Numerical method for hydrodynamic transport of inhomogeneous polymer melts

We introduce a mesoscale method for simulating hydrodynamic transport and self assembly of inhomogeneous polymer melts in pressure driven and drag induced flows. This method extends dynamic self consistent field theory (DSCFT) into the hydrodynamic regime where bulk material transport and viscoelastic effects play a significant role. The method combines four distinct components as a single coupled system, including (1) non-equilibrium self consistent field theory describing block copolymer self-assembly, (2) multi-fluid Navier-Stokes type hydrodynamics for tracking material transport, (3) constitutive equations modeling viscoelastic phase separation, and (4) rigid wall fields which represent moving channel boundaries, machine components, and nano-particulate fillers. We also present an efficient, pseudospectral implementation for this set of coupled equations which enables practical application of the model in periodic domains. We validate the model by reproducing well known phenomena including equilibrium diblock meso-phases, analytic Stokes flows, and viscoelastic phase separation of glassy/elastic polymer melts. We also demonstrate the stability and accuracy of the numerical implementation by examining its convergence under grid-size refinement.