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

我们开发了玻璃形成流体流动的多尺度描述。为此，我们将计算流体力学(CFD)模拟与微观理论相结合，给出了强粘弹性流体非线性响应的材料定律(本构方程)。通过瞬变积分(ITT)理论推导了广义格林-久保关系，将微观关联函数与远离平衡的粗粒流体应力张量联系起来。玻璃化转变的模耦合理论(MCT)与ITT相结合，提供了一个微观上合理的闭合材料模型。由此得到的本构方程具有明显的时程积分特征。实现了先进的有限元格式，以便在Navier-Stokes方程水平上处理这种积分本构方程，从而能够处理玻璃形成流体流动中明显的瞬变和记忆效应。使用这些工具，我们解决了玻璃在外加载荷下的缓慢变形，以及非晶软物质材料在不同工艺条件下制备时出现的与历史相关的材料特性。

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.