Abstract:

Starting with a basic concept of balance in engineering theories，a generalized differential expression of balance for various theoretical models in reaction engineering is described mathematically in terms of accumulation，divergence and source（reaction term）.The distributions of physical variables related to the intrinsic reaction kinetics，namely the mass field and the non-mechanical energy field in the reaction system will finally determine the macroscopic result of reaction.The common speciality of electrochemical systems is the existence of both electrochemical source and charge transport process in the systems，and hereby the generalized theoretical model of porous electrodes can be developed through reasonable simplifications.The mathematical model is a boundary problem of a set of non-linear second order differential equations to describe the coupled non-linear relationships among the concentration，ohmic and activation polarizations.The four dimensionless parameters in the model，s，μ，α and γ，can give the gist of the similarity of kinetics and transport process between porous electrode systems.Furthermore the Adomian decomposition method（ADM）and the parameterized ADM mathematica code（PAMC）developed by the author for automation of ADM，which are used for the approximate solution of the non-linear model，are briefly introduced.As an example，computation results of theoretical polarization curves for cylindrical and annular porous electrodes are presented.In conclusion，the study of nonlinearity and complexity in reaction systems will contribute to the further development of reaction engineering theory.