Aggregation of frictional particles due to capillary attraction

Capillary attraction between identical millimeter-sized spheres floating at a liquid-air interface and the resulting aggregation are investigated at low Reynolds number. We show that the measured capillary forces between two spheres as a function of distance can be described by expressions obtained using the Nicolson approximation at low Bond numbers for far greater particle sizes than previously assumed. We find that viscous hydrodynamic interactions between the spheres needs to be included to describe the dynamics close to contact. We then consider the aggregates formed when a third sphere is added after the initial two spheres are already in contact. In this case, we find that linear superposition of capillary forces describes the observed approach qualitatively but not quantitatively. Further, we observe an angular dependence of the structure due to a rapid decrease of capillary force with distance of separation, which has a tendency to align the particles before contact. When the three particles come into contact, they may preserve their shape or rearrange to form an equilateral triangle cluster-the lowest-energy state-depending on the competition between attraction between particles and friction. Using these observations, we demonstrate that a linear particle chain can be built from frictional particles with capillary attraction.