Analytical Solutions for Partitioned Diffusion in Laminates: I. Initial Value Problem with Steady Cauchy Conditions

• Published in: Transport in porous media Vol. 37; no. 1; pp. 93 - 128
• Main Authors: Trefry, Michael G., Whyte, David S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.10.1999; Springer Nature B.V
• Subjects: Balancing; Boundary conditions; Boundary value problems; Chemical partition; Contaminants; Coordinates; Earth sciences; Earth, ocean, space; Eigenvectors; Engineering and environment geology. Geothermics; Exact sciences and technology; Exact solutions; Formulations; Laminates; Mass transfer; Nutrients; Partitioning; Peclet number; Pollution transport; Pollution, environment geology; Porous media; advection; models; diffusion; eigenfunction; concentration; pollution; nutrients; physical models; solution; mathematical methods; separation; solution transport; boundary conditions; porous media
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1023/A:1006566125433

Studies of the transport of contaminants and nutrients in industrial and environmental systems are complicated by the heterogeneous nature of the supporting porous or permeable media, and by the numerical problems associated with high Peclet number advection and sharp interface models. In order to provide independent theoretical checks of numerical transport theories, this set of papers presents analytical solutions to diffusive transport equations in simplified (one-dimensional) laminate systems subject to partitioning interactions. Here, in Part I, a standard separation of variables technique is used to develop analytical eigenfunction expansions of the concentration solution in an N-laminate system subject to steady Cauchy (third-type) nonhomogeneous boundary conditions. Both Cartesian and radial (axisymmetric) coordinate systems are considered. The solutions are developed for two different interface partitioning formulations, allowing the partitioning processes to be described by instantaneous equilibration mechanisms, or in terms of gradual equilibration mediated by mass transfer coefficients. Worked examples are presented and limitations of the approach discussed.