Theory of electrophoretic separations. Part I: Formulation of a mathematical model

Abstract

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...

Sample dispersion in isotachophoresis

“…As mentioned above, conductivity gradients in ITP lead to distributions of net charge in the bulk liquid. However, as discussed by Saville & Palusinski (1986), in ITP the characteristic length scale of the conductivity interface is typically much larger than the electric length scale associated with regions of significant net charge (i.e. much larger than the Debye length).…”

Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

“…Component fluxes are computed on the basis of electromigration, diffusion and convection (imposed flow and/or electroosmosis). The models are composed of a set of balance laws governing the transport of components in electrophoretic separations [1,37,38,40,41,43] and comprise a coupled set of non-linear partial differential equations describing the appropriate balance laws and algebraic equations describing chemical equilibria. The statement of conservation of charge includes a term for the diffusion current (for importance of diffusion current compare data of [133] with those of [134]).…”

“…The widths of boundaries with a steady-state shape are dependent on the applied power level, i.e. boundary width is inversely proportional to the current density, and inversely proportional to the difference in mobilities of neighboring components [37,126]. This is shown with the cationic steady-state ITP boundary between pyridine and aniline having sodium, b-alanine and acetic acid as leading, terminating and counter components, respectively (Fig.…”

“…This is illustrated here with ZE, ITP, IEF and EKC separation examples. The data shown were produced with GENTRANS, the simulator based on the work of Bier, Mosher, Thormann, Breadmore and coworkers [1,37,38,44,[49][50][51][52][53][54]75].…”

“…11). Except for very simple cases, ITP boundaries with their steady-state shapes can only be described by simulation [2,3,18,37,125,126]. The data presented in Fig.…”