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Journal Articles Physical Review Fluids Year : 2022

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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Dates and versions

hal-03845409 , version 1 (09-11-2022)

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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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