We present a theory for dynamic longitudinal dispersion coefficient (D) for transport by Poiseuille flow, the foundation for models of many natural systems, such as in fractures or rivers. Our theory describes the mixing and spreading process from molecular diffusion, through anomalous transport, and until Taylor dispersion. D is a sixth order function of fracture aperture (b) or river width (W). The time (T) and length (L) scales that separate preasymptotic and asymptotic dispersive transport behavior are T = b2/(4D m), where Dm is the molecular diffusion coefficient, and L = b4 / 48μDm ∂p / ∂x, where p is pressure and μ is viscosity. In the case of some major rivers, we found that L is ∼150W. Therefore, transport has to occur over a relatively long domain or long time for the classical advection-dispersion equation to be valid.


Civil, Architectural and Environmental Engineering


This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security (CFSES) at the University of Texas at Austin, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award DE-SC0001114. Additional support was provided by the Geology Foundation of the University of Texas.

Keywords and Phrases

Dispersions; Fracture; Advection-dispersion equation; Anomalous transport; Dispersive transport; Fracture apertures; Longitudinal dispersion coefficient; Longitudinal dispersions; Molecular diffusion; Molecular diffusion coefficient; Natural systems; Poiseuille flow; Taylor dispersion; Rivers; Advection-diffusion equation; Channel flow; Flow modeling; Fracture flow; River flow; Theoretical study; Viscosity

International Standard Serial Number (ISSN)

0094-8276; 1944-8007

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2012 American Geophysical Union (AGU), All rights reserved.

Publication Date

01 Mar 2012