The Charged FENE-P Dumbbell model: explaining the rheology of dilute polyelectrolyte solutions

A robust model of dilute polyelectrolyte solutions is constructed based on kinetic theory arguments. The polyelectrolyte molecules are modelled by finitely elongated non-linear elastic dumbbells with beads carrying identical effective charges. The electric interaction between the beads is described in a simplified way through an electrostatic Coulomb force. With two pre-averaging approximations, the constitutive equations of the fluid model are formulated in closed form; and its rheological properties in steady and transient shear and elongational flows are investigated by analytical and simple numerical means. It is found that despite its simplicity, the model shows an excellent qualitative agreement with the results obtained by advanced numerical simulations of polyelectrolyte solutions and predicts most of the experimentally observed features of such fluids.