The van der Waals force between arbitrary-shaped particle and a plane surface connected by a liquid bridge in humidity environment

The van der Waals force (vdW force) between particulate matters at low humid condition and short distance contact is of great scientific importance in surface science. Due to the conventional theory for the van der Waals force between particles in single (vacuum or water) medium can not be directly applied in the humid condition, we present a mathematical model to calculate the van der Waals force between particle and surface linked by a liquid bridge in atmospheric humidity based on the surface integration method. In our model, the integration calculated the vdW force is divided into a wetting and a dry integrating region, and their boundary point is the radius of the wetting portion of the particle which is expressed as a function of relative humidity, contact angles and separation distance between the particle surface and the plane. For three basic contact geometries (sphere, cone and cylinder), the computational expressions of van der Waals force derived from our model are consistent with that by Butt. Moreover, our calculation results of the parabola particle model agree well with the published experimental data, which validated the rationality of the proposed model. In addition, our model can accurately calculate the vdW force between arbitrary-shaped particle and a plane surface in humidity environment.