A convection heat treatment that can replace existing chemical oxidation methods was developed for the preparation of hierarchically oxidized Cu meshes with various surface morphologies, representing a very simple and green route that does not involve toxic chemicals. Three types of Cu meshes [bumpy-like (BL) and short and long needle-like (NL) structures] exhibited similar separation efficiencies of 95-99% over 20 separation cycles, as indicated by their similar water contact angles (WCAs; 147-150°). However, these Cu meshes exhibited different flux behaviors. Excessively rough and excessively smooth surfaces of the Cu mesh resulted in increased resistance to flow and to a decrease of the penetration of oil. A surface with intermediate smoothness, such as the BL-Cu mesh, was necessary for high flux over a broad range of oil viscosities. Furthermore, a less rough surface was more suitable for the separation of highly viscous oil. Computational fluid dynamics (CFD) simulations were carried out to support our experimental results. The BL-Cu meshes also showed outstanding mechanical stability because of their low resistance to the flow of fluids.