HYDRODYNAMIC SIMILARITY IN AN OSCILLATING-BODY VISCOMETER

Hydrodynamic similarity can be used to calibrate simply and accurately an oscillating-body viscometer of arbitrarily complicated geometry. Usually, an explicit hydrodynamic model based on a simple geometry is required to deduce viscosity from the transfer function of an oscillating body such as a vibrating wire or a quartz torsion crystal. However, at low Reynolds numbers the transfer function of any immersed oscillator depends on the fluid's viscosity only through the viscous penetration depth delta=(2 eta/rho omega)(1/2). (Here eta and rho are the fluid's viscosity and density and omega/2 pi is the oscillator's frequency.) This hydrodynamic similarity can be exploited if the oscillator is overdamped and thus is sensitive to viscosity in a broad frequency range. Even an oscillator of poorly known geometry can be characterized over a range of penetration depths by measurements in a fluid of known eta and rho over the corresponding range of frequencies. The viscosity of another fluid can then be compared to that of the calibrating fluid with high accuracy by varying the frequency so that the penetration depth falls within the characterized range. In the present work, hydrodynamic similarity was demonstrated with a highly damped viscometer comprised of an oscillating screen immersed in carbon dioxide. The fluid's density was varied between 2 and 295 kg . m(-3) and the fluid's temperature was varied between 25 and 60 degrees C. The corresponding variation of the viscosity was 50%.