Can stainless steel rust? Why?

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Stainless does not "rust" as you think of regular steel rusting with a red oxide on the surface that flakes off. If you see red rust it is probably due to some iron particles that have contaminated the surface of the stainless steel and it is these iron particles that are rusting. Look at the source of the rusting and see if you can remove it from the surface. If the iron is embedded in the surface, you can try a solution of 10% nitric and 2% hydrofluoric acid at room temperature or slightly heated. Wash area well with lots and lots of water after use. Commercially available "pickling paste" can also be used.