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arXiv · 1001.2406

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

Pierre Degond·Alexei Lozinski·Robert G. Owens
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Abstract

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.

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Pierre Degond, Alexei Lozinski, Robert G. Owens. 2010-01-14. Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited. https://doi.org/10.1016/j.jnnfm.2010.02.007

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