IMA Postdoc Seminar (March 18, 2008)

Speaker: Kevin Dorfman (University of Minnesota)

Title: Taylor-Aris dispersion in entropy barriers

Abstract: Transport phenomena in channels with slowly varying cross-sectional widths has been of interest in the recent physics literature owing to the concept of an "entropy barrier." Explicitly, variations in the channel cross-sectional changes the number of states available to a Brownian particle contained therein, thus leading to an entropic driving force in the direction of the width gradient. While purely diffusive transport in entropy barriers is well understood via modified versions of the so-called Fick-Jacobs equation, further heuristic modifications of the Fick-Jacobs approach to convection-diffusion processes catastrophically fail as the driving force increases. We have shown that, for periodic channels, the convection-diffusion process can be modeled using a long wavelength asymptotic formulation of generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media. After reviewing the failures of the Fick-Jacobs equation and the foundations of macrotransport theory, I will present our results for the particle mean velocity and dispersivity of Brownian particles through entropy barriers under the influence of constant forces, electrophoresis, electroosmosis and pressure-driven flow.