The invention concerns a circuit comprising a bag (11) comprising two flexible films (45, 46) and a press (10) comprising a first (14) and a second (13) shell clamping the bag to form pipes having a passage and edges (41); the first shell comprising a valve (20) which comprises a movable member (24) and a pad (31), which pad has a resting configuration in which a second face (33) of the pad is concave and locally delimits a channel (18) and a pinching configuration in which the second face (33) is convex; said movable member and said pad being configured so that, when said valve is in closed position and said pad in pinching configuration, said passage is pinched by said movable member against said second shell channel and said edges (41) are pinched flat by said movable member against said second shell (13).