3D superwetting materials struggle to maintain high-flux steady-state demulsification for oil-in-water emulsions because the accumulated oil within the material is difficult to discharge rapidly. The water flow shear force can swiftly remove the oil from the anti-fouling surface. In this study, by introducing nanofibers and carbon nanotubes and chemical modification, a superhydrophilic-oleophobic copper foam with pores of several micrometers is prepared, which can achieve a continuous demulsification process with steady-state flux over 57000 Lm-2h-1 for oil-in-water emulsions and rapid hydraulic-driven oil release under an additional pressure of 5kPa. Thanks to the ultra-small pores of the copper foam, the steady-state demulsification efficiency can be still maintained at over 97.5%. During the demulsification process, the accumulation of oil and surfactants within the copper foam can be maintained at low levels, achieving dynamic equilibrium. With the aid of second-stage superhydrophilic copper mesh, the demulsified oil-water mixtures can be rapidly separated. This high-flux, steady-state, and efficient demulsification process shows great potential for industrial applications.