Viscoelastic effects in non-Newtonian flows through porous media

Abstract

An analysis is presented for the flow of polymer solutions through a tube having a periodically varying diameter; this geometry is often used to represent a porous medium. It is found that if the stretch rate is assumed constant, the stress depends not only upon the Deborah number, but also on the ratio of the maximum to the minimum diameter. If the latter dimensionless group is not too large, no shear thickening is predicted to arise irrespective of the value of the Deborah number. These results explain the observed lack of superposition of curves of the product of the friction factor with the Reynolds number plotted against the Deborah number when different porous media are used. In addition, they also, in a qualitative sense, explain the experimentally observed maxima in the plots of the relative pressure drop as a function of the deformation rate.