The glass-water interfaces in these experiments develop negative surface charge densities comparable to the spheres'. Both the surfaces and their charges must distort the simple ion distributions around nearby charged spheres. Complementary dipole distortions induced by parallel walls have been proposed [20] as a possible explanation for long-ranged colloidal attractions. The efficacy of a single wall [14], however, rules this out as a general mechanism.
Bowen and Sharif [21] suggested on the basis of numerical calculations that pair attractions arise naturally in confined geometries in the non-linear mean-field approximation. However, Neu [22] and Sader and Chan [23] (NSC) have demonstrated that this result must be incorrect by proving that the nonlinear Poisson-Boltzmann equation can only yield repulsions in confined geometries. The NSC proof holds for constant potential boundary conditions, at least some variants of constant charge boundary conditions, and for confining pores of arbitrary cross-section. This important result suggests that confinement-induced like-charge attractions are qualitatively inconsistent with the Poisson-Boltzmann formulation.
NSC also appear to contradict recent perturbation calculations [24] which find wall-induced attractions for constant charge boundary conditions. The disagreement might hinge on details of the boundary conditions [24], in which case wall-induced attractions would seem to be a rather specialized phenomenon. Other experiments, however, point to a broader context for like-charged colloidal attractions and thus a more general mechanism outside of mean-field theory.