  We provide a Boltzmann-type kinetic description for dilute polymer solutions
based on two-fluid theory. This Boltzmann-type description uses a
quasi-equilibrium based relaxation mechanism to model collisions between a
polymer dumbbell and a solvent molecule. The model reproduces the desired
macroscopic equations for the polymer-solvent mixture. The proposed kinetic
scheme leads to a numerical algorithm which is along the lines of the lattice
Boltzmann method. Finally, the algorithm is applied to describe the evolution
of a perturbed Kolmogorov flow profile, whereby we recover the major elastic
effect exhibited by a polymer solution, specifically, the suppression of the
original inertial instability.
