Abhishek M. Shetty and Michael J. Solomon. Chemical Engineering, University of Michigan, 2300 Hayward Street, 3074 H.H Dow Bldg, Ann Arbor, MI 48109
Poly(ethylene oxide) (PEO) is used in wastewater treatment, oil recovery, drilling fluid stabilization, as an additive in pharmaceutical formulations and in drag reduction. Aqueous solutions of PEO are in a state of molecular aggregation, which is hypothesized to be the source of their anomalous rheology and high drag reduction capability. Validation of models for prediction of the viscoelastic behavior of PEO solutions is hindered by the lack of appropriate experimental data. In this work, we apply methods of dynamic light scattering (DLS) and fluid mechanics to quantitatively establish the role of aggregation in the turbulent drag reduction of high molar mass poly(ethylene oxide) solutions. By means of DLS, we show that the aggregation state of dilute solutions of high molar mass PEO WSR-301 (Mw ~ 4 x 106 g/mole) can be manipulated by addition of the chaotropic salt guanidine sulfate (GuS) or the divalent salt magnesium sulfate (MgSO4). In aqueous solution, we find Γ~ q 2.8± 0.1, where Γ is the relaxation rate and q is the scattering vector. This scaling is consistent with internal motions of a large coil or aggregate. The above results provide molecular level evidence that support earlier rheological inferences (Tirtaatmadja et al., Physics of Fluids, 18, 043101, 2006) that the structure of WSR-301 at ~ 10-100 ppm concentrations is not consistent with the picture of an isolated polymer coil in a dilute solution. Addition of salt progressively decreases the scaling to Γ~ q 2.0± 0.1(at 0.5M) consistent with center of mass diffusion of isolated coils. We furthermore find that manipulating the aggregation state of PEO in this way shifts the critical condition for onset of turbulent drag reduction at dilute concentrations by a factor of 2.5. This critical condition is inversely proportional to the viscoelastic relaxation time of the polymer solution. The implication is that the aggregation state and the turbulent drag reduction behavior of PEO are strongly correlated. This correlation definitively confirms prior speculation (Dunlop et al., Nature, 249, 1974) that the high molar mass PEO commonly used in literature studies of turbulent drag reduction is in a state of aggregation.