Teat cup (30) and method for bringing a fluid into contact with a teat, the teat cup (30) exhibiting a housing and a teat-cup liner (32) arranged in the housing (31), said teat-cup liner separating a teat chamber from a pulsation chamber and exhibiting a head region (33), a shaft region and an end region which communicates with a milk hose. A valve is provided, with which a fluidic connection from the teat chamber to a milk hose is capable of being tightly closed. The head region (33) exhibits at least one exit region (34) which is so designed that a fluid, in particular a disinfectant, leaving the exit region (34) is directed, at least partially, radially inwards.