A generalized approach to the description of interaction boundaries in migrating systems

Patterns observed in the migration of a system of n solutes, where n ⋟ 1, are affected by the operation of either physical or chemical interactions or both. The effects of the two types of interactions have previously been considered separately by widely different approaches, leading in certain instances to the complete description of migration patterns. In the present work a unified and simplified approach is presented, which permits a complete mathematical description of all features of the migration pattern, provided the dependence of constituent velocities on total composition is defined for each constituent species. Emphasis is given to systems involving one or two migrating solutes. In particular, criteria have been established for sharp, spread and hypersharp boundary forms. The treatment, in common with some previous approaches, neglects the effects of diffusional spreading, and considers only time-independent interactions. The general theory is first illustrated with chemically associating systems, and the examples include descriptions of cases involving two solutes, which have been previously explained by physical argument alone. The operation of physical interactions is also treated by the theory, both by selecting appropriate models and by introducing general functions. Finally, the moving boundary equation is applied to selected migration patterns, modified by both physical and chemical interactions.