https://hal-cnrs.archives-ouvertes.fr/hal-03845409Talon, LaurentLaurentTalonFAST - Fluides, automatique, systÃ¨mes thermiques - UniversitÃ© Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueMinimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous mediaHAL CCSD2022[PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]Talon, Laurent2022-11-09 14:50:112022-12-06 04:08:012022-11-16 07:45:06enJournal articleshttps://hal-cnrs.archives-ouvertes.fr/hal-03845409/document10.1103/PhysRevFluids.7.L042101application/pdf1The minimization of dissipation is a general principle in physics. It stipulates that a nonequilibrium system converges toward a state minimizing the energy dissipation. In fluid mechanics, this principle is well known for Newtonian fluids governed by Stokes equation. It can be formulated as follows: among all admissible velocity fields, the solution of the Stokes equation is the one that minimizes the total viscous dissipation. In this paper, we extend these approaches to non-Newtonian fluids in macroscopic heterogeneous porous media, or fractures. The flow is then governed by a nonlinear Darcy equation that can vary in space. In this case, a minimization principle can still be written depending on the boundary conditions. Moreover, such minimization principle can be derived either for the velocity or pressure field.