Capillary interactions between nearby interfacial objects

Abstract

We develop a general method to study the capillary interactions between objects of arbitrary shape which float close to each other on an interface, a regime in which multipole expansion is not useful. The force is represented as a power series in the small distance between the objects, of which the leading order is finite. For objects with size a much larger than the capillary length lc, the force scales as $\\sqrt{a/l_c}$ and the prefactor depends on the mean radius of curvature R at the closest points. After contact the objects roll and/or slide with respect to each other to locally maximize R and therefore the force. For smaller objects ($a\\ll l_c)$ , the force scales as $(a/l_c)^{-1}\\log(a/l_c)^{-2}$ , and the prefactor depends only weakly on the shape and relative orientation of the objects.