## 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.