(color online) Sketch of two charged spherical colloids trapped in an air–water interface. Three coordinate systems are set in the system: two parallel spherical coordinates whose origins are fixed on the center of the colloids and one cylindrical coordinate whose origin is fixed on the center of the first particle-interface intersecting plane. The flat interface is on z = 0 and separates an upper air phase (dielectric constant ) from a lower electrolytic phase (dielectric constant ). Two colloids are trapped in the air–water interface with a center–interface distance h and the center–center distance d.