A device (1) comprises an intake duct (11) for taking in milk, an intake duct (15) for taking in a cleaning fluid, a central duct (13) in which both intake ducts (11, 15) are merging, and a pump (31) which is arranged in the central duct (13). Cleaning the device (1) involves filling both the central duct (13) and the milk intake duct (11) with the cleaning fluid. In particular, the pump (31) is a bi-directional pump, wherein filling the central duct (13) with the cleaning fluid is realized by operating the pump (31) in one direction while blocking the milk intake duct (11), and wherein filling the milk intake duct (11) with the cleaning fluid is realized by opening the milk intake duct (11) and operating the pump (31) in a reversed direction, wherein cleaning fluid is displaced from the central duct (13) to the milk intake duct (11).