  Liquid capillary-bridge formation between solid particles has a critical
influence on the rheological properties of granular materials and, in
particular, on the efficiency of fluidized bed reactors. The available
analytical and semi-analytical methods have inherent limitations, and often do
not cover important aspects, like the presence of non-axisymmetric bridges.
Here, we conduct numerical simulations of the capillary bridge formation
between equally and unequally-sized solid particles using the lattice Boltzmann
method, and provide an assessment of the accuracy of different families of
analytical models. We find that some of the models taken into account are shown
to perform better than others. However, all of them fail to predict the
capillary force for contact angles larger than $\pi/2$, where a repulsive
capillary force attempts to push the solid particle outwards to minimize the
surface energy, especially at a small separation distance.
