text: While the superposition approximation is actually exact at larger distances, it is no longer accurate at smaller separations. Solutions of the DH or PB equations in between the plates provide a more accurate picture at these conditions. Let us only discuss the symmetric situation within the DH model here. This discussion will introduce the notion of charge regulation, which suggests that the surface charge (and the surface potential) may vary (or regulate) upon approach.
  The DH equation can be solved exactly for two plates. The boundary conditions play an important role, and the surface potential and surface charge density 
   and  become functions of the surface separation h and they may differ from the corresponding quantities ψ and σ for the isolated surface. When the surface charge remains constant upon approach, one refers to the constant charge (CC) boundary conditions. In this case, the diffuse layer potential will increase upon approach. On the other hand, when the surface potential is kept constant, one refers to constant potential (CP) boundary condition. In this case, the surface charge density decreases upon approach. Such decrease of charge can be caused by adsorption of desorption of charged ions from the surface. Such variation of adsorbed species upon approach has also been referred to as proximal adsorption. The ability of the surface to regulate its charge can be quantified by the regulation parameter
  where C = ε  ε κ is the diffuse layer capacitance and C the inner (or regulation) capacitance. The CC conditions are found when p = 1 while the CP conditions for p = 0. The realistic case will be typically situated in between. By solving the DH equation one can show that diffuse layer potential varies upon approach as
  while the surface charged density obey a similar relation 
  The swelling pressure can be found by inserting the exact solution of the DH equation into the expressions above and one finds
  Repulsion is strongest for the CC conditions (p = 1) while it is weaker for the CP conditions (p = 0). The result of the superposition approximation is always recovered at larger distances but also for p = 1/2 at all distances. The latter fact explains why the superposition approximation can be very accurate even at small separations. Surfaces regulate their charge and not infrequently the actual regulation parameter is not far away from 1/2. 
  The situation is exemplified in the figure below. From stability considerations one can show that p < 1 and that this parameter may also becomes negative. These results can be extended to asymmetric case in a straightforward way.
  When surface potentials are replaced by effective potentials, this simple DH picture is applicable for more highly charged surfaces at sufficiently larger distances. At shorter distances, however, one may enter the PB regime and the regulation parameter may not remain constant. In this case, one must solve the PB equation together with an appropriate model of the surface charging process. It was demonstrated experimentally that charge regulation effects can become very important in asymmetric systems.