Dynamics of polymeric fluids: A combined Brownian dynamics finite element approach

The basic part of most polymer and composite manufacturing processes involves flow of polymers in cavities of arbitrary shape. The process throughput and the product quality are often limited by the onset of flow instabilities. Hence, in order to design, optimize and control various polymers and composites material processing techniques, robust and accurate simulation models are required. Over the past decade, tremendous progress has been achieved in development of robust and highly accurate numerical techniques for simulation of viscoelastic flows. These advances have made it possible to perform direct tests of constitutive models against experimental data in order to provide a critical evaluation of constitutive equations. To date these studies have demonstrated that the existing closed form constitutive equations for dilute and semi-dilute polymeric solutions are unable to quantitatively describe experimental measurements in complex kinematics flows. In this study a technique to study the dynamics of viscoelastic flows in complex without resorting to closed form constitutive equations for the polymer stress has been developed. Specifically, this approach relies on coupling Brownian dynamics simulations with time dependent finite element analysis (BDS/FEM) to study the dynamics of dilute and semi-dilute polymeric solutions in complex kinematics flows (i.e., flows with mixed kinematics). To demonstrate the capabilities of this simulation technique, a selected number of simulations in prototype flow geometries will be discussed. Specifically, the following issues shall be addressed: (1) Critical evaluation of various elastic dumbbell based models. This has been accomplished by comparing simulation results with experimental findings for complex flows like sedimentation of a sphere in a tube filled with a dilute polymeric solution. (2) Linear and non-linear stability analysis of viscoelastic flows in complex geometries. This has been accomplished by comparing the results of BDS/A-FEM simulations with continuum based analyses as well as discussing the stability results of kinetic theory based models that do not have a closed form counterpart. (3) Simulating advanced reptation models in complex flows. This has been accomplished by the introduction of a new technique that allows the simulation of almost any reptation model in complex flows, hitherto not possible with existing techniques. The feasibility of this method will be demonstrated in benchmark two-dimensional flows such as the plane Couette flow and flow past a cylinder.