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Mixing and finger morphologies in miscible non-Newtonian solution displacement


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 A more viscous solution was injected into the cell to displace a less viscous solution (divergent flow) and then withdrawn at the injection site (convergent flow).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.

Graphic abstract

We explore the geometry of injection of shear-thinning fluid into a water-filled cavity. Concentration maps for two xanthan gum injection/withdrawal experiments with apertures of 2.54 mm (A and B) and 0.762 mm (C and D) show that in narrow fissures, the displacement of water has a ragged interface, which was not expected. This irregular interface gave rise to radically different withdrawal geometries (right frames). These results suggest that the use of such fluids for chasing hydrocarbons, or for testing aquifer properties, will not follow standard theories which take displacement of less viscous fluids by more viscous fluids to have stable interfaces.

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The funding was provided by National Science Foundation under Grant No. NSF/EAR1446915. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Correspondence to John S. Selker.

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Mehr, N., Roques, C., Méheust, Y. et al. Mixing and finger morphologies in miscible non-Newtonian solution displacement. Exp Fluids 61, 96 (2020).

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