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%.