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This communication presents an extension of an earlier study by Christopher and Middleman of the applicability of a non-Newtonian generalization of the Blake-Kozeny equation to the laminar flow of non-Newtonian polymer solutions through porous media. The earlier work, done with dilute aqueous solutions of carboxymethylcellulose, indicated that the model put forth correlated data with an average error of 18 per cent and a standard deviation of the friction factor of 0.21 over a range of three orders of magnitude in a modified Reynolds number.
A survey of the literature available at that time indicated some evidence of viscoelastic effects, in contrast with the conclusions drawn by Christopher and Middleman it was decided to extend the earlier study by examining a more elastic fluid, polyisobutylene dissolved in toluene. In addition, data were obtained for tubes packed with sand, and for tubes packed with binary mixtures of glass spheres. We still fail to see viscoelastic effects.
The basic experimental techniques, and the methods of reducing and correlating the data, are as described by Christopher and Middleman and in more detail by Christopher and by Gaitonde. Polyisobutylene [PIB L-100, Enjay Co.] solutions in toluene were run at 25.0 deg C. Power-law parameters were obtained from capillary viscometry performed over a range of shear rates corresponding to the shear rates achieved in the porous medium. Table 1 shows the solution properties, including the zero-shear viscosities of the solutions and the viscosity average molecular weight of PIB L-100.
Fig. 1 shows the friction factor-Reynolds number correlation of the data obtained using tubes packed with glass spheres of a narrow size range. The data are correlated with an average error of 9.8, per cent and a standard deviation of 0.14 by