## 1 Introduction  
Superoleophobic surfaces refer to those surfaces that display contact angles that are greater than 150\({}^{\circ}\) along with low contact angle hysteresis for low surface tension liquids, such as oils and alcohols [1]. The contact interface for oil on a superoleophobic surface can either be solid-air or solid-water interface, depending on the media the surfaces are placed. For the latter, the interface can effectively be achieved under water. To this end, attention has increasingly been paid to the design of underwater superoleophobic surfaces, due to their potential application in anti-fouling coatings [2], oil-water separation [3], as well as anti-bioadhesion surfaces [4].  
Various approaches have been used to achieve superoleophobicity on surfaces under water. Some of these approaches include fabrication of re-entrant structures on surfaces of substrates [5], complicated etching methods such as lithography and anodization [6].  
Recently, however, high energy materials, such as oxides, have been used to achieve underwater superoleophobicity. For instance, underwater superoleophobicity has been achieved by coating stainless steel mesh with aligned ZnO nanorod film [7]. The ZnO nanorod coating was generated by a two-step process which involved dipping the steel mesh in ZnO sol gel and annealing at 450 \({}^{\circ}\)C. Underwater superoleophobic surfaces on copper substrate coated with copper oxide, formed as a product of aqueous corrosion in ammonium hydroxide solution, has been created [8]. [PERSON] and his co-workers further reported that the high amount of CaCO\({}_{3}\) as well as the micro-/nano-hierarchical structures of clam shells were responsible for the underwater, low adhesive superoleophobicity of clam shells [9]. Other examples include high energy organic-based materials that have been used to achieve underwater superoleophobicity. In this regards, high-energy poly-(\(N\)-isopropylacrylamide) hydrogel has been used to achieve superoleophobicity. The hydrogels were used to construct fish-like surfaces with micro-/nano-structures that showed robust underwater superoleophobicity [10].  
The process of thermal oxidation can be used to form oxide surface layers of varying thickness, morphology and chemical composition. These variations of the properties of the oxide surface layers can be induced by the control of the thermal oxidation conditions and can therefore be used to generate and sustain the superoleophobicity of metal alloys under water. The formation, thickness, chemical features and the morphology of oxide layers on metal alloys is dependent on the alloy composition, oxidation temperature, time of thermal oxidation, as well as the partial pressure and concentration of oxygen [11]. This paper addresses the effect of the thickness and surface morphology changes of thermally-grown oxide layers on the underwater contact angle and superoleophobic behavior of oil on the surfaces of C84400 copper alloy.  
The C84400 copper alloy is a typical leaded brass that contains copper, lead, zinc and tin [12]. This copper alloy is commonly used as plumbing fittings. The bio-fouling of such plumbing parts constitutes a serious problem that can be reduced if their surfaces exhibit underwater superoleophobicity [13]. Through the use of oxidizing gas mixtures that contain different amounts of oxygen during thermal oxidation, the thickness of the oxide layer can be controlled and different oxide morphologies generated to study the contact angle behavior of oil drops underwater. Though underwater superoleophobicity induced by high energy oxides have been reported, we report here, for the first time, such underwater superoleophobicity driven by the thickness of a porous, thermally-grown oxide layer.