Effects of molecular characteristics of polymers on drag reduction

Turbulent measurements in capillary tubes and in pipes were made on nonpolar solutions of seven polymer species, three at more than one molecular weight, over wide concentration ranges. A critical concentration, Cc, was taken as the minimum concentration for disappearance of the turbulence transition region. Above this concentration, friction factor‐generalized Reynolds number data show only a gradual deviation from extension of the laminar line. Cc increases with tube diameter and decreases with molecular weight. The critical dimensionless volume friction Cc [η] is less dependent on molecular weight. The levels of Cc [η] for different polymer species in a given tube show marked differences which are related to β, the molecular rigidity parameter. Low β values, or high flexibility, are associated with low Cc [η] values. Available data for Cc [η] in good and in poor solvents show little solvency effect. Polymer samples of low m′, the ratio of the polymer molecular weight to the critical tanglement molecular weight of the polymer, give solutions with little or no drag‐reducing capacity, even those with low β values. Samples must have m′ values of 50 or more to show significant drag reduction. This allows prediction of the minimum useful molecular weights for drag reduction for any polymer species. For solutions above Cc, all of these data and literature data (for aqueous and nonaqueous systems with a wide range of n′ values) fit a single f/fpv versus generalized Reynolds number relationship.