FE/MCT: Macroscopic CFD Simulations of Glass-Forming Fluids using Material Laws from Microscopic Theory

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We develop a multi-scale description of the flow of glass-forming fluids. To this end we combine computational fluid dynamics (CFD) simulations with microscopic theory to provide material laws (constitutive equations) of the nonlinear response of the strongly viscoelastic fluid. The integration-through transients (ITT) formalism is used to derive generalized Green-Kubo relations that link microscopic correlation functions to the coarse-grained fluid stress tensor far from equilibrium. The mode-coupling theory of the glass transition (MCT) is used together with ITT to provide a microscopically justified closed material model. The resulting constitutive equations are characterized by pronounced time-history integrals. Advanced Finite Element method (FEM) schemes are realized in order to deal with such integral constitutive equations on the level of the Navier-Stokes equations, to be able to address the pronounced transients and memory effects in the flow of glass-forming fluids. Using these tools, we address the slow deformation of glasses under applied load and the emergence of history-dependent material properties of amorphous soft-matter materials that arise when the material is prepared under different processing conditions.