Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited

✍ Scribed by Pierre Degond; Alexei Lozinski; Robert G. Owens

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 303 KB
• Volume: 165
• Category: Article
• ISSN: 0377-0257
• DOI: 10.1016/j.jnnfm.2010.02.007

✦ Synopsis

We propose a two-fluid theory to model a dilute polymer solution assuming that it consists of two phases, polymer and solvent, with two distinct macroscopic velocities. The solvent phase velocity is governed by the macroscopic Navier-Stokes equations with the addition of a force term describing the interaction between the two phases. The polymer phase is described on the mesoscopic level using a dumbbell model and its macroscopic velocity is obtained through averaging. We start by writing down the full phase-space distribution function for the dumbbells and then obtain the inertialess limits for the Fokker-Planck equation and for the averaged friction force acting between the phases from a rigorous asymptotic analysis. The resulting equations are relevant to the modelling of strongly non-homogeneous flows, while the standard kinetic model is recovered in the locally homogeneous case.