We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a one-dimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously supported by centre manifold theory. Errors of the derived model are quantified for improved predictions if necessary. The advection-diffusion equation is used to find that the optimal condition in a symmetric FFF for the separation of two species of molecules with similar diffusivities involves a high rate of cross-flow.
Journal of Mathematical Chemistry,
Vol. 26, no. 1-3 (Oct 1999), pp. 27-46