A tangential flow separator element for separating a fluid medium for treatment into a filtrate and a retentate, said separator element comprising a monolithic rigid porous support (2) of rectilinear structure with a single channel (3) formed therein for passing a flow of the fluid medium for treatment between an inlet (6) and an outlet (7) for the retentate, in order to recover a filtrate from the peripheral surface (5) of the support, the outside surface (5) of the support presenting a profile that is constant, the separator element being characterized in that the monolithic rigid porous support (2) defines obstacles (9) to the flow of the fluid for filtering, which obstacles extend from the inside wall (31) of said channel, are identical in material and porous texture to the support, and present continuity of material and of porous texture with the support, said obstacles (9) generating variations in the flow section of the channel.