Numerical Study of Dilute Polymer Solutions Using FENE Bead-Spring Chain Model

The numerical solution of viscoelastic fluid problems in complex geometries and free solutions has been an area of extensive research in polymer fluid mechanics. The governing equation for polymer chains was in terms of Brownian dynamics and finitely extensible nonlinear elastic (FENE). Explicit and semi-implicit predictor-corrector algorithms were employed to solve the Brownian dynamics problem. After all the chain displacements have been determined, the stress tensor will be calculated with the ensemble average technique. Molecular configurations, such as the maximum length of the molecular chain along the flow direction, the angle between molecular chain and the flow direction, and the mean configuration thickness of the molecule in the velocity gradient direction, are also calculated. In the procedure, the governing equation of the displacement of chain has been made dimensionless.