Three-dimensional model for capillary nanobridges and capillary forces

This paper presents a model for the computation of capillary forces (applied to water capillary condensation). For simple geometries (planes, spheres, cones, etc), this model complies well with the literature results. But the literature only provides results for simple shapes and meniscii geometries. Our model allows the computation of capillary force for non-axisymmetrical shapes, with a meniscus fulfilling the Kelvin equation (i.e. we do not assume the profile of the meniscus). Currently the model takes into account the contact angles, the relative humidity, temperature and the geometrical description of the problem. The complexity of the problem can result from object shape (modelling for example an AFM tip) and/or from geometrical configuration. Using the model, this article shows that the tilt angle of a tip cannot be neglected when computing capillary forces. It is also shown that the difference between a cone and a pyramid has a significant effect on the computation of the force. The authors propose a simplified formula to determine capillary forces for a range of tips from existing results for similar tips. Eventually, the paper also shows that this geometrical effect can be used to control the force between a tip and an object, allowing to pick it up and release it.