The invention concerns a device comprising a circuit comprising a bag (10) comprising two flexible films (65, 66), a press (9) comprising a first shell (16) disposed upright on a front face of a base of the device and a second shell (17) mounted on said first shell, which shells clamp said bag to form conduits (13); said press is provided with a system (170) for jamming at the location of a treatment zone (67) of the bag, which comprises a jamming member (171) provided with at least one jamming nipple (173) and a complementary jamming member (172) provided with a jamming channel (174) configured to receive said nipple; said jamming member (171) and complementary jamming member (172) and said bag (10) being configured in order for the latter to have a portion (175) in said treatment zone in which said films are jammed between said nipple and said channel.