Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 823452, 13 pages
doi:10.1155/2009/823452
Research Article

Analysis of Nonlinear Dynamics for Abrupt Change of Interphase Structure in Liquid-Liquid Mass Transfer

DongXiang Zhang,1 Min Sun,2 and Jing Li2

1School of Chemical Engineering and the Environment, Beijing Institute of Technology, Beijing 100081, China
2College of Applied Science, Beijing University of Technology, Beijing 100124, China

Received 22 December 2008; Revised 30 April 2009; Accepted 4 May 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 DongXiang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

As a liquid-liquid system is far from equilibrium state, the phase thickness is variable when mass transfer process with chemical reaction occurs in interphase zone, and a dispersible transitional layer called the interphase dispersed zone (IDZ) is formed. The IZD model composed of thermodynamically instable O/W or W/O microemulsion has reasonably explained enormous experimental phenomena in nonlinear mass transfer. To forecast the possible parameter ranges of IDZ process and abrupt change of liquid-liquid mass transfer rate, the dynamic characteristics of a molecular diffusion model are considered in this paper. We applied the bifurcation theory of planar dynamical system, Laplace transform, and maple software to investigate the model, and obtain different phase portraits of the system in different regions. The results obtained will play an important directive role in the study of IDZ model.