So far, no interaction measurement on isolated pairs of spheres has found attractions inconsistent with the DLVO theory. And yet evidence for many-body attractions abounds when the number density of the same spheres is increased. On this basis, we provisionally rule out any of the existing theories which predict pairwise attractions for isolated spheres. A definitive statement awaits additional experimental evidence concerning the interaction's dependence on thermodynamic control parameters; such experiments are now ongoing.
Anomalous attractions are observed on length scales extending to several micrometers. It seems unlikely, therefore, that the discrete structure of the solvent or the discrete size of the simple ions can play a role in mediating the attraction. In other words, the primitive model should suffice.
Image charges in the confining walls, or sphere-induced changes in the walls' charge state could conceivably lead to attractions. The additional repulsion observed for tightly confined spheres [see, for example, the lowest curve in figure 1(b)] provides one counter indication, however. Bulk phenomena such as the observed metastability of superheated colloidal crystallites further indicates that glass surfaces are not necessary to engender many-body colloidal attractions.
Fluctuations in ion density around the spheres seem another likely candidate. Existing calculations suggest that such fluctuations do indeed lead to attractions, but that they are doubly-screened and thus short-ranged [36]. Similarly, careful handling of the kinetics of ion adsorption onto colloidal surfaces leads to short-ranged attraction [37]. The experimentally observed attractions, on the other hand, are longer-ranged than the singly-screened pair repulsion. If ionic fluctuations are responsible, the mechanism must involve modes of fluctuation not yet considered.
Finally, we should not forget that the mean-field behavior predicted by the Poisson-Boltzmann formulation need not reflect the true saddle point behavior of the system. High-order correlations neglected in (5), if they could be treated analytically, might lead to interesting new predictions not only for charge stabilized colloidal suspensions but also for macroionic systems in general.