Aggregation of frictional particles due to capillary attraction

TL;DR

This study investigates how millimeter-sized particles at a liquid-air interface aggregate due to capillary forces, highlighting the importance of hydrodynamics and friction in the formation of stable structures.

Contribution

It provides a detailed analysis of capillary forces between particles, incorporating hydrodynamics and friction, and demonstrates the formation of particle chains through capillary attraction.

Findings

Capillary forces fit Nicolson approximation for large particles at low Bond numbers.

Hydrodynamic interactions are crucial near contact for accurate dynamics.

Linear superposition of forces qualitatively explains multi-particle approach.

Abstract

Capillary attraction between identical millimeter sized spheres floating at a liquid-air interface and the resulting aggregation is 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 hydrodynamics 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 in 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.