Theoretical analyses and numerical simulations of the torsional mode for two acoustic viscometers with preliminary experimental tests

A rigorous analysis of the torsional modes in both a cylindrical wave guide and the associated static viscous fluid field has been conducted from the solid and the fluid wave equations and the coupled boundary conditions. As a result, two acoustic viscometer models, along with four independent equations connecting the density and the viscosity of the fluid with the attenuation and the phase velocity of the torsional wave in the wave guide, have been developed. The analysis shows that the product of the viscosity and the density of the fluid can be measured from the end reflection coefficient of the torsional wave in the wave guide and that both the viscosity and the density can be determined simultaneously from either the phase velocity or the attenuation of the torsional wave in a single cylindrical wave guide. For the simultaneous measurements of the viscosity and the density, the independent equations have to be solved numerically, for example, using Matlab (The MathWorks, Natick, MA), given either the attenuation or the phase velocity in the wave guide that is surrounded by the fluid. To demonstrate the technical feasibility, numerical simulations have been conducted to discern viscosity, phase velocity, and density, all versus attenuation, at different frequencies, and with variable dimension of a molybdenum rod, so that both the advantages and the disadvantages of the simultaneous measurements can be explored. In the end, to test the two models, preliminary experiments on two viscous standards were conducted at 23 degrees C, and good agreements have been achieved between the viscosities measured from both models and for both standards.