Practical application of thixotropic suspension models

Abstract

The practical implementation of several thixotropic rheological models has been evaluated for a prototypical industrial application. We have studied the ability of the models to predict both steady and transient rheology of a suspension of alumina particles and the suitability of those models for full transient finite element calculations. The constitutive models for thixotropic materials examined include the Carreau-Yasuda model and first and second-order indirect structure models. While all of these models were able to predict the shear-thinning behavior of the steady viscosity, the first and second-order structure models were also able to capture some aspects of the transient structure formation and fluid history. However, they were not able to predict some more complex transient behavior observed in step shear experiments. For most thixotropic suspensions, the time constant required to form structure is longer than the time constant to break it down. For this suspension, the time constant at a given shear rate was also dependent on the previous shear rate. If the previous shear rate was high, the time required to reach equilibrium was longer than if the previous shear rate was lower. This behavior was not captured by the simple initial structure dependence in the previous models. By adding an additional dependence on the initial suspension structure, the prediction of the transient rheology was substantially improved while maintaining an excellent agreement with the steady shear viscosity. Finite element results are presented for extrusion of a suspension to form a fiber. This model two-dimensional problem contains many of the same complexities as practical three-dimensional mold filling simulations (i.e., nonviscometric and mobile free surface). Our results show that these direct structure models exhibit oscillations near the stick-slip point in finite element calculations similar to many polymeric constitutive equations, but are otherwise suitable for implementation in complex industrial modeling applications.