Alfred Pennyworth has also provided first aid up to and including suturing wounds and removing bullets, as well as occasional tactical support. He is also able to perform arthroscopy and other advanced medical procedures, thus limiting, if not eliminating, the need for hospital medical treatment even in the face of grievous injuries, helping to maintain Batman's secret identity by ensuring that Bruce Wayne has no need to visit hospitals for wounds inflicted as Batman. Nevertheless, Batman still requires professional medical treatment when Bane breaks his back ("") and Hush's machinations result in his suffering a skull fracture (""). On these occasions, Alfred
Butler–Volmer equation Butler–Volmer equation The Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current on an electrode depends on the electrode potential, considering that both a cathodic and an anodic reaction occur on the same electrode: or in a more compact form: where: The right hand figure shows plots valid for formula_15. The previous form of Butler–Volmer equation is valid when the electrode reaction is controlled by electrical charge transfer at the electrode (and not by the mass transfer