The profile of a capillary liquid bridge between solid surfaces

Abstract

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.

Primary Seal Deformation in Multipane Glazing Units

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Continuous and discontinuous transitions between two types of capillary bridges on a beaded chain pulled out from a liquid

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Responsive 3D Microstructures from Virus Building Blocks

“…The liquid bridge is formed using an aqueous suspension of filamentous virus loaded into a capillary (tip inner diameter: 1 µm) and positioned in close proximity to the substrate on which the 3D microarchitecture is to be fabricated. Upon capillary contact and withdrawal from the substrate, a liquid bridge is generated with a minimal surface shape, which may take the form of a catenoid, nodoid, or unduloid . The axisymmetrical liquid bridge shape depends on a number of parameters, including the bridge length, bridge volume, radius of the capillary, capillary pressure, and radius of the substrate–liquid footprint .…”