Computer simulation of pressure driven flow through particles in gel permeation chromatography

The objective of this work was to develop a mathematical model of diffusion within gel permeation chromatography particles including pressure driven flow effects. Although the partial differential equations governing the process are described, the problem was actually solved by first using a direct solution of Carslaw and Jaeger's equation for diffusion in a sphere with arbitrary concentration profile. The resultant concentration profile was moved a certain distance in the bulk flow direction to mimic pressure driven flow. A relationship for the effective diffusivity, D_eff, as a function of the bulk flow velocity, u, was derived. The model included two parameters, the ratio of bulk flow velocity to the pressure driven particle flow velocity in the particle, g, and the calculated effective diffusivity if there were no pressure driven particle flow, D₀. The model was used to analyze column data from the literature and some locally generated data for evidence of pressure driven flow effects. The model described the change in effective diffusivity of the data obtained from the literature very well with just two parameters and described experimentally obtained changes in diffusivity which are greater than can be ascribed to film diffusion or axial dispersion alone.