Birefringent strands drive the flow of viscoelastic fluids past obstacles

Abstract

The flow of polymer solutions past solid obstacles or through porous media gives rise to rich physical phenomena over a wide range of spatial and temporal scales. Viscoelasticity, in particular, can induce a strong nonlinear response with an increase of flow resistance even for a solution whose viscosity decreases in simple shear flow. Various hypotheses have been proposed to explain this phenomenon but a clear picture of the pore-scale mechanisms involved and their impact upon larger scales is still lacking. Here, we show that localized zones of large polymeric stress, known as birefringent strands, drive the flow of an Oldroyd-B fluid through two-dimensional arrays of cylinders. Combining a recently developed numerical scheme with high performance computing, we find that these strands generate a complete reorganization of the flow with an increase of stagnation zones, a reinforcement of preferential paths and a splitting of flow channels. Furthermore, we show that this reorganization is the source of an increase in the viscous dissipation of the solvent and also that the stretching of polymer molecules in the strands is associated with entropy production. Both these phenomena yield a global increase in dissipation that can be directly linked to the increase of flow resistance. Our results demonstrate that the birefringent strands – not the elongational viscosity – drive the flow of viscoelastic fluids through porous media and that the increase of flow resistance can occur even at steady state, before the transition to elastic turbulence.

Numerical study of viscoelastic upstream instability

“…The drag acting on the cylinder increases with Wi when Wi > ~0.5 (refer to data in table 5 for low- Wi range and data here in high- Wi range), no matter whether the flow is steady (Mokhtari et al. 2022) or unsteady. The time-averaged drag coefficient is ~532 at Wi = 80 but ~799 at Wi = 82.5.…”

“…Moreover, the logarithmic reconstruction method was also adopted by Mokhtari et al. (2022) and Kumar & Ardekani (2022) and the upstream recirculation was not reported in their simulations. However, the square root reconstruction method can successfully predict the upstream recirculation, which is, therefore, adopted in the present simulation.…”

A modified Darcy’s law for viscoelastic flows of highly dilute polymer solutions through porous media

“…Such apparent thinning, followed by apparent thickening, is a known phenomenon in the flow of polymer solutions through porous media [5,20]. We have hypothesized in Mokhtari et al [35] that, for steady flows, this is due to the presence of the birefringent strands. Interestingly, our homogenized model is able to capture this phenomenon.…”

“…This is because of the structure of the birefringent strands and the flow in this case. As discussed in Harlen [17], Mokhtari et al [35], Rallison and Hinch [40], the strands follow streamlines and can be thought of as a line distribution of forces in an otherwise Newtonian fluid. In the crystalline case, strands connect the circles on both sides and a large channel flow develops between lines of circles, see To assess the validity of our approach and its limits, we plot in Figs 4.2c and 4.2d the normalized trace of the conformation tensor and the average velocity for both the homogenized model and the average results of the direct numerical simulations for different values of β.…”

Effect of viscoelasticity on displacement processes in porous media

“…Thus, in order to construct such a model system, we must start by identifying the characteristic flow features in porous media. In fact, flow in porous media is composed of an interplay of regions of shear flow in the vicinity of solid walls, as well as of extensional regions of converging-diverging flows away from the walls and at stagnation points at the front and rear poles of obstacles in a flow James [85]; Kawale et al [37]; De et al [86]; Poole [87]; Mokhtari et al [88]. De et al De et al [86] performed direct numerical simulations to determine the flow type distribution for invasion of a viscoelastic fluid in a randomized porous medium assembled by bi-disperse disks.…”