Capillary and van der Waals force between microparticles with different sizes in humid air

Abstract

It is well known that surface effect forces, such as van der Waals force and capillary force, are the major contributions to adhesion when microsized particles are in contact in humid environment. But it is very complex to calculate the adhesion force between two smooth unequal particles. In conventional approaches, the effective particle radius approximation and the constant half-filling angle assumptions are often used for computing the van der Waals forces between two microparticles. However, the approximation and the assumption are actually difficult to accurately model the forces between unequal particle sizes when the surfaces are with different properties. In this paper, we present a theoretical study of the van der Waals force and capillary force between two microparticles with different radii and the surface properties linked by a liquid bridge. The proposed model provides the adhesion force predictions in good agreement with the previous formula and existing experiment data. Considering the solid particles are partially wetted by the liquid bridge, the van der Waals force is calculated by divided the particle surface into a wetted part and a dry portion in our stimulation. Since the wetted surface portion of the particle is determined by the half-filling angle, the relationship between two half-filling angles of the unequal size particles is developed from the geometrical consideration, which is relate to the size ratio of the particles, the contact angle, and the separation distance. Then, the van der Waals force is determined using the surface element integration. Moreover, the influences of humidity, particles size, contact angle, and separation distance toward the adhesion forces are discussed using the proposed method. Simulations indicate that a higher relative humidity leads to bigger liquid bridges, suggesting a higher capillary force, but at the same time, the van der Waals force decreases due to the decrease in surfaces energy. As for the influence of contact angle, results show that a higher contact angle, that is, a more hydrophobic surface, reduces the capillary force but increases the van der Waals force (absolute value). The simulations also show that the both the capillary force and the van der Waals force (absolute value) increase as the particle size increases. When the particles are separated from each other, the capillary force and van der Waals force decreases gradually. These results are helpful to understand and utilize the adhesion interaction between particles with unequal sizes at the ambient condition.