Multi-scale simulation of non-equilibrium phase transitions under shear flow in dilute polymer solutions

The phase transition of complex fluids is intrinsically a multi-scale problem. In this paper we propose a multi-scale two-fluid model that couples a coarse-grained microscopic method to the two-fluid framework for studying multi-phase fluids under shear flow. In this model the macroscopic viscoelastic stress is calculated by tracking the massive microscopic Brownian configuration fields in the simulation box. Both the macroscopic and microscopic equations are solved using a modified PISO iterative algorithm based on a finite volume discretization scheme. Our 2D numerical results reproduce numerous dynamic phenomena reported in literature and show that the theoretical model presented here could be a promising multi-scale approach to numerically study multi-phase viscoelastic fluids under flow.