How do they call in English that yellowish substance that is sometimes gathered in the corner of a human eye during the sleep?
You've got some great answers with the technical term for the substance. However, practically, I've never heard anyone refer to it as anything other than sleep. For example, "He sat up in bed and rubbed the sleep from his eyes."
- crusty matter present in the corner of an eye upon awakening
It's not the technical term, but if you actually call it "rheum" or "gound", no one's going to have any idea what you're talking about. Depending on how you intend to use the word, I thought that knowledge might help :)
It is rheum, a mucous discharge from the eye. The Wiki link gives a number of other words, including eye crust and eye gunk.