There is provided a teat cup (1) comprising a flexible liner (3) for engaging about a teat of an animal to be milked. The liner has a head portion (7) at one end of the liner and a milk discharge passageway (12) at another end of the liner. The head portion is provided with a mouth (9) through which the teat is engageable with the liner, and an injector (18) for injecting fluid into the head portion of the liner. The injector comprises a gravity biased diverter that controls, based on an orientation of the teat cup, an injection direction (FLT, FLF) in which the fluid is injected into the head portion. There is further provided a method for milking an animal using the teat cup.