Simulation of polymer melts using Radial Basis Function and Brownian configuration field method

Simulation of polymer melts using Radial Basis Function and Brownian configuration field method

Polymer melts are viscoelastic fluids and extremely complex fluids due to the existence of very high density of polymer molecules. Polymer melt rheology aims to understand and quantify the viscous and elastic properties of a polymer. In this work, the Integrated Radial Basis Function based Brownian configuration fields (IRBF - BCF) is further developed to simulate the dynamic behaviours of polymer melt flows. For the method, a polymer melt is governed by the macro-micro governing equations, which is processed for the solution of the primitive variables (velocity and pressure fields, and the kinetic behaviours of polymer melt for the flow’s stress tensor). In this paper, polymer melt is modelled using "single-segment" reptation models or tube models where the polymer stress is averagely computed from an ensemble of thousands of tube segments at each grid point. The use of a Cartesian grid-based 1D-Integrated RBF (IRBF) approximation not only helps to avoid any complex meshing process but also to ensure a fast convergence rate for the solution of macro-micro governing equations. Furthermore, the use of BCF maintains the correlation of polymer stress fields in the simulation and hence enhances the numerical stability of the method. As an illustration of the method, the start-up Couette polymer melt flow and the polymer melt flow over a cylinder in a channel are investigated using four classical reptation models including the Doi-Edwards, Curtiss-Bird, Reptating Rope and Double Reptation models.

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