Towards an accurate description of the capillary force in nanoparticle-surface interactions

We present a method to numerically calculate the exact (non-circular) meniscus profile from the Kelvin equation, and compare the results of the obtained capillary force with different previous approximations and experiments. We show that a circular meniscus profile gives correct results in most cases. We also compare different models of pull-off behaviour and show that the often used approximation of humidity independent capillary force is viable for spherical particles above 1μm radius, but below that there is a strong humidity dependence, as seen in experiments. At the same length scale the direct surface tension force component becomes important. We also discuss the vanishing of the capillary force at very low humidity, the effect of small initial separation between the particle and the surface and the effects of different particle shapes and contact angles on the capillary force. Finally, calculated results are compared with experimental measurements of the capillary force. (Some figures in this article are in colour only in the electronic version)