  A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is
derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as
finitely elongated nonlinear elastic dumbbells, where effective charges
(interacting through a simple Coulomb force) are added to the beads in order to
model the repulsion between the charged sections of polyelectrolyte chains. It
is shown that the relative strength of this repulsion is regulated by the
electric-to-elastic energy ratio, $E$, which is one of the key parameters of
the model. In particular, $E$ accounts for the intrinsic rigidity of
polyelectrolyte molecules and can be used to explain the impact of solvent
salinity on polyelectrolyte rheology. With two preaveraging approximations, the
constitutive equations of the resulting fluid model are formulated in closed
form. Material functions predicted by the model for steady shear flow, steady
extensional flow, small-amplitude oscillatory shear flow, and start-up and
cessation of steady shear flow are obtained and investigated using a
combination of analytical and numerical methods. In particular, it is shown how
these material functions depend on $E$. The two limiting cases of the model --
uncharged dumbbells ($E=0$) and rigid dumbbells ($E\to \infty$) -- are included
in the analysis. It is found that despite its simplicity, the model predicts
most of experimentally observed rheological features of polyelectrolyte
solutions.
