In this critical review we treat the phenomenon of capillarity in nanoscopic confinement, based on application of the Young-Laplace equation. In classical capillarity the curvature of the meniscus is determined by the confining geometry and the macroscopic contact angle. We show that in narrow confinement the influence of the disjoining pressure and the related wetting films have to be considered as they may significantly change the meniscus curvature. Nanochannel based static and dynamic capillarity experiments are reviewed. A typical effect of nanoscale confinement is the appearance of capillarity induced negative pressure. Special attention is paid to elasto-capillarity and electro-capillarity. The presence of electric fields leads to an extra stress term to be added in the Young-Laplace equation. A typical example is the formation of the Taylor cone, essential in the theory of electrospray. Measurements of the filling kinetics of nanochannels with water and aqueous salt solutions are discussed. These experiments can be used to characterize viscosity and apparent viscosity effects of water in nanoscopic confinement. In the final section we show four examples of appearances of capillarity in engineering and in nature (112 references).

We describe the fabrication of three-dimensional microstructures by means of capillary forces. Using an origami-like technique, planar silicon nitride structures of various geometries are folded to produce three-dimensional objects of 50–100 μm. Capillarity is a particularly effective mechanism since surface tension forces dominate over bulk forces at small scales. The spontaneous evaporation of water forms the driving mechanism for this microfabrication technique. Therefore the actuating liquid disappears in the final structure. A model describing the elastocapillary interaction of the folding process is compared with experiments. By tailoring the elastic and capillary properties a variety of three-dimensional micro-objects can be realized.

A reproducible wafer-scale method to obtain 3D nanostructures is investigated. This method, called corner lithography, explores the conformal deposition and the subsequent timed isotropic etching of a thin film in a 3D shaped silicon template. The technique leaves a residue of the thin film in sharp concave corners which can be used as structural material or as an inversion mask in subsequent steps. The potential of corner lithography is studied by fabrication of functional 3D microfluidic components, in particular i) novel tips containing nano-apertures at or near the apex for AFM-based liquid deposition devices, and ii) a novel particle or cell trapping device using an array of nanowire frames. The use of these arrays of nanowire cages for capturing single primary bovine chondrocytes by a droplet seeding method is successfully demonstrated, and changes in phenotype are observed over time, while retaining them in a well-defined pattern and 3D microenvironment in a flat array.

Scanning force microscopy, such as atomic force microscopy ͑AFM͒ is complicated by the capillary force of a water meniscus formed in air between the probe tip and the sample. This small liquid bridge between the hydrophilic sample and the sharp AFM tip can be formed by capillary condensation from the vapor phase. We present an analytical model that describes the shape of the meniscus in which the pressure difference across the curved liquid air interface is taken into account. The analysis is based on a minimization of the liquid surface energy, together with the boundary condition of a given pressure drop across the surface as determined by the relative humidity of the vapor. The capillary forces that the wetting liquid exerts on the AFM tip are derived from the model. The resulting expressions can be used to describe arbitrary axial symmetric liquid air interfaces with nonzero total curvature, such as fluid bridges between two surfaces and droplets under a uniform force. The model illustrates some of the basic concepts of capillarity, such as surface tension forces and interfacial pressure drops.

In this paper we analyze the characteristic shape of the liquid meniscus at the fluid air interface in nanochannels of less than 80 nm height capped by a flexible membrane. Because of the induced negative pressure difference between the liquid pressure and the pressure outside, the 0.18 microm thin membrane on top of the channels bends downward. This elastocapillary equilibrium between the surface tension of the wetting liquid and the mechanical forces in the capillary results in a very peculiar shape of the interfacial meniscus, visible from the top through the transparent membrane. For increasing deflection of the membrane, the meniscus is seen to protrude along the channel and its curvature changes from concave to convex in the center. We present an analytical model to describe the meniscus shape in the deformed channel for small membrane deflections. We also show that the protrusion length of the meniscus, which can be measured easily, is an accurate and useful indicator for the membrane deflection. Experimental results on nanochannels filled with ethanol and water are presented and the observed menisci are seen to be in good agreement with the proposed model.