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 A more viscous solution was injected into the cell to displace a less viscous solution (divergent flow) then withdrawn at the injection site (convergent flow).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

Interfacial instabilities in confined displacements involving non-Newtonian fluids

“…In results that are reminiscent of those reported in experiments involving a Newtonian fluid pair [19,20,46], proportionate pattern growth and suppression of the fingering instability were reported when shear-thinning granular cornstarch suspensions were displaced by glycerolwater mixtures at controlled viscosity ratios, 0.06 < η in /η out < 0.95 [47]. Interestingly, unstable to stable growth was observed when an aqueous shear-thinning Xanthan gum solution was displaced by mineral oil at η in /η out > 1 [48].…”

“…Analytical and numerical investigations are essential for acquiring fundamental knowledge of elasticity-driven interfacial instabilities. Appropriate models need to be developed to explain other novel phenomena that have been observed in experiments, for example, the formation of fringes [46], asymmetric [64] and reverse fingers [73], and dendritic fractures [72]. Many non-Newtonian fluids show chaotic flows at low Reynolds numbers and generate anomalous flow resistance [102].…”

“…Finite volume simulations of the displacement of a more viscous Newtonian fluid by a shearthinning fluid showed instability enhancement and finger coalescence [49]. Interestingly, when a shear-thinning fluid was injected/withdrawn through millimetre-sized apertures at appropriately high flow rates, radial growth of thin equispaced protrusions (fringes) and enhanced fluid mixing were reported [46]. These observations were unaffected by turbulence, diffusion, elongation and elastic effects.…”

Low-cost and precise inline pressure sensor housing and DAQ for use in laboratory experiments

“…Using a syringe pump, a viscous solution of 0.3 wt% xanthan gum, 1.5 wt% sodium chloride, and 0.025 wt% dye was injected between two radial parallel-plates, which was filled with a resident solution of 1.5 wt% saltwater [18] . A Canon EOS 50D camera was situated approximately a meter overhead to take images of the flow system once every second.…”

Displacement Patterns of a Newtonian Fluid by a Shear‐Thinning Fluid in a Rough Fracture

“…When non‐Newtonian fluids are involved in the multiphase flow process, coupling between the complex rheological behavior and the fracture's aperture heterogeneity may produce unexpected flow regimes. Numerous experimental and theoretical studies on shear‐thinning fluids flow in Hele‐Shaw cells or porous media have been conducted in order to explain the correlation between flow patterns and fluid rheology (Buka et al., 1986; Coussot, 1999; Kondic et al., 1998; Lemaire et al., 1991; Mehr et al., 2020; Nittmann et al., 1985; Rodríguez de Castro & Goyeau, 2022; Shah & Yortsos, 1995). Significant differences of morphological patterns in Hele‐Shaw cells induced by the non‐Newtonian rheology of the displacing or displaced fluids have been observed, for example, snowflake‐like patterns (Buka et al., 1986), fractal patterns (Nittmann et al., 1985) and fracture‐like patterns (Lemaire et al., 1991).…”