A more comprehensive mathematical theory for liquidchromatography is set forth, incorporating dynamical models for mixed solvents and solutes, and new mathematical models for adsorption, including adsorbent and exchange processes.The equations for solvent and solute are shown to possess unique solutions, using so-called energy methods. The solvent modulation of local velocity is found theoretically, as is solvent control of solute adsorption, diffusivity, and dispersion. The theory for solvent control of solute adsorption is found to be very accurate against experiment, and offers a useful method of treating normal phase, reversed phase, ion exchange, and ion pair liquid chromatography in a unified mathematical framework, under the name catalyzed adsorption. The long-recognised problemof solvent localization is modelled, and the model shown to be consistent with experiment. Another classical problem, solvent demixing, is explained in terms of the nonlinear multicomponent solvent model, wherein solvent gradients steepen according to the adsorption and shock formation. Perturbation theory, based on a small packing number d_p/L « 1 (where d_p is substrate particle diameter, L is column length), is applied to the solvent-controlled pulsed solute dynamical equations. When moment techniques are used in conjunction with perturbation theory, very useful and simplified system control equations are obtained. These control equations are used in some model problems to discuss HETP (Height Equivalent to a Theoretical Plate) variations with Peclet number, with relative solvent concentration, and between solutes. Finally, numerical methods for the solvent and solute equations are discussed.
