Equilibrium distances for the capillary interaction between floating objects

When small objects are placed at a water-air interface, attractive and repulsive interactions appear due to liquid deformations. Although it is commonly admitted that two floating objects deforming the liquid interface in the same way are only attracting, we show that in the case of objects whose height does not vary during the interaction, the situation is much more complex than expected. In fact, attraction and repulsion can coexist at different ranges, so that equilibrium distances are observed. A 1D model based on the capillary interaction between vertical plates immersed in water is used to illustrate and calculate these situations, giving a picture of capillary interactions. We show that the wetting condition plays a determinant role in the behaviour of the interaction between floating objects. We also demonstrate that the equilibrium distance is given by the logarithm of the capillary charge ratio, using the right capillary charge definition. We also discuss the particular case of the existence of an interaction with a zero-capillary charge. A general equation of the equilibrium distance is proposed. An experimental confirmation of this relation is also given.