Liquid morphologies and capillary forces between three spherical beads.

Equilibrium shapes of coalesced pendular bridges in a static assembly of spherical beads are computed by numerical minimization of the interfacial energy. Our present study focuses on generic bead configurations involving three beads, one of which is in contact to the two others while there is a gap of variable size between the latter. In agreement with previous experimental studies, we find interfacial "trimer" morphologies consisting of three coalesced pendular bridges, and "dimers" of two coalesced bridges. In a certain range of the gap opening we observe a bistability between the dimer and trimer morphology during changes of the liquid volume. The magnitude of the corresponding capillary forces in presence of a trimer or dimer depends, besides the gap opening, only on the volume or Laplace pressure of the liquid. For a given Laplace pressure, and for the same gap opening, the capillary forces induced by a trimer are only slightly larger than the corresponding forces in the presence of three pendular bridges. This observation is consistent with a plateau of capillary cohesion in terms of the saturation of a wetting liquid in the funicular regime, as reported in the experimental work [Scheel et al., Nat. Mater. 7, 189 (2008)1476-112210.1038/nmat2117].