Hydrodynamic dipole-driven theory for active flow control in heterogeneous porous media

Although significant efforts have been directed toward refining active control methods for porous media flows, limited explorations have been devoted to the effects of heterogeneous permeability on fluid flow in such environments. These gaps in understanding pose a challenge in developing effective strategies for regulating flow states in porous media with varying permeability. To address these issues, we propose a hydrodynamic dipole-driven theory, solely leveraging a pair of hydrodynamic point source and sink, to rectify flow in heterogeneous porous media systems, thus enabling precise manipulation of the flow field. By carefully tuning the moment of the hydrodynamic dipole, we demonstrate the complete elimination of flow disturbances arising from permeability heterogeneity, and this restoration of the original uniform flow state effectively homogenizes overall permeability. Furthermore, our theory transcends limitations associated with electroosmotic and magnetic methods that require fluids respond to such physical fields, offering broader applicability and minimizing potential contamination risks. Finally, the inherent relation between potential function and pressure distributions in Dracy's law is established with rigorous theoretical analysis, which lays the foundation for active hydrodynamic metamaterials assisted with hydrodynamic dipole strategy. We anticipate that our findings will significantly advance the field of active flow control, particularly in addressing heterogeneous permeability in complex porous media flows, and provide valuable insights for the development of hydrodynamic metamaterial without reliance on heterogeneous or anisotropic materials.