Simultaneous Measurement of Viscosity and Density with an Oscillating-Disk Instrument: The Effect of Fixed Plates

The period and damping of the free motion of a body oscillating in a fluid depend on the fluid's viscosity and density. Commonly, a working equation which expresses the damping as a function of the viscosity and density is solved for the viscosity, the damping being measured and the density being treated as an independently supplied parameter. Another working equation exists for the period, and, in general, the period depends on a combination of the viscosity and the density which is linearly independent of the combination that appears in the damping equation. It is, therefore, in principle, possible to determine both the viscosity and the density by a simultaneous solution of the two coupled working equations, since the period also is measured. In this paper, the working equations that describe the oscillating-disk viscometer are reviewed and their simultaneous solution is considered. The effect of fixed plates symmetrically located above and below the oscillating disk is of specific interest. The paper's main result is that fixed plates can dramatically increase the independence of the damping and period working equations, so that it becomes indeed feasible to determine the viscosity and the density of a fluid simultaneously from the damping and period of oscillating motion. A price is paid, however, because the instrument's working equations when plates are present have multiple solutions. Under special conditions, these multiple solutions can coalesce, and then one can only deduce the viscosity from the damping equation if the density is known a priori.