Relaxation effects in the flow of dilute polymer solutions through tubes and granular beds

The flow of dilute polymer solutions in water, through tubes and granular beds, has been compared with the flow of water and of glycerol solutions and common salt solutions through the same tubes and granular beds. Particular attention was paid to the value of the Reynolds number ( Re )prime at which the Hagen-Poiseuille law broke down for tubes and at which Darcy's law broke down for beds. The polymer solutions used were: 0·005, 0·01, 0·025 and 0·05% (w/w) polyacrylamide in water and 0·005% (w/w) `Cellofas' (a sodium carboxymethyl cellulose) in water. Two tubes were used; one was 0·30 m long with an internal diameter of 3·68 mm and the pressure difference was measured across it; the other was 0·70 m long with an internal diameter of 4·08 mm and the pressure difference was measured across the last 0·30 m. Two granular beds were made up, one with glass beads of diameter 2·06 mm, the other with glass beads of diameter 1·15 mm. Most experiments were performed at 25°C, but some were done at 15°C and others at 35°C so that the influence of temperature on the results could be studied. Destabilization occurred in the flow of polyacrylamide solutions through the tubes and the beds; that is ( Re )prime (polyacrylamide) < ( Re )prime (water). However, stabilization occurred in the flow of Cellofas solutions. Drag reduction occurred in the flow of polyacrylamide solutions through the tubes but not in the flow through the beds; no drag reduction occurred in the flow of the Cellofas solutions. The destabilization can be attributed to the release of energy stored in stretched molecules in the flow, and drag reduction can be attributed to energy absorbed by the molecules thus damping down some turbulent eddies.