Vibrating Fluid Densimeters: A Solution to the Viscosity Problem

The natural frequency of a resonator immerged in a fluid is density dependent. A major disadvantage of densimeters based on this principle is their poor accuracy for viscous fluids. We solve this difficulty by making an automatic control of the physical phase at which the resonator oscillates. This is done by a modulation technique which, additionally, gives the quality factor and, therefore, the viscosity in digital form. To discover what this physical phase should be and what the factors affecting it are, we made a detailed analytical and numerical study of the vibration of resonators in a viscous fluid. Two densimeters have been built using these results. Their density x viscosity span is 10-100 times larger than that of commercially available instruments of the wholly immersed type. This instrument has achieved an accuracy of ± 0.1 percent.