Transport modelling of a polyelectrolyte in membrane chromatography under an electric field

Electrophoretic separations were theoretically performed for large polyelectrolytes such as DNA in the membrane chromatography. This paper deals with the study of the mass transfer involved in multi-layered membrane chromatography in the presence of an electric field. The different contributions to mass transfer were considered in order to establish a relationship providing intramembrane convection effects as a function of an electric field since a polyelectrolyte is quickly oriented through pores in the field direction. Dimensionless transient mass balance equations were derived considering diffusion and electrophoretic convection, and the mass transfer was theoretically studied using two different Peclet numbers in the fluid and solid phases, showing how the concentration profiles of polyelectrolyte inside a membrane varies in the membrane according to values of Peclet number of an individual polyelectrolyte. Governing equations were solved by an operator theory.

A model was formulated to predict the transport behavior in a membrane column stacked with membranes. A complete analysis of the model equations was used in the transient state for a full description of the effects of system parameters, including diffusion coefficient and convective electrophoretic velocity. The relative ratio of electrophoretic convection and diffusion in solid phase and fluid phase, the Peclet number, became a factor determining the transport of polyelectrolyte inside a membrane, and the methods to enhance the concentration profiles in each membrane layer were predicted by the porosity and number of stacked membrane layer. The findings in this study provide a useful guide to the analysis and the design of devices in the laboratory and their scale-up required for a variety of bioseparations using the membrane chromatography.