Precision Falling Sphere Viscometry

Terminal velocity data of spheres falling in a polyisobutylene (PIB) solution were obtained in sealed tubes. The tubes were easily invertible so that the fall of a sphere could be repeated as often as desired. The sealed tubes have the further advantage that degradation of the fluid is greatly reduced when compared to similar experiments in open tubes. Precisely reproducible velocities were obtained by careful temperature control and by measurement of the radial eccentricity. From such data it is possible to calculate the zero-shear viscosity, η0, provided the range of effective shear rates is sufficiently small. To acquire data in this range it is necessary to use spheres with small effective mass (actual mass less the mass of the displaced fluid). Spheres of various materials (nylon, ruby, steel, and carbide) were used, and their properties were checked by dropping them in a Newtonian fluid of known viscosity. In some cases the sphere properties were found to fall outside the tolerances specified by the manufacturers. A test of the absolute accuracy of the falling sphere method was made with a calibrated oil supplied by the Cannon Instrument Company. The viscosity measured with the spheres is within half a percent of the value specified. The data have been analyzed with formulae derived from perturbation calculations based on the theory of Rivlin-Ericksen fluids. These formulae include the effects of walls and fluid inertia. The third order theory predicts the initial departure from Stokes law. Ideally η0 can be obtained by extrapolation of data in the range of the third order theory. However, for the PIB solution this range appears not to exist or else it falls below that of most of the data. Since the above extrapolation was not feasible, data were taken in tubes of four sizes, and η0 was then deduced from the wall effect formulas. The value so obtained was found to be in good agreement with the values obtained from an extrapolation which assumes the apparent viscosity based on Stokes law varies exponentially with the shear stress. This type of limiting behavior contradicts the third order theory but describes the data remarkably well.