Combined Effect of Surface Tension, Gravity and van der WaalsForce Induced by a Non-Contact Probe Tip on the Shape of Liquid Surface

Abstract

Aiming at understanding how a liquid film on a substrate affects theatomic force microscopic image in experiments, we present an analyticalrepresentation of the shape of liquid surface under van der Waalsinteraction induced by a non-contact probe tip. The analyticalexpression shows good consistence with the corresponding numericalresults. According to the expression, we find that the vertical scaleof the liquid dome is mainly governed by a combination of van der Waalsforce, surface tension and probe tip radius, and is weekly related togravity. However, its horizontal extension is determined by thecapillary length.