Adsorption maxima have been reported for adsorption at the hydrophilic solid/water interface based on measurements on powders and solution analysis. Many would claim that this is an impurity effect and the explanation in the literature, which is based on the mass action effect, is incorrect. We have results on the adsorption of anionic surfactants on a single sapphire surface that should be free from experimental artefacts. We also have a new hypothesis that would explain the maximum, in which micelles above a certain concentration interact directly with the adsorbed layer. This hypothesis can be tested by observing the pattern of adsorption for a series of surfactants of different chain length. Adsorption is determined by the concentration relative to the CMC whereas the interaction depends on the absolute concentration. We propose to study adsorption of cationic surfactants on silica.