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.
L. Wang et al., "Theory for Dynamic Longitudinal Dispersion in Fractures and Rivers with Poiseuille Flow," Geophysical Research Letters, vol. 39, no. 5, American Geophysical Union (AGU), Mar 2012.
The definitive version is available at https://doi.org/10.1029/2011GL050831
Civil, Architectural and Environmental Engineering
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)
Article - Journal
© 2012 American Geophysical Union (AGU), All rights reserved.
01 Mar 2012