Darcy's law survival from no-slip to perfect-slip flow in porous media.

The article delves into the development of a macroscopic model for perfect-slip flow in porous media through the use of the adjoint method and Green's formula. It highlights the symmetric and positive nature of the permeability tensor, Kps, obtained from solving the closure problem, and establishes relationships between Kps, Ks, and K. Numerical simulations validate the macroscopic model and the connection between Kps and K, while also exploring the symmetry and positivity of Ks and K. The document provides a thorough examination of various studies and models in fluid mechanics, particularly focusing on slip flow in porous media, with contributions from researchers like Lasseux and Valdés-Parada. References to microfluidics, numerical simulations, and boundary conditions in fluid mechanics are also included, offering valuable insights into fluid behavior in porous media and enhancing the understanding of fluid dynamics. [Extracted from the article]