The system has modules having a micro fluidic unit and an electrical control unit and held next to each other in a rear wall unit. A fluid line (27) for a rinsing fluid runs into the unit and a branch pipe leads to the modules from the line. The pipe flows into a distributor chamber (30) delimited opposite to inside of the modules by a distribution plate, where the inside at its lower or back side has an outlet for the rinsing fluid.
