(168l) Exact Averaging of Laminar Dispersion

We use the Liapunov-Schmidt (L-S) technique of bifurcation theory to derive a low-dimensional model for laminar dispersion of a non-reactive solute in a tube. Unlike other techniques, the L-S formalism leads to an exact averaged model that is valid for all times and converging for arbitrary initial or inlet conditions, including point sources. We analyze the temporal evolution of the spatial moments of the solute and show that they do not have the centroid displacement or variance deficit predicted by the coarse-grained models derived by other methods. Finally, we show that laminar (Taylor) dispersion phenomena are better described in terms of hyperbolic models using either a single experimentally measurable convective mode or multiple concentration modes coupled through the concept of a transfer coefficient. We present and analyze a truncated hyperbolic model for the classical Taylor-Aris dispersion that has a larger domain of validity. We show that the hyperbolic model has no physical inconsistencies that are associated with the traditional parabolic model and can describe the dispersion process accurately.