Phase angle between nonlinear viscoelastic

The deep-channel viscometer could also be adapted for measurement of the nonlinear interfacial rheological behaviour of the film [52]. In this case several small tracer particles are placed on the fluid interface at different radial positions and the angular velocities are determined from measurements of the period of revolution. When used to measure viscoelastic properties, the deep-channel viscometer is operated in an oscillatory mode, in which case the floor of the viscometer is oscillated sinusoidally. Simultaneous measurements of the phase angle between the surface motion and the oscillating motion of the bottom dish, and the surface-to-floor amplitude ratio, may permit determination of the viscoelastic properties of the fluid interface, presuming knowledge of an appropriate rheological model [52]. 

Recent studies show that nonlinear stress response can be represented in terms of a time-dependent phase angle difference 8 between the nonlinear elastic stress and viscoelastic stress. This approach appears to have an advantage over the numerical treatments used by previous workers because it provides some information about the reversible structural changes which occur during the cycle. However, such analyses require instruments which can subject the specimen simultaneously to two cyclic deformations of different amplitude and frequency. 

In Figure 5, the elastic stress curve falls between the strain curve and the viscoelastic stress curves during the contracting phase, showing that a part of the phase angle difference between the strain and viscoelastic stress is contributed by the nonlinear elasticity of the specimen. 

Phase Angle Difference between the Nonlinear Viscoelastic Stress and Nonlinear Elastic Stress. The phase angle difference 8 between the nonlinear viscoelastic stress and nonlinear elastic stress is defined by the relation ... 

---