A multi-scale method for complex flows of non-Newtonian fluids

TL;DR

This paper presents a novel multi-scale simulation method combining micro-scale molecular dynamics with macro-scale continuum equations to accurately model complex non-Newtonian fluid flows, emphasizing the importance of local flow-dependent material response.

Contribution

The paper introduces a data-driven, model-free multi-scale approach that incorporates local flow type dependence, improving the simulation of polymeric fluid dynamics.

Findings

The method accurately predicts complex polymeric fluid flows.

Local flow-dependent stress calculation improves simulation fidelity.

Extensional rheology is crucial for realistic flow modeling.

Abstract

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.