The subject matter of the invention concerns a tangential flow separation element comprising a rigid, porous, single-piece support member (2) in the interior of which there is at least one channel (41) for the circulation of the fluid medium to be treated, which channel has a flexuous circulation volume (V1) defined by the movement of a generatrix cross-section about a reference axis along a curvilinear path; this reference axis does not pass through the generatrix cross-section and is contained within the interior of the porous support member.