Achieving the efficacious and rapid separation of mixed water/oil streams has emerged as a fundamental imperative in order to facilitate extraction of fossil fuels by methods such as cyclic steam stimulation as well as to mitigate the potentially calamitous impact of oil spills in natural aquatic environments. Here, we demonstrate functionalized ZnO nanotetrapodal membranes combining the micrometer-scale texturation of underlying stainless steel meshes with the nanoscale texturation of an enmeshed interconnected porous network of ZnO tetrapods, the conformal adhesion afforded by an amorphous silica layer, and the low surface energy of surface-deposited perfluorinated sulfonate layers. The membranes exhibit pronounced differential wettability and selectively permeate water whilst retaining oil. The multivariate design space of the architectures has been evaluated to determine the mesh size and ZnO loading that yield the highest separation efficiencies. Oil content in recovered water is reduced to <300 ppm while maintaining a flux rate of greater than 325 L/(m(2).h). The functioning of the membranes can be understood in terms of the creation of differential Cassie-Baxter nonwetting and Wenzel wetting regimes for oil and water, respectively.