A microstructural criterion for yielding: linking thixotropy and the yield stress

The concept of fluid “yield” is important but controversial since it was proposed. Traditionally, when the applied stress is larger than a critical value, the deforming solid began to show liquid-like behavior. This critical value of stress is named as the “yield stress,” which is well known to act as the criterion of yield. In this paper, we focused on the yield attributed to thixotropy, which was believed closely related to the micro-structure state of the thixotropic fluid (Bonn and Denn 2009 ). Instead of the “yield stress,” a critical state of the micro-structure, which is identified with parameter λ c , is defined as a new yield criterion. It was considered that the destruct process of the micro-structure will accelerate, as long as this critical state is achieved. This new yield criterion can be applied to thixotropic materials in both equilibrium and non-equilibrium states. It is consistent with the traditional one, while the thixotropic material is in an equilibrium state. Validation of this new yield criterion is carried out based on the Stokes’ second problem of Coussot fluid. When the oscillating period of the boundary wall is long enough to keep the thixotropic fluid in an equilibrium state, the distributions of unyielded regions identified according to the new yield criterion are consistent with those identified according to the traditional criterion. However, when the oscillating period is small, the traditional criterion could not be valid anymore, but the new yield criterion is still available.