(391b) A Thermodynamically Consistent, Microscopically-Based Model of Aggregating Particle Suspension Rheology

In this work, we outline the development of a thermodynamically consistent, microscopically based, model for a suspension of aggregating particles under arbitrary inertia-less deformation. Aggregating suspension rheology is influenced by the aggregation and breakage processes at the mesoscale that results in complex time-dependent and non-linear behaviors, including thixotropy, viscoelasticity, and yield stress. 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] developed a population balance-based constitutive relation for capturing the kinetics of aggregation and breakup of particles; however, as a result of their empirically constructed stress tensor this model is only limited to shear flows.

We show how the combination of a population balance-based description of the aggregating particle microstructure along with the use of the single generator bracket description of nonequilibrium thermodynamics [2] leads naturally to the formulation of the model equations. Notable elements of the model are: a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation & breakup processes, and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting model is evaluated in steady and transient shear and elongational flows and shown to offer predictions that are consistent with the observed rheological behavior of typical systems of aggregating particles. Additionally, the thermodynamic consistency of this model is illustrated through entropy production. We also compare the entropy production between various dissipative phenomena involved in a flow process.

(This work is support by National Science Foundation award CBET - 1804911)

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. Beris, A.N. and B.J. Edwards, Thermodynamics of Flowing Systems: with internal Microstructure. 1994: Oxford University Press.