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. U sually, an explicit hydrodynamic model based on a simple geometry is r equired to deduce viscosity from the transfer function of an oscillati ng body such as a vibrating wire or a quartz torsion crystal. However, at low Reynolds numbers the transfer function of any immersed oscilla tor depends on the fluid's viscosity only through the viscous penetrat ion depth delta=(2 eta/rho omega)(1/2). (Here eta and rho are the flui d'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 ran ge. Even an oscillator of poorly known geometry can be characterized o ver 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 flui d with high accuracy by varying the frequency so that the penetration depth falls within the characterized range. In the present work, hydro dynamic similarity was demonstrated with a highly damped viscometer co mprised 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 tem perature was varied between 25 and 60 degrees C. The corresponding var iation of the viscosity was 50%.