On the modelling of generalized Taylor-Aris dispersion in chromatographs via multiple scales expansions

This paper is devoted to the computation of effective equations for the tra nsport of a solute in a chromatograph. We focus our attention on models tha t retain dispersion effects. A chromatograph is a biporous periodic heterog eneous medium, made up of macropores, and of small porous adsorbing crystal s that have a retention effect on the solute. We use the method of multiple scales expansions. Various macroscopic behaviours appear, according to the respective orders of magnitude of the dimensionless characteristic paramet ers: Peclet number in the macropores, ratio of the characteristic time of d iffusion in the macropores to the characteristic time of diffusion in the c rystals, adsorption coefficient. Dispersion occurs for a Peclet number of o rder epsilon(-1). We then discuss the effective behaviour of the solute, wi th respect to the orders of magnitude of the other characteristic parameter s. To our knowledge, most of the models are new. Our modelling is not restr icted to chromatographs. It applies to various situations of physic and che mical engineering: fixed bed reactors, catalytic cracking, ground water for instance.