(140b) Early Time Analysis of Transport Processes
This paper explores the utility of a well-established but rarely applied technique for solving linear partial differential equationd (PDE's) of the type commonly encountered in the analysis of nonsteady-state transport processes. Simple reconfiguration of the PDE's Laplace transform yields, upon inversion, a series solution that requires a decreasing number of terms to converge as time approaches zero. It has therefore been referred to as an "early-time solution." Crank (The Mathematics of Diffusion, 2nd ed., Oxford Univ. Press, New York, 1975) credits its apparent developer by naming it "Holstein's solution." By comparison, the conventional series solution obtained via separation of variables requires an increasing number of terms to converge as time approaches zero and is, therefore, a "long-time solution." We have previously shown that truncation after the lead terms in early and long-time solutions suffices to accurately model classic single-membrane permeation (and analogous heat transfer) phenomena. Here we further demonstrate the utility of Holstein's solution by applying it to reactive and nonreactive, heterogeneous and homogeneous barrier films, and "controlled release" phenomena associated with localized drug delivery.