Analysis of the oscillating-cup viscometer for the measurement of viscoelastic properties

We present calculations for the analysis of torsional oscillator measurements of the mechanical properties of viscoelastic fluids and solids. The usefulness of this measurement technique is analyzed and discussed in detail. A right circular cylinder is chosen as a well-defined geometry for accurate calculations. Exact expressions for calculating the fluid viscosity and elasticity from the oscillator response in this geometry are presented and discussed. We believe this to be the first exact treatment of the problem. Simplified expressions valid for certain special cases are presented for ease of calculation and compared to those previously obtained. The range of operation and optimal oscillator designs for general applications are suggested. Finally, use of this technique for measuring the frequency dependence of viscoelastic properties is also examined.