Equilibration in momentum space in the kinetic theory of polymer solutions

In the kinetic theory of dilute polymer solutions it is customary to assume a Maxwellian velocity distribution for the “beads” in the bead-spring models. For the sake of simplicity this velocity distribution function is generally taken to be Maxwellian about the fluid velocity at the center of mass of the macromolecule. In Brownian dynamics simulations it is more natural to assume that the velocity distribution is Maxwellian about the fluid velocity at the “beads”. It is found that the differences between the two approaches are important only at very high velocity gradients. This could be a confusing point in high-shear-rate Brownian-dynamics simulations. The extra terms arising in the constitutive equation because of bead-centered Brownian motion are non-objective.