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The release of catanionic mixtures embedded in gels: An approximate analytical analysis
Author(s) -
Frenning Göran,
Gråsjö Johan,
Hansson Per
Publication year - 2011
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12368
Subject(s) - nonlinear system , micelle , ordinary differential equation , mole fraction , mathematics , diffusion , integral equation , partial differential equation , thermodynamics , reduction (mathematics) , chemistry , mathematical analysis , differential equation , physics , geometry , quantum mechanics , aqueous solution
We present an approximate analytical analysis of the release of catanionic mixtures from gels. The starting points are the monomer–mixed micelle equilibrium, described by using regular solution theory, and the one‐dimensional diffusion equation. Focusing on a half‐infinite planar system, we first point out an exact reduction of the problem to a system of ordinary differential equations. By using the pseudo‐steady‐state approximation and the integral‐balance method, we then derive a single nonlinear equation for the mole fraction of drug in micelles at the extraction front. This equation may be readily solved numerically (or graphically), and once the solution is found, all quantities of interest may be determined in closed form. Comparisons with numerical solutions of the fully nonlinear problem indicate that the errors resulting from the approximations typically do not exceed 10 %. © 2010 American Institute of Chemical Engineers AIChE J, 2011