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Minimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous media

Abstract : The 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.
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https://hal-cnrs.archives-ouvertes.fr/hal-03845409
Contributor : Laurent Talon Connect in order to contact the contributor
Submitted on : Wednesday, November 9, 2022 - 2:50:11 PM
Last modification on : Tuesday, December 6, 2022 - 4:08:01 AM

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Laurent Talon. Minimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous media. Physical Review Fluids, 2022, 7 (4), pp.L042101. ⟨10.1103/PhysRevFluids.7.L042101⟩. ⟨hal-03845409⟩

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