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

Laurent Talon

  • Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France

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Phys. Rev. Fluids 7, L042101 – Published 25 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.L042101

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 the 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 Letter, 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 a minimization principle can be derived either for the velocity or the pressure field.

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Phys. Rev. Fluids 7, L042101– Published 25 April, 2022
  • Received 14 October 2021
  • Accepted 7 April 2022
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