A general mathematical model was derived that describes the process of adsolubilization, i.e. the adsorption of hydrophobic organic compounds (HOCS) onto a packed bed of surfactant-modified alumina. Analytic solutions of the limiting forms of the model were presented for the case where a constant surfactant loading was maintained (i.e. continuous supply of make-up surfactant). Under this condition, classical concentration (C/C-0) profiles and breakthrough curves resulted. However, when the surfactant loading was not maintained constant (i.e. no supply of make-up surfactant), numerical solutions showed that the synergistic equilibrium between the HOC and the bound surfactant results in concentration pulses (C/C-0 much greater than 1) in the HOC profile. It was suggested that the latter mode of operation might be a simple means of concentrating dilute solutions. To demonstrate the adsolubilization process, a laboratory adsorber column was fabricated for continuous operation. Residence time distribution (RTD) experiments were conducted to determine the dependence of the axial dispersion coefficient (an important model parameter) upon the fluid velocity. This information will be valuable when comparing model predictions with experimental data collected in Part III of this series.