(448ai) A Population Balance Based Model to Describe the Rheology of Thixotropic Suspensions with a Yield Stress

A systematic development of an evolution equation to describe the structural dynamics in a thixotropic dispersion is presented. Ideal thixotropy is defined as the continuous decrease of viscosity with time when flow is applied to a sample that has been previously at rest and the subsequent recovery when flow is discontinued [1]. Yield stress is also frequently observed in thixotropic suspensions [2] presenting additional challenges in modeling these systems. At the heart of these modeling efforts is the complex effects of flow on the microstructure such as aggregation and breakage that give rise to thixotropic behavior. In this work, population balance modeling is adopted as a framework to describe the microstructure evolution that underlies thixotropy. A key advantage of using population balances is the incorporation of parameters in the aggregation and breakage kernels with a clear physical meaning that can be connected to specific properties of the colloidal aggregates through independent experiments.

Starting from the population balance equation for colloidal dispersions, a monodisperse closure rule is used to develop a coarse grained structure evolution equation. Moving beyond previous efforts, important modifications are made to account for dynamic arrest of aggregation kinetics at the onset of the yield stress and to enforce a minimum particle size below which breakage is not feasible. The resulting population balance model is coupled to a simple constitutive equation to complete the model allowing us to predict the effects of aggregation and breakage processes on the rheology. The overall model provides a reasonable representation of experimental data for a model thixotropic suspension available in the literature [3]. The resulting model is able to capture the dominant thixotropic timescales for unidirectional shear flows in step-up and step-down transient experiments. In addition, predictions of rheology under large amplitude oscillatory shear (LAOS) and flow reversal experiments are also compared to experimental measurements. The coarse grained model equations are also compared to prevalent structure kinetics models and shown to be distinct, emphasizing the novelty of using a population based model as a basis for thixotropic suspension modeling.

References

[1] Mewis J,Wagner NJ. Colloidal suspension rheology. Cambridge University Press 2012.

[2] Hoffmann H, Rauscher A. Aggregating systems with a yield stress value Colloid and Polymer Science. 1993; 271:390â??395

[3] Armstrong MJ, Beris AN, Rogers SA, Wagner NJ. Dynamic shear rheology of a thixotropic suspension: Comparison of an improved structure-based model with large amplitude oscillatory shear experiments Journal of Rheology. 2016; 60:433-450.