Theory of an Oscillating Coaxial Cylinder Viscometer for Viscoelastic Materials

Abstract

A theory of an oscillating coaxial cylinder viscometer for viscoelastic materials is presented. The outer cylinder is fixed and the inner cylinder is suspended by a wire, the upper end of which is twisted sinusoidally. A viscoelastic material is placed in the annular space between the two cylinders. The inner cylinder oscillates with the same frequency, but with different phase. There must be relationships between the amplitude and phase lag of the inner cylinder and the dynamic shear modulus and dynamic viscosity of the viscoelastic material. As is well known, the relationships become very simple, if the inertia effect of the viscoelastic material is neglected. The inertia effect upon the relationships is investigated in this paper. It is shown that the exact treatment of the problem requires the use of Bessel functions and the relationships are extremely complicated. Following the method of Markovitz, formulae for the dynamic shear modulus and the dynamic viscosity are obtained to the first approximation. A new method of calculation has been devised to obtain the second approximation without using Bessel functions.