Effect of contact angle on the orientation, stability, and assembly of dense floating cubes

In this paper, the effect of contact angle, density, and size on the orientation, stability, and assembly of floating cubes was investigated. All the cubes tested were more dense than water. Floatation occurred as a result of capillary stresses induced by deformation of the air-water interface. The advancing contact angle of the bare acrylic cubes was measured to be 85°. The contact angle of the cubes was increased by painting the cubes with a commercially available superhydrophobic paint to reach an advancing contact angle of 150°. Depending on their size, density, and contact angle, the cubes were observed to float in one of three primary orientations: edge up, vertex up, and face up. An experimental apparatus was built such that the sum of the gravitational force, buoyancy force, and capillary forces could be measured using a force transducer as a function of cube position as it was lowered through the air-water interface. Measurements showed that the maximum capillary forces were always experienced for the face up orientation. However, when floatation was possible in the vertex up orientation, it was found to be the most stable cube orientation because it had the lowest center of gravity. A series of theoretical predictions were performed for the cubes floating in each of the three primary orientations to calculate the net force on the cube. The theoretical predictions were found to match the experimental measurements well. A cube stability diagram of cube orientation as a function of cube contact angle and size was prepared from the predictions of theory and found to match the experimental observations quite well. The assembly of cubes floating face up and vertex up were also studied for assemblies of two, three, and many cubes. Cubes floating face up were found to assemble face-to-face and form regular square lattice patterns with no free interface between cubes. Cubes floating vertex up were found to assemble in a variety of different arrangements including edge-to-edge, vertex-to-vertex, face-to-face, and vertex-to-face with the most probably assembly being edge-to-edge. Large numbers of vertex up cubes were found to pack with a distribution of orientations and alignments.