A mathematical model for the interactions between non-identical rough spheres, liquid bridge and liquid vapor

[Display omitted] ► Filling angles for a liquid volume between two spheres depend on the size ratio and surface roughness of the spheres. ► Liquid volume and capillary force relate to the suction, contact and filling angles, spheres roughness, and size ratio. ► The calculated equilibrium relations are shown to possess non-uniqueness. ► For any given humidity of the pore air, the suction increases with increasing particle size and increasing size ratio. Investigation of the interactions between the skeleton of an unsaturated particulate material and the contained liquid involves the general interaction model consisting of a liquid bridge in contact with two rigid smooth spherical particles of unequal size and dissimilar material, at a separation determined by their actual surface roughness, and surrounded by a gas with a vapor pressure at equilibrium with the liquid. The liquid retention and capillary force of the system are related to the capillary suction, liquid–solid contact angles, filling angles, roughness of the particles, and the ratio of particle radii in normalized terms by assuming a circular arc for the shape of the liquid profile. The normalized suction is also related to the corresponding relative humidity of the pore air. The calculated equilibrium relations are shown to possess non-uniqueness, which is interpreted in terms of mechanical properties of unsaturated particulate materials. The model is able to provide new insights into the behavior of an unsaturated particulate material.