Stress-controlled oscillatory flow initiated at time zero: A linear viscoelastic analysis

Abstract

In a recent article [Lee et al., J. Rheol. 63, 863–881 (2019)], the start-up of stress-controlled oscillatory flow both theoretically and experimentally was considered. In particular, they derive an analytical expression for the nonzero value around which the resulting strain (relative to the configuration before start-up) ultimately oscillates. Their derivation is based on the concept of recovery rheology, in which strain is decomposed into a sum of recoverable and unrecoverable components. Here, the same problem is treated based directly on the general theory of linear viscoelasticity. In this analysis, a transiently decaying contribution emerges that is not present in the Lee expression. This contribution is important since it gives an assessment of the time scale on which steady time-periodic oscillatory flow is established.