Viscoelastic behavior of dilute polyelectrolyte solutions in complex geometries

Abstract

In this work, we develop a theoretical model describing the viscoelastic behavior of dilute polyelectrolyte (PE) solutions using Onsager’s variational principle, with the effect of the polyelectrolyte charge and solvent salinity accounted for. The PE molecules are described as finitely extensible charged dumbbells suspended in a solvent containing ionic species which screen the charged sites on the macromolecules. The performance of the model was examined and compared against experimental data in simple flows, accounting for the magnitude of charge on the PE molecules and counterion screening effects. Numerical simulations of the flow past a single cylinder and an idealized porous medium with multiple cylinders were carried out and compared to flow of uncharged polymers in the same geometries to explore the effect of intramolecular electrostatic repulsion on the flow behavior. The extra rigidity offered by the repulsion between the charged monomeric units of the PE, and screening of these charged sites by the ionic species in the solvent led to significantly different behavior in complex flows when compared to that of uncharged polymers. The normal stresses generated in a complex flow show an increase with the polyelectrolyte molecule charge density, whereas enhanced screening of the charged sites by counterions suppresses this effect, showing behavior closer to that of uncharged polymers. Drag on a cylinder placed in the flow and pressure drop across the porous geometry increased with charge density of the molecules, exhibiting rheological behavior in complex geometries not shown by their uncharged counterparts. The results show the effects of the degree of hydrolysis and solvent salinity on the flow behavior of dilute PE solutions in complex geometries and has implications for biological systems in which PE species are commonly encountered, as well as operation of industrial processes such as enhanced oil recovery, which frequently involve the flow of dilute polyelectrolyte solutions in porous media. • Macroscopic flow behavior of dilute polyelectrolyte solutions is investigated. • Onsager’s Variational Principle used for developing model from first principles. • Reformulation of charged dumbbell model for simulating flows in complex geometries. • Polyelectrolyte charge density and solvent salinity influence flow behavior. • Drag coefficients and normal stresses increase with charged nature of molecules.