Data-driven and physics-aware microstructural modeling of flowing complex fluids

Real flows used to process complex materials are almost always a mixture of rotational and extensional deformations that has a profound influence on the final microstructure of the material. In applications such as flexible electronics, this microstructure is key to performance. In contrast to flows generated in rheometers, real processing flows are never viscometric. Furthermore, we lack accurate first-principles models to relate flow, microstructure, and stress for many (most) complex fluids. Finally, spatially resolved microstructure measurements (i.e. scattering) are rarely available in complex flows. The present work uses new advances in experimental methodology and machine learning to circumvent these limitations. On the experimental side, we take advantage of scanning small-angle X-ray scattering (sSAXS) measurements in a fluidic four-roll mill (FFoRM). The FFoRM-sSAXS approach provides a large data set of microstructural measurements along diverse 2D Lagrangian deformation trajectories. We propose a machine learning framework in which FFoRM-sSAXS data is used to train a model which can predict the microstructural evolution of the fluid for an arbitrary deformation (velocity gradient tensor) history input. We first use autoencoders to learn a highly accurate reduced-order representation of the microstructure from scattering data. We then learn the time evolution of the microstructure in the reduced representation using a neural ODE framework that is constructed to automatically satisfy the key symmetry of microstructural evolution: material frame indifference. Finally, we learn a transformation from the state data embedded in the scattering intensity to the stress exerted on the fluid. The framework is tested with synthetic data for suspensions of Brownian rigid rods, using CFD results for flow kinematics and Brownian dynamics simulations for the microstructural evolution.