(326c) A Multiscale Tensorial Approach for Modeling the Rheology of Thixotropic Aggregating Suspensions

Aggregating suspensions exhibit complex rheological characteristics including shear-thinning, viscoelasticity, yield-stress, and thixotropy. Among these, thixotropy remains the most challenging aspect to account for as it depends on the kinetics of structure formation at the mesoscale. Numerous models have been proposed over the years for shear rheology, primarily using a structure kinetics approach that tracks the extent of structure formation using a scalar structure parameter. Mwasame et al. [1] have shown that population balances can be incorporated in the rheological modeling as they accurately capture the aggregation and breakage kinetics in shear flow and replace some empiricism in the structure kinetics modeling. A full tensor description remains to be explored rigorously, but a promising framework has been proposed by Stephanou and Georgiou [2], where the authors derive a constitutive model based on non-equilibrium thermodynamics (NET) [3] by including a conformation tensor to describe the structure and thixotropic effects in a thermodynamically consistent fashion.

In this work, we show that previously established rheological model based on population balances, along with a polydisperse description of suspension viscosity, can be recast such that the kernels and constitutive models become consistent with the scaling in the NET framework. Specifically, we address the breakage kernel, which has been shown to scale as a function of stress for both shear and extensional flows [4] such that resulting tensorial model can be used to describe full three-dimensional macroscopic flows. The model predictions for both simple shear and uniaxial extensional flow are compared against the existing models. As the non-equilibrium thermodynamics offers a more consistent tensor description, we also explore how the model can capture inhomogeneities and effects such as stress-induced migration.

References

1. Mwasame, P.M., et al., A constitutive equation for thixotropic suspensions with yield stress by coarse-graining a population balance model. AIChE Journal, 2017. 63(2): p. 517-531.
2. Stephanou, P.S. and G.G. Georgiou, A nonequilibrium thermodynamics perspective of thixotropy. J. Chem. Phys., 2018: p. 11.
3. Beris, A.N. and B.J. Edwards, Thermodynamics of Flowing Systems: with internal Mircrostructure. 1994: Oxford University Press.
4. Ren, Z., Y.M. Harshe, and M. Lattuada, Influence of the Potential Well on the Breakage Rate of Colloidal Aggregates in Simple Shear and Uniaxial Extensional Flows. Langmuir, 2015. 31(21): p. 5712-5721.