Analysis of diffusion through composite membranes—I. Mathematical development

✍ Scribed by Vladimir Mitlin; Lev Bromberg

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 882 KB
• Volume: 47
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(92)80019-9

✦ Synopsis

Ahstrac

-This paper presents a mathematical analysis of linear diffusion in a composite membrane, the cylindrical pores of which are filled with longitudinal layers of various phases aligned parallel. It is shown that radial heterogeneity leads to appearance of eigenvalues and eigenfknations of the transverse problem which are coupled with the only corresponding eigenfimction of the longitudinal problem_ This coupling, typical of nonlinear models, necessitates a generalization of the universally adopted procedure of separation of variables to construct. in closed form, a general solution for an arbitrary number of layers_ For determining the coefficients of the general solution, a special system of piecewise smooth basis functions is introduced. A special function space in which the basis functions are orthogonal in pairs is used. A transcendental equation for the computation of the relaxation times is obtained. A general structure of the solution of a problem of this type is constructed. The limitations of the method used are discussed.