A molecular approach to predicting the onset of drag reduction in the turbulent flow of dilute polymer solutions

Abstract

The significant variables in drag reduction have been separated into two classifications, flow variables and solution variables. A theory has been offered which permits prediction of the critical Reynolds number in the turbulent flow of polymer solutions. The theory states that the relaxation time of the polymer molecule in solution equals a characteristic flow time for the tube in question at the point of incipient turbulent suppression. This is equivalent to a Deborah number near unity. Reasonable agreement has been shown between the experimental results of this investigation and predictions of flow rates based on this theory for the presence or absence of drag reduction and for the onset of turbulence suppression. No adjustable parameters were used in the analysis. The theory seems to be applicable at values of C[η] greater than 0·10. The theory leads to the prediction that the wall shear rate at the point of incipient turbulence suppression decreases as the product of reduced viscosity, molecular weight and solvent viscosity increases. Thus for large effects this product should be made as large as possible. Friction factor measurements in both good and poor (Theta) solvents showed that the maximum drag reduction in the poor solvent was only about 40% of that in the good solvent at similar flow rates in the same tube. Thus the effect of an expanded configuration of the polymer molecule in solution is to increase drag reduction.