Answer
I say, and with God's success: The "sour" linguistically means the remainder of something, and its plural is "asaar." The "sour" in terminology refers to the name for the remainder after drinking that the drinker has left behind, and it is only called "sour" if it is little; it is not referred to as such for something like a river from which one drinks. See: Lisan al-Arab 3: 92, and the footnote by al-Tahawi, pages 28-29, and God knows best.