Polymer injection is a widely used enhanced oil recovery technique. Optimizing this process requires a thorough understanding of the nature of polymer flows through the porous medium. The current approach involves using an apparent viscosity, as described by the Darcy's law. Such an apparent viscosity is an effective parameter which accounts for effects introduced by the porous medium and the bulk rheology of polymer solutions. These effects include excluded pore volume, inaccessible pore volume, adsorption/retention, shear-thinning, shear-thickening due to converging-diverging channels, non-uniform flow channels, and viscoelasticity. To explain the apparent shear-thickening behaviour in porous media, the existing models use an ad hoc hypothesis; that is, the experimental evidence for these effects is missing. The objective of this study is to obtain a mechanistic picture. We study the effect of pore shape on the apparent viscosity, as the shear rate is varied.
Microfluidic devices containing 2D planar porous media with different pore shapes are fabricated using lithography techniques. The devices are essentially periodic arrays of obstacles in square and diamond layouts. Simultaneously measuring the pressure drop while visualizing the flow field allows us to map the flow-field variations on an apparent-viscosity map. We visualize the flow by seeding the polymer solution with fluorescent particles. A time-steady flow field is observed in the shear thinning region, whereas, flow instabilities are observed at the range of shear rates where the shear thinning region ends and the shear thickening region starts. This suggests that the shear-thickening region is somehow connected to those instabilities.
Power spectral density is calculated by applying Fast Fourier Transform to the pressure drop time-series data. The power spectral density in the shear-thickening region reveals power law scaling. This power law scaling indicates that the energy from large vortices is gradually transferred to smaller vortices, until it is dissipated as thermal energy. Such an energy cascade system is a typical characteristic of large Reynolds number turbulent flow. However, in our experiments the Reynolds is low, whereas the Weissenberg number is large. Under these conditions, the flow instabilities that we observe originate from an interplay of the shear thinning viscosity and the elastic stresses in the polymer solution.