A general model is developed for the electrophoresis of soluble materials. The model describes the evolution of concentration fields for a set of compounds which undergo transport by flow, diffusion, and migration in an electric field and simultaneously participate in rapid dissociation-association reactions. Modes of electrophoresis requiring special treatment can now be studied in a unified context. As an example of its utility, the model is used analytically to study a process known as isotachophoresis. In Part I1 two electrophoretic separation processes are simulated numerically, demonstrating the model's versatility.
D. A. SAVILLE Department of Chemical EngineeringPrinceton University Princeton, NJ 08544
A. PALUSINSKI Biophysics Technology Laboratory and
Department of Electrical and Computer
Engineering
University of ArizonaTucson, AZ 85721
SCOPEWhen a solution containing amphoteric compounds is exposed to an electric field, the migration of ions and uncharged species occurs in the presence of rapid dissociation-recombination reactions. If a zone containingseveral species is inserted in a column containinga homogeneous buffer, the various species will migrate at different rates according to their relative electrophoretic mobilities. Conversely, if the ends of the column are made impermeable to the amphoteric species, a stationary pH gradient will eventually be formed and sample constituents will migrate to their equilibrium isoelectric points under the influence ofthe electric field. These phenomena form the basis of several separation methodologies that have been difficult to model mathematically. The purpose of this paper is to present a generally applicable model of electrophoretic processes and apply it to a specific situation. The application is designed to illustrate the interplay between reaction, electromigration, and diffusion in simple configurations where complications due to lateral boundaries, bulk flow, and nonuniform temperature are supressed. The situation studied in detail is isotachophoresis in a one-dimensional column; more diverse applications that require numerical treatment of the equations are described in Part 11.
CONCLUSIONS AND SIGNIFICANCEAlthough electrophoretic processes can be described by familiar conservation relations, the structure of the mathematical model differs from that used to describe systems with strong electrolytes due to the presence of rapid dissociation-recombination reactions that tie the concentrations of ionic species to those of the undissociated solutes. It is shown that since the reactions are fast relative to transport by diffusion and electromigration, it is possible to treat the reactions as being in local equilibrium. Similarly, the ratio of an electrical length (the Debye scale) to the physical scale of the process is small, and this leads to the electroneutrality approximation. The model that is developed consists of a set of conservation equations for the total concentration of each amphoteric compound and the current. Appended to this set of partial...