The Short-range Capillary Force on Floating Objects

We develop a general method to study the capillary force 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 $l_c$, 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 $R$. 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.