Capillary force and rupture of funicular liquid bridges between three spherical bodies

Capillarity in wet granular materials induces cohesion and increases the material strength due to the attractive forces acting on capillary bridges. In the funicular state, water bridges may be not only formed between two grains but also binding three or more particles, which breaks the axial symmetry of the liquid bridge. This work presents a fundamental study on capillary forces and rupture behaviours of funicular water bridges between three spherical bodies at equilibrium (or static) configurations. Funicular water clusters are numerically solved by an energy minimization approach. Experimental comparisons are made by measuring capillary forces and these confirm the validity of the numerical solutions. Evolutions of capillary forces and rupture distances are investigated systematically by moving two spheres away from the centre. The fixed water volume condition and the constant mean curvature condition are studied respectively. Comparisons are made between the un-coalesced pendular liquid rings and the coalesced funicular bridge. For a same fixed total water volume, the capillary force is weakened by water bridge coalescence to a funicular bridge when the spheres are packed together, but the situation may vary for different contact angles and inter-particle distances. For the constant mean curvature condition, water bridge coalescence does not alter capillary force significantly when particles are packed closely, but the discrepancy is larger by increasing the gap. Funicular water bridge rupture criteria are also proposed based on the studied configurations. It is observed that in general the transmission from pendular to funicular state extends the rupture distance when it has a relatively high water volume or low air-water pressure difference.