APPLICATIONS OF SELF-ADJOINT OPERATORS TO ELECTROPHORETIC TRANSPORT, ENZYME-REACTIONS, AND MICROWAVE-HEATING PROBLEMS IN COMPOSITE MEDIA .2. ELECTROPHORETIC TRANSPORT IN LAYERED MEMBRANES

The problem analyzed in this paper is a specific application of the ge neral M-layered composite reaction/diffusion/convection formulation gi ven by Locke and Arce. The analysis considers electrophoretic transpor t of a single solute species across a one-dimensional three-layered sy stem and the solution is obtained using operator-theoretic methods. Th e geometrical structure of the spectrum of the operator is determined for the complete range of the various parameters including the distrib ution coefficients, applied electrical field, electrophoretic mobiliti es, and diffusion coefficients. The structure of the spectrum allows a complete characterization of all the eigenvalues of the system in ter ms of all of these physical parameters. Calculation of the first eigen value for a number of cases shows its variation with the applied elect rical field for various medium porosities and allows a priori estimate s of the dynamics of the process. Concentration profiles are given to illustrate the solution.