**« Non-Newtonian fluids through porous media : what drives the flow ? the rheology or the porous structure ? "**

**Yohan Davit ** , Institut de Mécanique des Fluides de Toulouse

** Vendredi 22 Juin de 11h à 12h **, Salle de Conférences du bâtiment Nanobio 570 rue de la Chimie rdc (badge pour entrer).

The creeping flow of complex fluids through porous media embraces a wide variety of applications such as blood flow in the microcirculation or processes of enhanced oil recovery. Understanding and modeling such systems has proven a considerable challenge, as they intricately couple the non-linear effects of non-Newtonian fluids with the multiscale nature of porous media. Linear transport phenomena in porous materials can often be described using homogenized equations encapsulating the large deviations induced by the multiscale heterogeneities in a limited number of effective parameters. When the large deviations induced by the porous structure are further coupled with the rich nonlinear behaviors displayed by the flow of complex fluids—shear thickening and thinning ; yield and cutoff effects ; time-dependent mechanisms ; confinement, sorption and surface effects—it becomes unclear whether such average descriptions accurately describe momentum transport and if alternative approaches exist.

In this talk, I will primarily focus on the flow of dilute polymer solutions (Xanthan, HPAM) through porous media, in the limit where elastic effects can be neglected and the solution essentially behaves as a Carreau fluid. Even for this simplified case, I will highlight difficulties in mathematical approaches used for upscaling pore-scale equations and derive Darcy-scale homogenized models. As an alternative approach, we can compute the 3D flow in various classes of porous structures and use these results to better understand the physics. In particular, I will show that the constraints that the porous structure poses on the flow can dominate over rheological effects, sometimes in a counterintuitive manner. For example, we would expect that a strong nonlinear response in the flow of shear-thinning fluids may generate preferential flow paths where the fluid primarily flows at large velocity in regions where it exhibits a relatively small viscosity, while leaving almost at rest other regions where it exhibits a higher viscosity. Our simulations show that this is not the case and that the distribution of the velocity field is not that different from that of a Newtonian fluid. By studying the pattern of viscous dissipation in the porous structure, I will show how we can characterize transitions between Newtonian and non-Newtonian regimes with relatively few parameters. I will also consider several other properties that characterize the flow of dilute polymer solutions through porous media (wall slip, changes in the main flow direction, …) and assess their impact on a larger scale. Finally, I will discuss how some of these results might be extended to other classes of non-Newtonian fluids flowing through porous media.

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