tension of water.

We study the slow dynamics of water evaporation out of hydrophobic cavities by using model porous silica materials grafted with octylsilanes. The cylindrical pores are monodisperse, with a radius in the range of 1-2 nm. Liquid water penetrates in the nanopores at high pressure and empties the pores when the pressure is lowered. The drying pressure exhibits a logarithmic growth as a function of the driving rate over more than three decades, showing the thermally activated nucleation of vapor bubbles. We find that the slow dynamics and the critical volume of the vapor nucleus are quantitatively described by the classical theory of capillarity without adjustable parameter. However, classical capillarity utterly overestimates the critical bubble energy. We discuss the possible influence of surface heterogeneities, long-range interactions, and high-curvature effects, and we show that a classical theory can describe vapor nucleation provided that a negative line tension is taken into account. The drying pressure then provides a determination of this line tension with much higher precision than currently available methods. We find consistent values of the order of -30 pN in a variety of hydrophobic materials.

New device to measure dynamic intrusion/extrusion cycles of lyophobic heterogeneous systems.

Lyophobic heterogeneous systems (LHS) are made of mesoporous materials immersed in a non-wetting liquid. One application of LHS is the nonlinear damping of high frequency vibrations. The behaviour of LHS is characterized by P - ΔV cycles, where P is the pressure applied to the system, and ΔV its volume change due to the intrusion of the liquid into the pores of the material, or its extrusion out of the pores. Very few dynamic studies of LHS have been performed until now. We describe here a new apparatus that allows us to carry out dynamic intrusion/extrusion cycles with various liquid/porous material systems, controlling the temperature from ambient to 120 °C and the frequency from 0.01 to 20 Hz. We show that for two LHS: water/MTS and Galinstan/CPG, the energy dissipated during one cycle depends very weakly on the cycle frequency, in strong contrast to conventional dampers.

Hydrodynamic interaction between a spherical particle and an elastic surface: a gentle probe for soft thin Films.

We study the hydrodynamic interaction between a sphere and an elastic surface at a nanoscale with a dynamic surface force apparatus. We show that the interplay between viscous forces and elastic deformations leads to very rich scaling properties of the force response, providing a unique signature of the surface elastic behavior. These properties are illustrated on three different examples: a thick elastomer, a thin elastomer film, and a layer of micrometric bubbles. We show that this fluid probing allows one to measure the Young's modulus of surfaces and soft thin layers at distance, without any direct solid-solid contact.

Capillary force between wetted nanometric contacts and its application to atomic force microscopy.

We extend to the case of perfect wetting the exact calculation of Orr et al. (J. Fluid. Mech. 1975, 67, 723) for a pendular ring connecting two dry surfaces. We derive an approximate analytical expression for the capillary force between two highly curved surfaces covered by a wetting liquid film. The domain of validity of this expression is assessed and extended by a custom-made numerical simulation based on the full exact mathematical description. In the case of attractive liquid-solid van der Waals interactions, the capillary force increases monotonically with decreasing vapor pressure up to several times its saturation value. This accurate description of the capillary force makes it possible to estimate the adhesion force between wet nanoparticles; it can also be used to quantitatively interpret pull-off forces measured by atomic force microscopy.

Amplification of electro-osmotic flows by wall slippage: direct measurements on OTS-surfaces.

The control of water flow in Electrostatic Double Layers (EDL) close to charged surfaces in solution is an important issue with the emergence of nanofluidic devices. We compare here the zeta potential governing the electrokinetic transport properties of surfaces, to the electrostatic potential directly measured from their interaction forces. We show that on smooth hydrophilic silica these quantities are similar, whereas on OTS-silanized hydrophobic surfaces the zeta potential is significantly higher, leading to an enhanced electro-osmotic velocity. The enhancement obtained is consistent with an interfacial water slippage on the silanized surface, characterized by a constant slip length of approximately 8 nm independent of the salt concentration in the range 10(-4)-10(-3)M.

Nanofluidics, from bulk to interfaces.

Nanofluidics has emerged recently in the footsteps of microfluidics, following the quest for scale reduction inherent to nanotechnologies. By definition, nanofluidics explores transport phenomena of fluids at nanometer scales. Why is the nanometer scale specific? What fluid properties are probed at nanometric scales? In other words, why does 'nanofluidics' deserve its own brand name? In this critical review, we will explore the vast manifold of length scales emerging for fluid behavior at the nanoscale, as well as the associated mechanisms and corresponding applications. We will in particular explore the interplay between bulk and interface phenomena. The limit of validity of the continuum approaches will be discussed, as well as the numerous surface induced effects occurring at these scales, from hydrodynamic slippage to the various electro-kinetic phenomena originating from the couplings between hydrodynamics and electrostatics. An enlightening analogy between ion transport in nanochannels and transport in doped semi-conductors will be discussed (156 references).