Problem Statement and Motivation

Key Achievements and Future GoalsTechnical Approach

Rheology of Polymeric and Complex Nanostructured FluidsInvestigator: Ludwig C. Nitsche, Chemical Engineering Department

Collaborator: Lewis E. Wedgewood, Chemical Engineering Department

• Derive macroscopic constitutive laws from stylized molecular models of polymers and complex fluid substructure in dilute solution.

• Obtain probability density functions describing external (translational) and internal (conformational) degrees of freedom of suspended bead-spring entities.

• Manipulate complex fluids with flow geometry and external fields.

• Developed model of cross-stream migration of polymers in flows with gradients in shear.

• The first asymptotic PDF for the classic problem of FENE dumbbells stretching in elongational flows.

• Rigorous basis for the recent “L-closure”, and analytical explanation for the numerically observed collapse of transient stress-birefringence curves for different polymer lengths.

• Numerical simulations by atomistic smoothed particle hydrodynamics (ASPH).

• “Smart swarms” of particles solve the Smoluchowski equation for translational and conformational motions of dumbbell models of polymers in dilute solution.

• Asymptotic theory (singular perturbations and multiple scales) consolidates numerics and extracts formulas for probability density profiles, scaling laws and rheological constitutive equations.

Numerical versus asymptotic PDF’s for a linear-locked dumbbell

Closure relations for the conformatioally averaged Smoluchowski equation