Electro-elastic instability in electroosmotic flows of viscoelastic fluids through a model porous system

Abstract

Electrokinetic transport phenomena in porous media are encountered in many practical applications such as electro-chromatography, micro-pumping, chemical remediation of contaminated soil, etc. These applications often deal with various complex viscoelastic fluids (such as polymers, emulsions, suspensions, different kinds of biofluids, etc.) along with simple Newtonian ones. This study presents a detailed numerical investigation on this electrokinetic transport of both Newtonian and viscoelastic fluids in a model porous system consisting of a long micropore with step expansion and contraction. Over the whole range of conditions encompassed in this study, a steady and symmetric flow field is observed for a Newtonian fluid. However, for a viscoelastic fluid, we observe a transition in the flow field from steady and symmetric to unsteady and asymmetric once the Weissenberg number (ratio of the elastic to that of the viscous forces) exceeds a critical value. We show that this transition is caused due to the onset of an electro-elastic instability in the system. The critical value of this Weissenberg number (at which this transition occurs) depends on various factors. In particular, we find that this value increases with the polymer viscosity ratio and expansion and contraction lengths of the micropore. At fixed values of the electric field strength, polymer viscosity ratio, contraction and expansion lengths of the micropore, we observe the existence of different vortex dynamics within this model porous system as the Weissenberg number gradually increases, such as the emergence of the entrant and re-entrant lip vortices, oscillating lip vortices, multi vortices, etc. Therefore, the electrokinetic flow dynamics of viscoelastic fluids in a porous system is much more complex than that of simple Newtonian fluids. We hope this study for a model porous system would facilitate a better understanding of the electrokinetic transport phenomena of viscoelastic fluids in an actual porous media. Furthermore, we show how this model system of a long micropore with step expansion and contraction could also be successfully utilized for other practical applications such as mixing two viscoelastic fluids.