When the surfaces are sufficiently far apart, the potential profiles originating from each individual surface will not be much perturbed by the presence of the other surface. This approximation thus suggests that one can simply add (superpose) the potentials profiles originating from each surface as illustrated the figure. Since the potential profile passes through a minimum at the mid-plane, it is easiest to evaluate the disjoining pressure at the midplane. The solution of the DH equation for an isolated wall reads
where z is the distance from the surface and ψ the surface potential. The potential at the midplane is thus given by twice the value of this potential at a distance z = h/2. The disjoining pressure becomes
The electrostatic double layer force decays in an exponential fashion. Due to the screening by the electrolyte, the range of the force is given by the Debye length and its strength by the surface potential (or surface charge density). This approximation turns out to be exact provided the plate-plate separation is large compared to the Debye length and the surface potentials are low.
This result can be simply generalized to highly charged surfaces, but only at larger separations. Even if the potential is large close to the surface, it will be small at larger distances, and can be described by the DH equation. However, in this case one has to replace the actual diffuse layer potential ψ with the effective potential ψ. Within the PB model, this effective potential can be evaluated analytically, and reads
The superposition approximation can be easily extended to asymmetric systems. Analogous arguments lead to the expression for the disjoining pressure
where the super-scripted quantities refer to properties of the respective surface. At larger distances, oppositely charged surfaces repel and equally charged ones attract.