Eur. Phys. J. B 6, 225-231 (1998)
https://doi.org/10.1007/s100510050545

Tracer dispersion in power law fluids flow through porous media: Evidence of a cross-over from a logarithmic to a power law behaviour

¹ Unité de Phytopharmacie et Médiateurs Chimiques, INRA, route de Saint-Cyr, 78026 Versailles Cedex, France
² FAST (UMR CNRS n° 7608.) , Btiment 502, Campus Universitaire, 91405 Orsay Cedex, France

Corresponding author: ^a chaplain@versailles.inra.fr

Received: 22 July 1997
Accepted: 2 July 1998
Published online: 15 November 1998

Abstract

An analytical model is presented to describe the dispersion of tracers in a power-law fluid flowing through a statistically homogeneous and isotropic porous medium. The model is an extension of Saffman's approach to the case of non-Newtonian fluids. It is shown that an effective viscosity depending on the pressure gradient and on the characteristics of the fluid, must be introduced to satisfy Darcy's law. An analytical expression of the longitudinal dispersivity is given as a function of the Peclet number Pe and of the power-law index n that characterizes the dependence of the viscosity on the shear rate . As the flow velocity increases the dispersivity obeys an asymptotic power law: . This asymptotic regime is achieved at moderate Peclet numbers with strongly non-Newtonian fluids and on the contrary at very large values when n goes to 1 ( for n=0.9). This reflects the cross-over from a scaling behaviour for towards a logarithmic behaviour predicted for Newtonian fluids (n=1).