Mixing and finger morphologies in miscible non-Newtonian solution displacement

Abstract

Unexpected interface complexities were found resulting from the miscible displacement of saltwater by a miscible shear-thinning solution (xanthan gum) in a radial Hele-Shaw cell, for both convergent and divergent flow. Such complex patterns have not been described before for either Newtonian or non-Newtonian solutions. A more viscous solution was injected into the cell to displace a less viscous solution (divergent flow) and then withdrawn at the injection site (convergent flow). A variegated mixing fringe between the solutions developed during the injection phase, against the stabilizing viscous effects, which would tend to promote a stable piston-like displacement. This interface geometry is markedly different from what is seen in displacement experiments performed with glycerol under otherwise similar viscosity contrast and flow conditions. The concentration field heterogeneity resulting from the presence of the fringe, quantified using a spatial autocorrelation measure, is mostly controlled by the applied shear rate, or equivalently, by the ratio of the volumetric flow rate to the flow cell’s aperture. It is significantly correlated with the radial width of the mixing zone. In addition to producing a large volume of blended solution during the injection phase, the mixing fringe impacted the development of viscous fingers (VFs) during the withdrawal phase. Such VFs are expected due to the viscosity ratio, but the initial roughness of the interface from which they develop and, hence, their later dynamics are controlled by the geometry of the mixing fringe at the end of the injection. We characterize the dynamics as a function of the imposed flow rate and cell thickness. The observed complexities of miscible displacement involving shear-thinning solutions have implications for subsurface engineering applications such as oil recovery and groundwater remediation.