Abstraet-An exact analysis of the reservoir effect for the Row of a Newtonian fluid in a parallel-plate rotational viscometer is presented. The determination of the velocity field and the torque involves the solution of a mixed boundary value problem. The analysis makes it possible to obtain accurate values of the viscosity of a fluid from torque measurements taken using a sample reservoir. The predictions of the exact solution are in good agreement with experimental data obtained using the parallel-plate geometry with a sample reservoir.
INTRODUCIION
Rotational viscometers provide a convenient method of measuring the viscosities of Newtonian fluids and the viscosities of non-Newtonian materials at low shear rates. The utilization of rotational rheometers is sometimes facilitated by the inclusion of a sample reservoir (Cheng, 1968; Olabisi and Williams, 1972; Crawley and Graessley, 1977) for the cone-and-plate and parallel-plate geometries. The use of the liquid reservoir makes it possible to obtain data on lowviscosity materials. Furthermore, the analysis of edge effects in the viscometer is effectively not complicated by free surface effects (Griffiths and Walters, 1970; Walters, 1975). On the other hand, installation of a reservoir leads to an additional contribution to the torque caused by the increased frictional drag of the reservoir. This additional torque contribution is of course not accounted for in the simple analysis of the flow field for a rotational viscometer. Consequently, it is not in general possible to use the torque data taken with a reservoir to obtain accurate values of the viscosities of Newtonian fluids or of the viscosities of non-Newtonian materials in the zero shear rate limit. The objective of this paper is to present an exact analysis of the reservoir effect for the flow of a Newtonian fluid in a parallel-plate geometry in the absence of inertia. This analysis makes it possible to obtain accurate values of the viscosity of a fluid from torque measurements taken using a reservoir. The predictions of the exact solution to the problem are compared with experimental data obtained using the parallel-plate geometry with a sample reservoir.