Numerical investigation of multistability in the unstable flow of a polymer solution through porous media

The flow of viscoelastic polymeric fluids through porous media is common in industrial applications such as oil recovery and groundwater remediation. Polymeric stresses can lead to an elastic-induced instability of the flow. Here, we numerically study the flow of a polymeric fluid in a channel consisting of multiple diverging and converging physical constraints, mimicking the pore bodies and throats of an ordered porous medium. Inertial stresses here are negligible, and instead the flow is dominated by elasticity and viscosity; their relative effects are characterized by the Weissenberg number. There is a critical Weissenberg number below which eddies appear on the top and the bottom of each pore. Above the critical Weissenberg number, eddies form in different regions of the pores and multiple distinct unstable flow structures occur. The stretched polymeric chains inside the pore facilitate eddy formation, whereas relaxed chains lead to eddy-free regions. We quantify the eddy area and correlations between the flow patterns of different pairs of pores, as well as polymeric stress and pressure drop across the tortuous channel to better understand the mechanism behind the observed flow patterns.