Drag coefficients of spheres in poly(ethylene oxide) solutions

Article type: Research Article

Authors: Sanders, James V.

Affiliations: Naval Postgraduate School, Monterey, California

Abstract: The hydrodynamic properties of polymer solutions were studies by measuring the terminal velocities of steel spheres dropped in aqueous solutions of poly(ethylene oxide). Polymers used were WSR 301, WSR 205, WSR 35, and N 3000. Concentrations ranged from 10 weight parts per million to 2%. Sphere diameters ranged from 0.038 in. to 1.000 in. When the flow is characterized by a fully developed wake, significant drag reduction is obtained with the same polymers that are known to reduce turbulent skin friction and maximum drag reduction is achieved using minute amounts of polymer (100 ppm for WSR 301). It is postulated that the polymer reduces the diameter of the wake by delaying the separation of the laminar boundary layer. Under laminar flow conditions, the spheres exhibit a dual terminal-velocity. This behavior is explained by assuming that the fluid can exist in one of two different structures and the structure which exists when the fluid is at rest becomes unstable when a critical shear stress is exceeded. Calculations of this critical shear stress are in agreement with the value found for a similar transformation observed in viscometer measurements. The polymer solution studied can be described by means of a modified viscosity which depends only on the concentration and on whether the flow is associated with the fast or slow terminal velocity. Using this dual viscosity, a plot of drag coefficient vs Reynolds number results in a single curve for each type of polymer. This curve follows the Stokes solution to a higher Reynolds number than does the curve for a Newtonian fluid, The Reynolds number where the polymer leaves the Stokes solution moves to lower values as the molecular weight of the polymer decreases. Each curve approaches the same value of the drag coefficient at the higher Reynolds numbers. Only those polymers that have a dual viscosity have the ability to reduce drag.

DOI: 10.3233/ISP-1967-1415203

Journal: International Shipbuilding Progress, vol. 14, no. 152, pp. 140-157, 1967