%0 Journal Article %T Homogenization of ferrofluid flow models in porous media with Langevin magnetization law %+ Laboratoire de Mathématiques Blaise Pascal (LMBP) %+ Pôle Universitaire Léonard de Vinci (PULV) %A Amirat, Youcef %A Hamdache, Kamel %< avec comité de lecture %@ 0022-247X %J Journal of Mathematical Analysis and Applications %I Elsevier %8 2023 %D 2023 %R 10.1016/j.jmaa.2023.127129 %K Ferrofluid flow in porous media %K Stokes equations %K Langevin magnetization law %K homogenization %K two-scale convergence %K Darcy law %Z Mathematics [math]Journal articles %X The paper is concerned with the homogenization of the equations describing the flow of a ferrofluid through a heterogeneous porous medium $\Omega$ in the presence of an applied magnetic field. We discuss two models where the magnetization $M$ is parallel to the magnetic field $H$. In the first one $M$ and $H$ satisfy the relation$M=\lambda_0 \, {1}_{\Omega_f} H\, \mbox{ in } \Omega,$where $\lambda_0$ is a positive constant and ${1}_{\Omega_f}$ is the characteristic function of $\Omega_f$ (the pore space). In the second model, $M$ and $H$ satisfy the Langevin magnetization law$M= M_s \frac{L(b_1\, |H|)}{|H|} {1}_{\Omega_f} \, H,$where ${L}$ is the Langevin function given by $L(x)= \frac{1}{\tanh x} - \frac{1}{ x}$,$M_s$ is the saturation magnetization and $b_1$ is a positive physical constant.The velocity and the pressure satisfy the Stokes equation with a Kelvin magnetic force. We perform the homogenization of the equations of each of the two models. Using the two-scale convergence method, we rigorously derive the homogenized equation for the magnetic potential and determine the asymptotic limit of the magnetization. Then we rigorously derive a Darcy law. %G English %2 https://hal.uca.fr/hal-03995934/document %2 https://hal.uca.fr/hal-03995934/file/AMIRAT.HAMDACHE.2023.pdf %L hal-03995934 %U https://hal.uca.fr/hal-03995934 %~ PRES_CLERMONT %~ CNRS %~ INSMI %~ UMR6620 %~ ACL-SF %~ TEST3-HALCNRS