(717b) Mathematical Aspects of Modeling the Rheology of Complex Material

Recent work using small angle neutron scattering under flow has identified the existence of a microstructure that is dependent on flow conditions in soft colloidal systems. Additionally, over the last twenty years, a large number of empirically based, thixotropic rheological models has been developed that involve, albeit phenomenologically, a single scalar structural parameter, lambda. These models involve the combination of a lambda-dependent decomposition of the shear stress to an elastic and a viscous contribution with a relaxation-based evolution equation for lambda. The rich behavior of the soft colloidal systems is primarily due to the interaction of the structure and the hydrodynamic force and this can be particularly enhanced applied through in transient flow, and/or large amplitude oscillatory shear flow. Additionally there is an analogous family of viscoelastic models, starting with the Oldroyd-8 family that has successfully modeled shear-thinning behavior. More recently there has been “unified” approaches in literature that attempt to combine the best features of both the viscoelastic and thixotropic modelling.

To successfully model thixo-elastic-visco-plastic (TEVP) complex material systems each modelling technique employs between 2 – 4 ODEs, and several algebraic equations, meaning that any optimization strategy attempting to fit models to rheological data must involve robust, and accurate ODE solvers. Due to the stiffness of the models, the ODE solvers must seamlessly be able to incorporate implicit ODE solution techniques. In addition we will discuss several other viscoelastic models like the recent work of Horner et al. (2018), de Souza Mendes and Thompson and the Blackwell and Ewoldt model using a modified Jeffrey’s model with a structural, thixotropic parameter, whose evolution is modeled with an ordinary differential equation in time.

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