Capillary bridge force between non-perfectly wettable spherical particles: An analytical theory for the pendular regime

Abstract

An analytical theory has been developed for the capillary bridge force between non-perfectly wettable, equal-sized spherical particles for the pendular regime. In this theory, the meridional profile of the axisymmetric capillary bridge is represented by part of an ellipse. The geometrical parameters in this description are determined from the boundary conditions at the three-phase contact circle at the spherical particles and at the neck and by the condition that the mean curvature be equal at the three-phase contact circle and at the neck. Thus, the current theory takes into account properties of the governing Young-Laplace equation. These geometrical parameters are expressed in terms of the volume of the capillary bridge and the separation distance between the spherical particles. The theory results in a rupture criterion that agrees well with a rupture criterion from literature that is based on many numerical solutions to the Young-Laplace equation. The predicted dependence of the capillary force on capillary bridge volume and interparticle separation agrees well with that obtained from numerical solutions of the Young-Laplace equation, without having introduced any calibrated fitting parameters, when the contact angle θ is in the range 0° ≤ θ ≤ 20° and when the ratio of capillary bridge volume to the radius of the spheres cubed is smaller than 10−3.