Characteristic mechanical impedance of rheometers with axial symmetry. A theoretical and numerical analysis

Abstract

The strain wave field generated in a linear viscoelastic medium confined between two infinitely large parallel planar surfaces, one fixed and the other oscillating sinusoidally in its own plane, has been well accounted for (Schrag, 1977). Here, we describe the strain wave field generated between a cylinder and a coaxial surrounding tube, both infinitely long. The tube or the cylinder remains stationary while the complementary component undergoes sinusoidal angular displacements around the common symmetry axis. This geometry is frequently used in dynamic rheometers. Both exact analytic expressions for the characteristic mechanical impedance and series expansions valid close to gap loading or surface loading conditions are provided. The exact analysis is valid for arbitrary gap width, cylinder radius, and linear viscoelastic properties of the medium within the rheometer gap. We also show how standard, modern desktop computers can be used to rapidly obtain accurate numerical values of the characteristic mechanical impedance of rheometers with axial symmetry using the exact analytic expressions.