Multiscale rheological constitutive relations for aggregating suspensions

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University of Delaware
Aggregating colloidal suspensions can be encountered in many materials; examples include food products, biological fluids, printer inks, paints, and slurries. Describing the rheology of these suspensions remains challenging as their flow behavior directly connects to the mesoscale structure and aggregation kinetics. Transient flows in such suspensions show complex dynamics due to yield stress, viscoelasticity, and flow history dependence, i.e., thixotropy, and as a result can be classified as thixotropic elasto-viscoplastic (TEVP) materials. ☐ In the first part, an improved population balance-based rheological constitutive framework for polydisperse aggregating suspensions is derived by incorporating detailed models for orthokinetic and perikinetic aggregation and shear breakage processes. The framework accounts for critical properties such as dynamic arrest, viscoelasticity, kinematic hardening, thixotropy, and yield stress to generate a full range of TEVP responses. The model connects the rheological response to the structural descriptors such as the size distribution of agglomerates, mean sizes, fractal dimension and agglomerate volume fraction. Predictions are compared against a wide range of shear rheology measurements data for model thixotropic suspensions of fumed silica and carbon black, including large amplitude oscillatory shear (LAOS), as well as ultra-small angle neutron scattering under steady shear (Rheo-uSANS). A coarse-grained version of this model is also applied to understand blood rheology and we find that a population balance-based constitute model for blood is able to capture its characteristic transients for a wide range of physiologically relevant flow rates. ☐ The next contribution discusses how the combination of a population balance-based description of the aggregating particle microstructure and the use of nonequilibrium thermodynamics leads to the formulation of a model for fluid flow. The most significant contribution is the incorporation of specific measures of microstructure, such as moments of size distribution, into a thermodynamically consistent macroscopic continuum model of thixotropy and viscoelasticity. This approach enables a population balance-based model of the aggregation and breakage processes, as well as a conformation tensor-based viscoelastic description of the agglomerate network. The model is evaluated for shear and elongational flows offering consistent predictions for typical systems of aggregating particles. This first-principles, multiscale modeling approach resolves long-standing issues such as thermodynamic inconsistency and lack of connection to the fluid microstructure when describing the dynamics of aggregating suspensions. Furthermore, it has the potential to represent aggregating suspensions that are subjected to arbitrary three-dimensional flows. ☐ Finally, we extend the coarse-grained population balance-based constitutive model to include the ability to describe concentration inhomogeneities, which are often observed in particulate suspensions, in addition to the thixotropic effects. The description of the dynamics is further explored through numerical simulations of steady state and transient pressure-driven pipe flows. Although the capabilities of this modeling paradigm can be illustrated using these idealized flow simulations, additional microscopic theories, experimental measurements, and model refinement are needed for the full realization of this approach. ☐ The outcomes of this thesis establish a connection, for the first time, between the thermodynamically consistent modeling of rheological behavior of flow-sensitive aggregating suspensions at the continuum-level and a microscopically relevant, independently measured underlying microstructure. It simultaneously offers a systematic theoretical foundation to enable the development of more complex models that incorporate insights from novel experiments and microscopic simulations.
Aggregating suspensions, Non-equilibrium thermodynamics, Population balance modeling, Rheology, Thixotropy, Viscoelasticity, Rheological constitutive