Hydrogen peroxide is a solution of hydrogen peroxide in water. This is very oxidant, it destroys components of the cells. This substance is unstable, decomposes in water and oxygen almost instantaneously. When it is decomposing, the gaseous O2 "escapes" in the form of bubbles. These decomposition conditions are very slow, but they change when there is a catalyst (substance that accelerates the reaction). There are many catalysts: metals, salts and also enzymes (proteins). During metabolic processes, the cells of our existence produce waste, such as hydrogen peroxide. As it is an oxidant, to prevent the cells from getting damaged, they need to get rid of it quickly. They do this thanks to an enzyme called catalase that catalyzes its decomposition into oxygen and water. When we cut and put oxygenated water in the wound, the catalase does not know where the peroxide came from so the bubbles and the white foam appear. Nothing else is gaseous oxygen escaping. This is good because the pathogenic bacteria are anaerobic (they can not live with oxygen) and most of them die thanks to that white foam. Conclusion: The cut was not infected and those bubbles do not indicate that we have killed all the microorganisms.

