APPLICATIONS OF SELF-ADJOINT OPERATORS TO ELECTROPHORETIC TRANSPORT, ENZYME-REACTIONS, AND MICROWAVE-HEATING PROBLEMS IN COMPOSITE MEDIA .1. GENERAL FORMULATION

Analytical solutions for transient and steady-state convection, diffusion, and reaction problems in one-dimensional M-layer composite media are developed. Three cases are considered: (1) electrophoretic transport; (2) first-order reactions; and (3) zero-order reactions. Solutions are obtained for both Dirichlet and generalized well-mixed boundary conditions. Operator-theoretic methods are utilized to solve the transient problems. The structure of the eigenvalue problems is considered in order to illustrate the methodology for the construction of the solutions to the transient problems. Steady-state solutions are presented for all the cases investigated.