The Floatability of Single Spheres versus Their Pairs on the Water Surface.

Particle floatability at the water surface encountered in nature and industrial systems often occurs in the presence of many particles, but the available theoretical developments are based on the flotation of single particles. Here experiments were conducted to compare the floatabilities of single and multiple spheres on the air-water interfaces. Specifically, the forces on floating single spheres and their pairs versus the depth of deformed interface were measured using a force sensor combined with high-speed video microscopy and modeled based on the 3D Young-Laplace equation which was numerically solved. The experimental and theoretical results for the vertical forces supporting the floatability of the pairs of spheres agree well. The maximum measured forces on the pairs were equal to the sum of the maximum forces measured on two single spheres individually, but the forces measured on the single spheres and their pairs at different depths of interface deformation were different. The vertical forces supporting the floatability of the sphere pairs can better tolerate the interface deformation than the same force on two single particles. This evidence is also supported by the experiments with multiple particles floating at the surface of water-ethanol mixtures. Adding ethanol into water reduced the surface tension of water and the floatability of particles at the water surface, but the floatability of multiple particles was sustainable at much lower critical surface tensions than that for single particles, invalidating the classical theories. Lateral interparticle interactions influence the floatability of particles and should be considered in its modeling.