Effect of yield stress in a two phase pore network model

Non newtonian fluids in porous media flow offers complex interplays that are not fully understood. The Bingham rheology is an approximation of the rheology of a non-Newtonian fluid presenting yield stress, which are useful in several engineering applications, as reinforcement of soils by injection of slurries [1] and in the timely topic of fracking processes [2]. The subject is notoriously hard to study numerically, as we have a nonlinear rheology in a complex porous structure, but there has been recent advances in the field, for instance in characterizing a Darcy law [3]. This work aims to investigate the flow conditions of the Bingham body in complex geometries by using a Pore Network Model with a fairly novel numerical solver in the Augumented Lagrangian Method -- a method recently introduced by Talon and Hansen [4]. We are using the model to describe the qualitative behaviors of the yield stress effect, and have characterized a power law behavior that deviates from existing litterature, as found in [3] and [5]. References [1] : Coussot, P.: Rheometry of pastes, suspensions, and granular materials: applications in industry and environment. John Wiley and Sons, New York, NY (2005) [2] : Talon, L., Auradou, H., Hansen, A., 2014. Effective rheology of Bingham fluids in a rough channel. Frontiers in Physics 2. https://doi.org/10.3389/fphy.2014.00024 [3] : Liu, C., De Luca, A., Rosso, A., Talon, L., 2019. Darcy’s law for yield stress fluids. Phys. Rev. Lett. 122, 245502. doi:10.1103/PhysRevLett.122.245502. [4] : Talon, L., Hansen, A., 2020. Effective rheology of bi-viscous non-newtonian fluids in porous media. Frontiers in Physics 7. doi:10.3389/fphy.2019.00225. [5] : Chen, M., Rossen, W., Yortsos, Y.C., 2005. The flow and displacement in porous media of fluids with yield stress. Chemical Engineering Science 60, 4183–4202. doi:https://doi.org/10.1016/j.ces.2005.02.054.